Heat transfer engineering an international journal, tập 31, số 5, 2010

Heat Transfer Engineering, 31(5):335–343, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903359784 Mixed Convective Heat Transfer Due to Forced and Thermocapillary Flow Around Bubbles in a Miniature Channel: A 2D Numerical Study CRISTINA RADULESCU and ANTHONY J ROBINSON Department of Mechanical and Manufacturing Engineering, Trinity College Dublin, Ireland Marangoni thermocapillary convection and its contribution to heat transfer during boiling has been the subject of some debate in the literature Currently, for certain conditions, such as microgravity boiling, it has been shown that Marangoni thermocapillary convection has a significant contribution to heat transfer Typically, this phenomenon is investigated for the idealized case of an isolated and stationary bubble resting on a heated surface, which is immersed in a semi-infinite quiescent fluid or within a two-dimensional cavity However, little information is available with regard to Marangoni heat transfer in miniature confined channels in the presence of a cross flow As a result, this article presents a two-dimensional (2D) numerical study that investigates the influence of steady thermal Marangoni convection on the fluid dynamics and heat transfer around a bubble during laminar flow of water in a miniature channel with the view of developing a refined understanding of boiling heat transfer for such a configuration This mixed convection problem is investigated under microgravity conditions for channel Reynolds numbers in the range of to 500 at liquid inlet velocities between 0.01 m/s and 0.0 5m/s and Marangoni numbers in the range of to 17,114 It is concluded that thermocapillary flow may have a significant impact on heat transfer enhancement The simulations predict an average increase of 35% in heat flux at the downstream region of the bubble, while an average 60% increase is obtained at the front region of the bubble where mixed convective heat transfer takes place due to forced and thermocapillary flow INTRODUCTION Based on the experimental results published in 1855 by Thomson [1], Marangoni [2] later offered a viable explanation of the effect of surface tension on drops of one liquid spreading upon another Subsequent to this several numerical and experimental studies [3, 4] established that thermocapillary– Marangoni convection is a physical phenomenon that takes place at gas–liquid and liquid–liquid interfaces The thermocapillary flow that forms is the result of surface tension gradients, which can be brought about by variations in the liquid concentration or temperature Once the existence of this phenomenon was confirmed, the main focus of the scientific research work was We gratefully acknowledge the support from the Science Foundation Ireland that sponsored this research Address correspondence to Dr Anthony Robinson, Department of Mechanical and Manufacturing Engineering, Trinity College Dublin, Parsons Building, Dublin 2, Dublin, Ireland E-mail: arobins@tcd.ie to quantify the impact on heat transfer enhancement Starting with the experimental results of McGrew et al [5] and followed by the early numerical work of Larkin [6], thermal Marangoni convection and its contribution to heat transfer during boiling became the subject of some debate in the open literature [7] Recently, it has been established that for certain conditions, such as microgravity boiling, the thermocapillary induced flow has associated with it a significant enhancement of heat transfer due to the liquid flow in the vicinity of the bubble interface [8– 10] Despite the research conclusions presented in the literature there is still insufficient information available with regard to Marangoni flow contribution on the heat transfer in miniature confined channels [11, 12], especially when it takes place in the presence of a cross flow under microgravity conditions To the best of our knowledge, this configuration has only been investigated by Bhunia and Kamotani [13] Their numerical study is focused on the fluid motion due to thermocapillary flow around a bubble situated on the heated wall of a channel The fluid mechanics aspects of the problem were characterized based on 335 336 C RADULESCU AND A J ROBINSON Reynolds number (Rσ ) and velocity (Vσ ) due to surface tension effect As a result, with this work as a reference, our study aims to present supplementary information regarding the heat transfer enhancement based on quantifying heat flux distribution around the bubble The work is focused on the mixed convective heat transfer due to forced and thermocapillary flow It is aimed to offer a baseline case for comparison and together with the generalized mathematical formulation presented by Bhunia and Kamotani [13] to provide information related to the fluid flow and to quantify the impact on heat transfer enhancement due to the thermocapillary effect The particular configuration selected for our investigation is the laminar flow of water in a miniature channel at low liquid inlet velocities 0.01 m/s ≤ Vavg ≤ 0.05 m/s for 100 ≤ Re ≤ 500 as defined in the literature by Shah et al [14] A single isolated bubble is located near the entrance and the heat transfer enhancement due to thermocapillary flow is quantified taking into account the confinement effects The cases under study have a significant importance for a wide range of applications where boiling heat transfer needs to be clearly understood Boiling heat transfer in minichannels has become an increasingly important topic due to its application in the compact heat exchanger design such as those required for electronics thermal management or for miniature power generators, to give just two examples Typically, nucleate boiling is the preferred regime of operation for such applications because the small increase in wall superheat is accompanied by a disproportionately large increase in the wall heat flux [15, 16] Apart from the high rates of heat transfer at relatively low volumetric flow rates, the isothermal nature of two-phase convective boiling makes this a very attractive technology in contrast with single-phase channel cooling The objective of this article is to provide qualitative and quantitative information regarding the fluid motion and the influence on heat transfer enhancement due to thermocapillary flow around the centerline of a bubble placed on the bottom heated wall of a rectangular-section minichannel (1 × 20 mm) in a cross-flow configuration as illustrated in Figure This mixed convection problem is investigated for laminar flow of water for increasing the inlet mass flow rate For a fixed inlet temperature the Marangoni number (Ma) is varied in the range of ≤ Ma ≤ 17,114 by increasing the temperature of the channel bottom heated wall Furthermore, the influence of the bubble dimension on the flow pattern and heat transfer is taken into consideration for the following geometrical characteristics: Rb /H = 0.1 (B1), Rb /H = 0.5 (B2), and Rb /H = 0.75 (B3) Figure Physical domain showing a hemispherical bubble near the entrance of the miniature channel heat transfer engineering MATHEMATICAL FORMULATION Figure shows the simplified schematic of the channel through which water at a mean inlet temperature Tm flows with the average velocity Vavg The flow is assumed to be hydrodynamically fully developed at the inlet with a parabolic velocity profile The heated bottom wall is maintained at a constant temperature (Twall ), while the top wall is considered to be insulated The hemispherical gas bubble is situated on the heated wall, creating a cross-flow configuration due to the bulk liquid flow directed perpendicular to the bubble axis This is located near the entrance of the channel, since this is the expected region of the nucleate boiling flow regime [17], with stratified or slug flow regimes being more likely downstream It was concluded that the bubble nucleus grows slowly to visible size in the laminar inlet flow [17] As a result, the flow and heat transfer problem has been simplified by considering steady-state conditions for three different dimensions of the bubble, starting with the incipient stage of growth and at the final stage before bubble sliding is anticipated [11] The bubble shape deformation is neglected as the capillary number Ca = µVavg /σT is much less than unity [13] and also taking into consideration the imposed low bulk liquid inlet velocities Lastly, it is well known that the flow around the bubble within a small channel is inherently a three-dimensional problem However, at the mid-plane of the spherical bubble the flow is approximately two-dimensional (2D) In this respect the problem can be treated qualitatively as a two-dimensional phenomenon consistent with the previous work of Bhunia and Kamotani [13] Governing Equations The governing continuity, momentum, and energy equations for steady flow are as follows [18–21]: The continuity equation is solved in the following form: ∇ u=0 (1) Conservation of momentum is described by Eq (2): u ∇ u = − ∇p + ν∇ u ρ (2) The energy equation without internal heat generation is reduced to u ∇T = α ∇ T (3) The governing equations are solved subject to the following assumptions and boundary conditions: (i) The bubble is represented as hemispherical, (ii) the heat flux is zero at the bubble interface, (iii) the top wall is insulated, (iv) the inlet flow is hydrodynamically fully developed, (v) the bottom wall is heated at a constant temperature, (vi) gravitational effects are negligible, (vii) apart from surface tension, temperature variations in physical properties are not considered, (viii) the liquid is incompressible, and (ix) the no-slip condition is applied to all surfaces vol 31 no 2010 C RADULESCU AND A J ROBINSON 337 except the Marangoni stress boundary condition for the bubble [6, 22, 23]; the shear stress applied at its interface is assumed to be balanced by viscous effect as quantified in Eq (4): ∂σ ∂u = ∇S T (4) ∂n ∂T Here, n is the unit vector normal to the bubble interface and ∇S T is the temperature gradient The governing equations were solved numerically with the computational fluid dynamics (CFD) package Fluent Version 6.3.26 [18, 24], and the physical domain and grid were created in Gambit Version 2.2.30 [19] Cartesian coordinates were used with a nonuniform grid of 14,400 cells In order to resolve the flow and temperature fields accurately, grid clustering near the bubble was implemented The accuracy of the resulting simulations has been confirmed by reproducing the numerical results of Bhunia and Kamotani [13] and Radulescu and Robinson [25], as well as assuring that the solutions were grid independent u · n = 0µ RESULTS AND DISCUSSION The results presented in this study have been carried out for water, which has a surface tension gradient of dσ/dT = – 0.1477 × 10−3 N/mK The problem is investigated for channel Reynolds numbers in the range of ≤ Re ≤ 500 by increasing the inlet average velocity for 0.01 m/s ≤ Vavg ≤ 0.05 m/s The Marangoni number is in the range of 50 ≤ Ma ≤ 17,114 obtained due to variations of the difference between the liquid inlet temperature and the wall temperature of the channel ( T = Twall – Tm ) for 1◦ C ≤ T ≤ 30◦ C Consistent with [9], [13], and [22] the Marangoni number has been defined as: Ma = (∂σ/∂T )(Twall − Tm ) Rb2 = Rσ P r µα H (5) To approximate different stages of bubble growth, i.e., nucleation to bubble sliding [11], the bubble size relative to the channel height has been investigated for Rb /H = 0.1 (B1), Rb /H = 0.5 (B2), and Rb /H = 0.75 (B3) The primary objective of this study is to provide a qualitative description of the effect of thermocapillary convection on the flow field and to quantify the heat transfer enhancement during bubble growth in a miniature channel The Effect of Marangoni Convection on the Flow Field Figure presents the streamlines for steady flow around the bubble for the case Rb /H = 0.1, Re = 100, and Ma = 0, 50, 100, and 300 To provide a baseline case for comparison, steady flow around a bubble with no thermocapillary effect has been simulated for this test case and each test case to follow [26] This is equivalent to imposing a constant surface tension (∂σ/∂T = 0) such that Ma = even though there are temperature gradients along the interface Due to these, the surface tension is highest heat transfer engineering Figure Streamlines of steady flow for Rb /H = 0.1 (B1) at Re = 100 near the top of the bubble and lowest near the heated wall This surface tension variation generates thermocapillary flow along the bubble surface, away from the hot wall toward the bulk liquid Figure illustrates clearly that increasing the driving potential for thermocapillary flow, which in this situation is T = Twall – Tm , the influence of the surface tension driven flow becomes stronger, which is apparent from the increased deformation of the streamlines as compared with the baseline Ma = case Upstream (front) side of the bubble In this region the thermocapillary action accelerates the liquid flow along the bubble surface The shear driven flow at interface has the effect of drawing the relatively colder bulk liquid downward toward the front corner of the bubble, as apparent from the deformation of the near-wall streamlines toward the hot front corner of the bubble for the Ma = 50 and 100 cases Downstream side of the bubble In this region a sizable vortex is formed even at low Marangoni numbers (Ma = 50) when the recirculation cell is strong enough to cross over the line of symmetry of the bubble toward the front region For the highest Marangoni number obtained for Rb /H = 0.1 (i.e., Ma = 300) the high shear rate at the front bubble interface interacts with the strong rear vortex to form a recirculation cell near front region of the bubble With regard to the rear vortex itself, increasing Ma has the effect of increasing the strength of the vortex, as is evident from the higher concentration of the streamlines, as well as increasing the vortex size, as it is seen to penetrate vol 31 no 2010 338 C RADULESCU AND A J ROBINSON Figure Magnitude of x-velocity and separation point position for B1, B3 at Re = 100 and T = 10◦ C deeper into the bulk liquid and along the heated wall, as well as moving forward along the bubble surface In order to visualize the velocity magnitude on the x coordinate, Figure shows the case of Ma = 100 together with information for the geometrical dimensions of the recirculation thermocapillary cell Near the downstream end the surface velocity due to the bulk liquid flow is in an opposite direction, with the recirculation cell created by the thermocapillary flow The point on the bubble surface where the forward and reverse flow meet is known in the literature as the separation point [13] As is evident in Figure 2, and discussed later in more detail, this separation point appears to move closer to the front region of the bubble with increasing Ma Figure presents the influence of the bubble dimension (B1 and B3) on the separation point position (defined by the angle β) for the same Re = 100 and temperature difference T = 10◦ C It is noticed that this point is situated closer to the front region of the bubble (at higher separation angle β) for the smaller bubble dimension (B1) Figure illustrates the influence of inertial effects of the channel flow by considering the identical configuration as in Figure but for the higher Reynolds number case of Re = 300 As one would expect, the increase in the cross-flow velocity has an important impact on the flow structure by suppressing the influence of the Marangoni flow This is clear considering that for Re = 300 it takes a Marangoni number of Ma = 300 to roughly reproduce the flow structure that a Marangoni number of Ma = 100 was able to produce for Re = 100 With the view of future development of a dynamic bubble growth model, it seemed instructive to investigate the influence of the bubble size on the flow and heat transfer within the channel for this idealized case of steady two-dimensional flow Figures and show the simulated flow patterns around bubbles with aspect ratios Rb /H = 0.5 and 0.75, respectively, for a fixed Reynolds number of Re = 100 heat transfer engineering Figure Streamlines of steady flow for Rb /H = 0.1 (B1) at Re = 300 Increasing the relative size of the bubble from Rb /H = 0.1 to Rb /H = 0.5 has a notable influence on the flow pattern, as evident from Figure It must first be noted that the Ma number increases disproportionately compared with the increase in T and Rb /H, since the length scale has been chosen as R2b /H for this study to incorporate the influence of confinement on the flow and heat transfer Compared with the relatively unconfined case depicted in Figure for Rb /H = 0.1, the flow structure within the liquid for the more confined case of Rb /H = 0.5 indicates that the thermocapillary induced convection has a more profound influence on flow for a like driving temperature differential and a significantly higher Ma The presence of the confining upper wall tends to form elongated yet more concentrated recirculation zones at the downstream end of the bubble, compared with the more unconfined case at identical T For T = 30◦ C, Figure shows that confinement effects result in the formation of three recirculation zones—in particular, an elongated vortex spanning a considerable portion of the top region of the bubble interface Figure illustrates the extreme situation of Rb /H = 0.75 where the bubble is at its maximum growth dimension before sliding in the minichannel due to the inertial forces of the bulk liquid flow [11] It is noticed that the flow pattern is altered notably compared with the previous two cases In this case the confining and adiabatic top wall tends to restrict the rear vortex from encroaching on the frontal region with increasing T This pinching of the rear vortex is strong enough that for the vol 31 no 2010 C RADULESCU AND A J ROBINSON 339 Figure Streamlines for steady flow for Rb /H = 0.75 (B3) at Re = 100 Figure Streamlines of steady flow for Rb /H = 0.5 (B2) at Re = 100 highest driving potential of T = 30◦ C no secondary recirculation zones develop since the separation point is far enough back on the bubble interface that it does not significantly obstruct the frontal shear flow This is also illustrated in Figure 3, where it is shown that the separation point on the bubble surface, where the forward and reverse flows meet, has the tendency to occur at smaller separation angles, β, for the larger bubbles at identical T and Re The Effect of Marangoni Convection on the Thermal Field and Wall Heat Transfer The flow and thermal fields are directly coupled via the nonlinear convection term in Eq (3) and more indirectly through the Marangoni stress boundary condition given in Eq (4) As a result, the interaction of the flow and thermal fields must be understood in relation to one another in order to elucidate the effect on less global parameters such as the stagnation angle, bubble surface temperature distribution and resulting wall heat transfer in the vicinity of the bubble Figure illustrates the thermal profile for the Rb /H = 0.1, Re = 100, and Ma = 0, 50, and 300 case For Ma = the heat transfer engineering presence of the bubble has a small influence on the thermal field, acting as a simple obstruction to the flow [26] However, for the same wall temperature but with thermocapillary Marangoni convection, a nonsymmetric jet of warm fluid is forced into the bulk of the flow The size of the warm jet is consistent with the size of the vortices observed in Figure 2, and the penetration depth of the warm jet increases with Ma in the same way as the size of the recirculation regions is increased in Figure Near the front edge of the bubble it is clearly evident that the deformation of the streamlines observed in Figure has associated with it the drawing in of the cooler bulk liquid, which will have important implications with regard to the wall heat transfer Figure 8a and b presents the wall heat flux distribution for Rb /H = 0.1, Re = 100 and 300, with Ma = 30, 50, 100, and 200 The corresponding heat flux distribution for the situation of no Marangoni flow is also plotted for each temperature differential It is clear that the thermal and flow fields resulting from thermocapillary convection have a direct impact on the heat transfer in the vicinity of the bubble, as is evident from the peaks in the wall heat flux that appear around it Upstream (front) side of the bubble In this region the increase in the heat flux is stronger due to the combined effect of forced and thermocapillary convection with the thermocapillary component drawing the cooler bulk liquid toward the heated wall and thinning the thermal boundary layer as depicted in vol 31 no 2010 340 C RADULESCU AND A J ROBINSON Figure Wall heat flux distribution for B1 at Re = 100 and 300 Figure and 300 Temperature profile for Rb /H = 0.1 at Re = 100 and Ma = 0, 50, Figures 2, 4, and For Re = 100 a two- to threefold increase in the local heat flux is evident As expected, the enhancement decreases somewhat with increasing Re; however, it is still substantial Downstream of the bubble The increase in the wall heat transfer is only evident for the higher Ma number because it is primarily the warm liquid that was extracted from the frontal region that is being recirculated in this area Here the local heat flux increases by a factor of nearly 1.2 for Re = 100 and Ma = 200 and tends to improve with increasing Re, with a 1.4 times improvement for Re = 300 and Ma = 200 The bubble dimensionless interface temperature distributions for Rb /H = 0.1, Re = 100, and Ma = 0, 30, 50, 100, 200, and 300 are plotted in Figure Considering the Ma = and Ma = 50 cases, which both correspond with T = 5◦ C, it is clear that Marangoni convection tends to diminish the thermal gradients over the majority of the bubble surface For Ma > the general shape of the temperature profiles are similar In the front region of the bubble the gradients are steep due to the combined influences of the forced and thermocapillary convecheat transfer engineering tion as cold bulk fluid is drawn toward the surface and accelerated along it The surface temperature decreases to a minimum at the separation point Behind the separation point the temperature gradients along the bubble surface are less steep as the flow transitions from a combined convection region to a dominantly thermocapillary-driven recirculation region where the average liquid temperature is generally much higher than the bulk liquid Increasing the Marangoni number has two notable effects on the bubble surface temperature profile First, the Figure Bubble B1 interface temperature for Re = 100 and Ma = 0, 30, 50, 100, 200, and 300 vol 31 no 2010 C RADULESCU AND A J ROBINSON 341 stagnation point moves closer to the bubble front region with the increase in Ma numbers However, further variations at a higher Ma beyond Ma = 200 have a minimal effect on the position of the separation point Second, increasing Ma tends to flatten the temperature profile along the bubble interface, with large gradients isolated to the front and rear of the bubble Figure 10 shows the effect of the top confining wall on the thermal field around the bubble for which Rb /H = 0.5 for the same T values in Figure Compared with the small bubble, the confinement effects tend to keep the warm recirculation zone near the rear of the bubble with strong effects on the front region, where the shear flow causes entrainment of the cold bulk fluid toward the wall, which thins the thermal boundary layer in this region more so than for the Rb /H = 0.1 case Figure 11 illustrates this point more clearly where the heat flux profiles for Rb /H = 0.1, 0.5, and 0.75 are plotted for Re = 100 and T = 10◦ C It is clear that the peak heat flux at the front of the bubble increases notably with increasing Rb /H The peak local heat transfer enhancement at the rear side also tends to increase at higher Rb /H but to a much lesser extent CONCLUSIONS Figure 10 Temperature distribution for B2 at Ma = 0, 1260, and 7600 Figure 11 Heat flux distribution for Rb /H = 0.1, 0.5, and 0.75 at Re = 100 and T = 10◦ C heat transfer engineering This article presents a two-dimensional numerical model that investigates the influence of steady thermal Marangoni convection on the fluid dynamics and heat transfer around a bubble during laminar flow of water in a rectangular minichannel At the downstream side of the bubble a sizable vortex is formed even at low Marangoni numbers ( T = 5◦ C, i.e., Ma = 50 for B1) The recirculation cell is strong enough to cross over the line of symmetry of the bubble toward the front region For the high Marangoni numbers obtained at the maximum T = 30◦ C under consideration (i.e., Ma = 300 for B1) the shear rate at the front bubble interface interacts with the strong rear vortex to form a recirculation cell near the front region of the bubble With regard to the rear vortex itself, increasing Ma has the effect of increasing the strength as well as the vortex size, which penetrates deeper into the bulk liquid and along the heated wall as well as moving forward along the bubble surface It is concluded that thermocapillary flow has a significant impact on heat transfer enhancement for this configuration, with an average increase of 35% in the heat flux figures at the downstream of the bubble, while the mixed convective heat transfer due to forced and thermocapillary flow results in an average of 60% increase at the front side of the bubble As presented, the 2D numerical approach employed in this work provides information related with the flow pattern, thermal field, and heat flux at the mid-plane of spherical bubbles of several dimensions Future work will involve simulations which include three-dimensional effects as well as unsteady effects due to bubble growth vol 31 no 2010 342 C RADULESCU AND A J ROBINSON NOMENCLATURE REFERENCES B1 B2 B3 Ca Dh hMa H lM L Ma n p Pr Rb [1] Thomson, J., Capillary Action, Philosophy Magazine, vol 4, no 10, pp 330, 1855 [2] Marangoni, C G M., Ueber Die AusBreitung Der Tropfen Einer Flussigkeit auf der Oberflache einer anderen, Annalen der Physik und Chemie (Poggendorff), vol 143, ser 7, pp 337–354, 1871 [3] Benard, H., Tourbillons Cellulaires dans une nappe liquide transportant de la chaleur par convection en regime permanent, Annales de Chimie et de Physique, vol 23, ser 7, pp 62–144, 1901 [4] Pearson, J R A., On Convection Cells, Journal of Fluid Mechanics, vol 4, no 5, pp 489–500, 1958 [5] McGrew, J L., Bamford, F L., and Rehm, T R., Marangoni Flow: An Additional Mechanism in Boiling Heat Transfer, Science, New Series, vol 153, no 3740, pp 1106–1107, 1966 [6] Larkin, B K., Thermocapillary Flow Around a Hemispherical Bubble, AIChE Journal, vol 16, pp 101–107, 1970 [7] Sefiane, K., and Ward, C C., Recent Advances on Thermocapillary Flows and Interfacial Conditions During the Evaporation of Liquids, Advances in Colloid and Interface Science, vol 134–135, pp 201–223, 2007 [8] Kao, Y S and Kenning, D B R., Thermocapillary Flow Near a Hemispherical Bubble on a Heated Wall, Journal of Fluid Mechanics, vol 53, part 4, pp 715–735, 1972 [9] Reynard, C., Santini, R., and Tadrist, L., Experimental Study on the Gravity Influence on the Periodic Thermocapillary Convection Around a Bubble, Experiments in Fluids, vol 4, no 31, pp 440– 446, 2001 [10] Hadland, P H., Balasubramaniam, R., Wozniak, G., and Subramanian, R S., Thermocapillary migration of bubbles and drops at moderate to large Marangoni number and moderate Reynolds number in reduced gravity, Experiments in Fluids, vol 26, no 3, pp 240–248, 1999 [11] Mukherjee, A., and Kandlikar, S G., Numerical Study of the Effect of Surface Tension on Vapour Bubble Growth During Flow Boiling in Microchannels, Proceedings of the ICNMM2006, Fourth International Conference on Nanochannels, Microchannels and Minichannels, Limerick, Ireland, paper no ICNMM 2006–96050, 2006 [12] Clokner, P S., and Naterer, G F., Interfacial Thermocapillary Pressure of an Accelerated Droplet in Microchannels: Part I Fluid Flow Formulation, International Journal of Heat and Mass Transfer, vol 50, issues 25–26, pp 5269–5282, 2007 [13] Bhunia, A., and Kamotani, Y., Flow Around a Bubble on a Heated Wall in a Cross-Flowing Liquid Under Microgravity Condition, International Journal of Heat and Mass Transfer, vol 44, no 20, pp 3895–3905, 2001 [14] Shah, R K., Kraus, A D., and Metzger, D., Compact Heat Exchangers, Hemisphere Publishing Corporation, Taylor & Francis Group, New York, pp 123–149, 1990 [15] Bintoro, J S, Akbarzadeh, A., and Mochizuki, M., A Closed-Loop Electronics Cooling by Implementing Single Phase Impinging Jet and Mini Channels Heat Exchanger, Applied Thermal Engineering, vol 25, no 17–18, p 2740, 2005 [16] Narumanchi, S., Troshko, A., Bharathan, D., and Hassani, V., Numerical Simulations of Nucleate Boiling in Impinging Jets: Applications in Power Electronics Cooling, International Journal of Heat and Mass Transfer, vol 51, no 1–2, pp 1–12, 2008 Re first bubble under consideration second bubble under consideration third bubble under consideration capillary number hydraulic diameter [14] height of Ma recirculation cell [m] height of the channel [m] length of Ma recirculation cell [m] length of the minichannel [m] Marangoni number (thermocapillary) unit normal vector (height of the boundary) static pressure [N/m2 ] Prandtl number bubble radius (RB1 , RB2 , RB3 radius of B1, B2, B3, respectively) [m] ρV Dh Reynolds number avg [14] µ Rσ T Tm Twall T∗ Vavg Vσ u x, y X* T surface tension Re number l µref b [13] l temperature [◦ C] avg bulk liquid temperature at inlet [◦ C] heated wall temperature [◦ C] dimensionless temperature (T − Tm )/ T liquid inlet average velocity [m/s] σ T thermocapillary velocity Tµ| [13] [m/s] l velocity vector Cartesian coordinates dimensionless x coordinate by Rb (x/Rb ) temperature difference Twall − Tm [◦ C] ρV R Greek Symbols α β µ σ σT ρ ν ∇ ∇S T thermal diffusivity [m2 /s] stagnation point angle dynamic viscosity [Ns/m2 ] liquid surface tension [N/m] surface tension gradient [N/mK] density [kg/m3 ] kinematic viscosity [m2 /s] Laplace divergence operator temperature gradient at the bubble interface Subscripts avg b m Ma ref average bubble bulk liquid Marangoni reference heat transfer engineering vol 31 no 2010 C RADULESCU AND A J ROBINSON [17] Wen, D S., Youyou, Y., and Kenning, D B R., Saturated Flow Boiling of Water in a Narrow Channel: Time-Averaged Heat Transfer Coefficients and Correlations, Applied Thermal Engineering, vol 24, no 8–9, pp 1207–1233, 2004 [18] Fluent software, http://www.fluent.com [19] Gambit, http://www.fluent.com/software/gambit/index.htm [20] Tritton, D J., Physical Fluid Dynamics, Oxford Science Publication, Clarendon Press, Oxford, pp 162–172, 1998 [21] Panton, R L., Incompressible Flow, John Wiley & Sons, New York, pp 102–106, 1993 [22] Petrovic, S., Robinson, A J., and Judd, L R., Marangoni Heat Transfer in Subcooled Nucleate Pool Boiling, International Journal of Heat and Mass Transfer, vol 47, no 23, pp 5115–5128, 2004 [23] O’Shaughnessy, S., and Robinson, A J., Numerical Investigation of Marangoni Convection Caused by the Presence of a Bubble on a Uniformly Heated Surface, Proceedings of ITP2007 Interdisciplinary Transport Phenomena V: Fluid, Thermal, Biological, Materials and Space Sciences, Bansko, Bulgaria, paper ITP-0744, 2007 [24] FLUENT User Guide, User Service Center, http://www.fluent com [25] Radulescu, C., and Robinson, A J., The Influence of Gravity and Confinement on Marangoni Flow and Heat Transfer Around a Bubble in a Cavity: A Numerical Study, Microgravity Sci- heat transfer engineering 343 ence and Technology Journal, vol 20, no 3–4, pp 253–259, 2008 [26] Straub, J., The Role of Surface Tension for Two-Phase Heat and Mass Transfer in the Absence of Gravity, Experimental Thermal and Fluid Science, vol 9, no 3, pp 253–273, 1994 Cristina Radulescu is a postdoctoral researcher at Trinity College Dublin She received her Ph.D in 2005 from Galway-Mayo Institute of Technology, Ireland Her main research work at present is related to the mechanism of heat transfer during nucleate pool boiling and the influence of thermocapillary convection on heat transfer Anthony Robinson is a lecturer in fluid mechanics and heat transfer at Trinity College Dublin, Ireland He received his Ph.D at McMaster University, Canada, in 2002 His research interests are in the field of two-phase flow and heat transfer vol 31 no 2010 416 O S MOTSAMAI ET AL It should be noted that this methodology cannot replace the empirical and semi-empirical design tools for preliminary design, but it is very useful when optimizing the final designs to achieve certain performance requirements Though the method was applied to the combustor exit temperature profile, it can possibly be used for other performance requirements as long as the objective function and constraints can be written in an analytical equation or approximated function The current results have not been validated against experimental results, but the proposed strategy was initially tested on a base case design example, on which model validation was performed with a wellresearched Berl combustor before this work was carried out, in order to cultivate the ability to reproduce correct reacting flow results [2] [3] [4] [5] [6] NOMENCLATURE aj , bj , cj A, Bj , C f f (x) gj (x) hj (x) I i k Le P (i) ˆ p(x) Rn T x βk ε δj µi ρj kˆ kˇ approximated curvatures of objective and constraint functions of subproblem Hessian matrices mixture fraction objective function j -th inequality constraint function k-th equality constraint function identity matrix or turbulence intensity iteration turbulence kinetic energy (m2 /s2 ) turbulence length scale (m) approximate optimization subproblem penalty function n-dimensional real space temperature (K) design vector penalty parameter rate of dissipation specified move limit for i-th design variable penalty parameter penalty parameter lower bound upper bound [7] [8] [9] [10] [11] [12] [13] [14] Sub-/Superscripts i o i, j, k inlet outlet indices [15] [16] REFERENCES [1] Qingjun, Z., Huise, W., Xiaolu, Z., and Jianzhong, X., Numerical Investigation on the Influence of Hot Streak Temperature Ratio in a High-Pressure Stage of Vaneless Counter-Rotating Turbine, heat transfer engineering [17] International Journal of Rotating Machinery, vol 2007, article ID 56097, 14 pages, doi:10.1155/2007/56097, 2007 Barringer, M D., Thole, K A., and Polanka, M D., Effects of Combustor Exit Profiles on High Pressure Turbine Vane Aerodynamics and Heat Transfer, Proc ASME Turbo Expo Conf., Barcelona, paper GT2006-90277, 2006 Mongia, H C., A 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A., Dadone, A., Manodoro, D., and Saporano, A., Efficient Design Optimization of Duct-Burner for Combined-Cycle and Cogeneration Plants, Engineering Optimisation, vol 38, no 7, pp 801–0, 2006 Becz, S., and Cohen, J M., Characterization of Mixing for a Jet in Cross-flow Using Proper Orthogonal Decomposition, Proc ASME TURBO EXPO Conf., Reno-Tahoe, NV, 2005-0307, 2005 Morris, R M., Snyman, J A., and Meyer, J P., Jets in Crossflow Mixing Analysis Using Computational Fluid Dynamics and Mathematical Optimization, Journal of Propulsion and Power, vol 23, no 3, pp 618–8, 2007 Dispierre A., Stuttaford P J., and Rubini, P A., Preliminary Gas Turbine Combustor Design Using a Genetic Algorithm, Proc ASME IGTI Conf., Amsterdam, paper 97-GT-72, 1997 Rogero, J M., A Genetic Algorithm Based Optimisation Tool For the Preliminary Design of Gas Turbine Combustors, Ph.D Thesis, School of Mechanical Engineering, Cranfield University, UK, 2002 Zomorodian, R., Khaledi, H., and Ghofrani, M., A New Approach to Optimisation of Cogeneration Systems Using Genetic Algorithm, Proc ASME TURBO EXPO Conf., Barcelona, paper GT2006-90952, 2006 Stuttaford, P J., and Rubini, P A., Preliminary Gas Turbine Combustor Design Using Network Approach, Proc ASME IGTI Conf., Birmingham, UK, paper 96-GT-135, 1996 Snyman, J A., and Hay, A M., The Dynamic-Q Optimization Method: An Alternative to SQP?, International Journal of Computers and Mathematics with Applications, vol 44, no 12, pp 1589–98, 2002 Kingsley, T., Design Optimization of Containers for Sloshing and Impact, M.Sc dissertation, University of Pretoria, Pretoria, South Africa, 2005 vol 31 no 2010 O S MOTSAMAI ET AL [18] Craig, K J., De Kock, D J., and Snyman J A., Using CFD and Mathematical Optimization to Investigate Air Pollution Due to Stacks, International Journal of Numerical Mathematics in Engineering, vol 44, pp 551–5, 1999 [19] De Kock, D J., Craig, K J., and Pretorius, C.A., Mathematical Maximisation of Minimum Residence Time for Two Strand Continuous Caster, Iron Marking and Steel Marking, vol 30, no 3, pp 229–4, 2003 [20] Morris, R M., An Experimental and Numerical Investigation of Gas Turbine Research Combustor, M.Sc dissertation, University of Pretoria, Pretoria, South Africa, 2000 [21] Custer, J R., and Rink, N K., Influence of Design Concept and Liquid Properties of Fuel Injection Performance, Journal of Propulsion, vol 4, no 4, 1987 [22] Crowe, C T., Sharma, M P., and Stock, D E., The Particle SourceIn-Cell (PSI-CELL) Model for Gas-Droplet Flows, Journal of Fluids Engineering, vol 99, pp 325–2, 1997 [23] Faith, G M., Evaporation and Combustion of Sprays, Progress in Energy and Combustion Science, vol 9, pp 1–76, 1983 [24] Sabnis, J S., Gibeling, H J., and McDonald, H A., Combined Eulerian–Lagrangian Analysis for Computation of Two-Phase Flow, AIAA paper, 87-1419, 1987 [25] FLUENT, Software package, Ver 6.2.16, Fluent, Inc., Lebanon, NH, 2004 [26] Tap, F A., Dean, A J., and Van Buijttenen, J P., Experimental and Numerical Spray Characterization of a Gas Turbine Fuel Atomizer in Cross Flow, Proc ASME TURBO EXPO Conf., Amsterdam, paper GT-2002-30100, 2002 [27] Dukowicz, J K A., Particle Fluid Numerical Model for Liquid Sprays, Journal of Computational Physics, vol 35, pp 229–3, 1980 [28] O’Rouke, P J., Collective Drop Effects in Vaporizing Liquid Sprays, Ph.D thesis, Princeton University, and Los Alamos National Laboratory Report, LA-9069-T, US, 1981 [29] Rosin, P., and Rammler, R., The Laws Governing the Fineness of Powdered Coal, Journal of the Institute of Fuel, pp 29–36, 1933 [30] Libby, P A., and Williams, F A., Turbulent Reacting Flow, Academic Press, New York, 1994 [31] Fluent News, The Berl Combustor Revisited, vol xii, issue 1, 2003 [32] Sayre, A., Lallemant, N., Dugue, J., and Weber, R., Scaling Characteristics of Aerodynamics and Low-Nox Properties of Industrial Natural Gas Burners, The Scaling 400 Study, Part IV: The 300 kW Berl Test Results, IFRF Doc No F40/y/11, International Flame Research Foundation, The Netherlands, 1996 [33] Sivaramakrishna, G., Muthuveerappan, N., Shankar, V., and Sampathkumaran, T K., CFD Modeling of the Aero Gas Turbine Combustor ASME Turbo Expo, 2001-GT-0063, 2001 [34] Smiljanovski, V., and Brehm, N., CFD Liquid Spray Combustion Analysis of a Single Annular Gas Turbine Combustor, Proc ASME IGTI Conf., Indianapolis, paper, 99-GT-300, 1999 [35] Fuligno, L., Micheli, D., and Poloni, C., An Integrated Design Approach for Micro Gas Turbine Combustors: Preliminary 0D and Simplified CFD Based Optimization, ASME Turbo Expo, GT2006-90542, 2006 [36] Durbin, M D., Vangsness, M D., Balla, D R., and Katta, V R., Study of Flame Stability in a Step Swirl Combustor, Conf ASME IGTI Conf., Hawaii, paper 95-GT-111, 1995 heat transfer engineering 417 [37] Schmit, L A., and Farshi, B., Some Approximation Concepts for Structural Synthesis, AIAA Journal, vol 12, no 5, pp 692–699, 1974 [38] Haftka, R T., and Gurdal, Z., Elements of Structural Optimization, Kluwer Academic, Boston, p 221, 1992 [39] Mongia, H C., Aero-Thermal Design and Analysis of Gas Turbine Combustion Systems: Current Status and Future Direction, Conf ASME IGTI Conf., Cleveland, paper 98-3982, 1998 [40] Rinz, A., and Mongia, H C., Gas Turbine Combustor Design Methodology, Conf ASME IGTI Conf., Dusseldorf, paper 86-131, 1986 [41] Baumal, A E., McPhee, J., and Calamai, P H., Application of Genetic Algorithms of an Active Vehicle Suspension Design, Computer Methods in Applied Mechanics and Engineering, vol 163, pp 87–94, 1998 [42] Eberhard, P., Schiehlen, W., and Bestle, D., Some Advantages of Stochastic Methods in Multi-criteria Optimization of Multibody Systems, Archive of Applied Mechanics, vol 69, pp 543–554, 1998 [43] Els, P S., and Uys, P E., Investigation of the Applicability of the Dynamic-Q Optimisation Algorithm to Vehicle Suspension Design, Mathematical and Computer Modelling, vol 37, nos 9– 10, pp 1029–46, 2003 [44] Visser, J A., and De Kock, D J., Optimization of Heat Sink Mass Using the Dynamic-Q Numerical Optimization Method, Communications in Numerical Methods in Engineering, vol 18, no 10, pp 721–727, 2002 [45] Snyman, J A., The LFOPC Leap-Frog Algorithm for Constrained Optimization, Computers and Mathematics with Applications, vol 40, pp 1085–1096, 2000 [46] Toolkit for Design Optimization (TDO) software, version 1.2d, Department of Mechanical and Aeronautical Engineering, University of Pretoria, Praetoria, South Africa [47] Vanoverberche, K P., Van Den Bulck, E V., and Tummers, M J., Confined Annular Swirling Jet Combustion, Combustion Science and Technology, vol 175, pp 545–578, 2003 Oboetswe Motsamai is a Ph.D student at the University of Pretoria, Department of Mechanical and Aeronautical Engineering, South Africa He received the B.Eng Mechanical from the University of Botswana in 1996 and M.Sc in thermal power and fluids engineering from the University of Manchester Institute of Science and Technology in 2000 He has previously worked for Kentz Botswana (1997) as a junior engineer and later worked for G4 Consulting Engineers (1998) as an engineer He is currently working for the University of Botswana as lecturer in the department of mechanical engineering He is doing his research on developing a design optimization methodology for gas turbine combustors Jan Snyman received B.Sc (Hons.) degrees in both physics and mathematics from the Universy of Cape Town and University of Pretoria, respectively, in 1961 and 1964, an M.Sc degree in physics from the University of South Africa in 1964, and the Ph.D degree in theoretical physics from the University of Pretoria in 1975 He started his career as a research officer at the National Physical Research Laboratory of the South African Council for Scientific and Industrial Research in Pretoria in 1962 He worked in the vol 31 no 2010 418 O S MOTSAMAI ET AL computer industry from 1966 to 1968, first as a programmer and then as a systems analyst at English Electric Computers and IBM, respectively In 1969 he was appointed lecturer in physics at the Pretoria Technikon and in 1971 he joined the faculty of the University of Pretoria as lecturer in the Department of Applied Mathematics, where he was promoted to full professor in 1983 In 1990 he joined the Department of Mechanical Engineering, where he teaches dynamics, numerical methods, and mathematical optimization at both undergraduate and graduate level After his retirement in 2005 he has, as emeritus professor, continued to be involved in the activities of the department His research focuses mainly on two interrelated aspects of mathematical optimization: the development of new optimization algorithms and optimization methodologies of particular importance for the solving of physical and engineering design problems, and the application thereof in design problems of practical importance to industry He has received several prizes and awards for his research, including the Centenary Research Medal (1908–2008) of the University of Pretoria In 2004 an honorary professorship (professor honoris causae Facultatis Mechanicae) was conferred on him by the University of Miskolc in Hungary He is the author or co-author of 86 scientific journal articles and one book heat transfer engineering Josua Meyer obtained his B.Eng (cum laude) in 1984, M.Eng (cum laude) in 1986, and his Ph.D in 1988, all in mechanical engineering from the University of Pretoria, and is registered as a professional engineer After his military service (1988–1989), he accepted a position as associate professor in the Department of Mechanical Engineering at the Potchefstroom University in 1990 He was acting head and professor in mechanical engineering before accepting a position as professor in the Department of Mechanical and Manufacturing Engineering at the Rand Afrikaans University in 1994 He was chairman of Mechanical Engineering from 1999 until the end of June 2002, after which he was appointed professor and head of the Department of Mechanical and Aeronautical Engineering at the University of Pretoria from July 2002 At present he is the chair of the School of Engineering He specializes in heat transfer, fluid mechanics, and thermodynamic aspects of heating, ventilation, and air conditioning He is the author and co-author of more than 250 articles, conference papers, and patents and has received various prestigious awards for his research He is also a fellow or member of various professional institutes and societies (i.e., South African Institute for Mechanical Engineers, South African Institute for Refrigeration and Air-Conditioning, American Society for Mechanical Engineers, American Society for Heating, Refrigeration and Air-Conditioning) and is regularly invited to be a keynote speaker at local and international conferences He has also received various teaching and exceptional achiever awards He is an associate editor of Heat Transfer Engineering vol 31 no 2010 Heat Transfer Engineering, 31(5):419–429, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903375475 Comparison of Conventional Flat-Plate Solar Collector and Solar Boosted Heat Pump Using Unglazed Collector for Hot Water Production in Small Slaughterhouse CHATCHAWAN CHAICHANA,1 TANONGKIAT KIATSIRIROAT,1 and ATIPOANG NUNTAPHAN2 Department of Mechanical Engineering, Chiang Mai University, Chiang Mai, Thailand Thermal Technology Research Laboratory, Mae Moh Training Center, Electricity Generating Authority of Thailand, Mae Moh, Lampang, Thailand This study presents simulated results of solar water heating systems in a small slaughterhouse using two techniques The first one is a normal solar water heating system using a flat-plate solar collector and the second one uses a solar-boosted heat pump system having a corrugated metal sheet roof as a solar collector The number of solar collector units is between and 5, and the volume of water in a storage tank is 300–1200 L The heat pump in this work uses refrigerant mixture R22:R124:R152a of 20%:57%:23% as the working fluid The weather conditions of Chiang Mai, Thailand, are taken as the input data In the case of the normal solar water heating system, the shortest payback periods for 300, 600, 900, and 1200 L water are 3.63, 3.12, 2.95, and 2.82 yr, respectively The suitable number of collectors for 300 L water is unit with 600–900 L water storage; units of collectors is suitable in the case of 1200 L water, and units of collectors gives the shortest payback period However, in the case of a solar heat pump system, the suitable payback periods for 300, 600, 900, and 1200 L water are 2.74, 1.79, 1.83, and 1.88 yr, respectively In our case, unit of this collector gives the shortest payback period INTRODUCTION At present, utilization of solar water heater in household and industrial applications seems to be increasing because of its low fuel cost compared to that of the conventional heater For the case of a slaughterhouse in Thailand, 80◦ C hot water is used in the nighttime for cleaning the animal’s skin and removing its hair This hot water comes from a conventional heater using liquefied petroleum gas (LPG) as fuel The efficiency of this heater is rather low, approximately 25% [1], and the cost of LPG continuously increases To reduce the fuel cost and the The authors gratefully acknowledge the financial support provided by the Thailand Research Fund and the Commission on Higher Education, Thailand, for carrying out this study Address correspondence to Professor Tanongkiat Kiatsiriroat, Department of Mechanical Engineering, Chiang Mai University,Chiang Mai, 50200, Thailand E-mail: kiatsiriroat t@yahoo.co.th related environmental problem, solar water heating seems to be a good solution There are many types of solar collectors matching with this application, such as flat- plate, thermosyphon heat pipe, and evacuated tube The flat-plate solar collector is a popular one because of its low investment cost Also, a solar-boosted heat pump, which is a heat pump combined with a solar collector, has been recommended for better overall performance Ito et al [2] studied the thermal performance of a heat pump using a direct expansion solar collector Huang et al [3] took a longterm test of a solar water heater combined with a heat pump for more than 20,000 h and found that the electrical energy cost was approximately 0.019 kW-h per liter of hot water at 57◦ C Hawlader et al [4] reported a coefficient of performance (COP) of a solar-assisted heat pump water heating system of around 4–9 For a small slaughterhouse, less than 20 pigs are killed daily during the nighttime; therefore, using solar energy for 419 420 C CHAICHANA ET AL the economic evaluation is also considered in both cases The result could served for the application of solar water heating for slaughterhouse and other similar applications RESEARCH METHODOLOGY Figure Schematic of a normal solar water heating system generating hot water during the daytime seems to be very appropriate In this research work, two solar water heating systems, in which the heat generating comes from a conventional solar collector and or from a solar-boosted heat pump, are considered For the latter case, a non-azeotropic refrigerant, R22/R124/R152a, is used due to its better performance compared with a single refrigerant, due to its lower degree of irreversibility in exchanging heat at the condenser and at the evaporator [5] Many research works have reported the increasing of heat pump performance when using non-azeotropic refrigerant Troxel and Braven [6] investigated the COP of a heat pump using R22/R11 and R22/R114 refrigerant mixtures and found that the COP of the heat pump was increased 26% for R22/R11 and 34% for R22/R114 compared to that using R11 or R22 He et al [7] reported that the COP of a heat pump using R22/R142b refrigerant blend was higher than those of R22 and R142b by approximately 3.5% Kiatsiriroat and Na Thalang [8] recommended that a suitable mass fraction of R22 in the refrigerant blend R22/R124/R152a for air-conditioning system was approximately 20–40% This result agreed well with the report of Kiatsiriroat and Euakit [5], which used the same refrigerant for an automobile airconditioning system In this research, the suitable sizes of the solar collector and storage tank are also found out for cases of conventional solar hot water heating system compared with a solar-boosted heat pump water heater that used an unglazed solar collector Moreover, Figure shows a schematic sketch of the normal solar hot water heating system A flat-plate solar collector is used for producing hot water, which is kept in the storage tank during the daytime, and the hot water is used in the slaughterhouse in the nighttime The second solar water heating system is a solar water heater combined with a heat pump Figure shows a schematic sketch of this system Hot water from a solar collector transfers heat to the refrigerant in the evaporator of the heat pump Then the refrigerant is compressed by the compressor and transfers heat at the condenser to the water in the storage tank Since the collector operates at low temperature, an unglazed solar collector modified from corrugated metal roof is used to reduce the investment cost The detail of the solar collector is shown in Figure The thermal performances of this collector type have been investigated from the experiment of Nuntaphan et al [9] The simulation program for calculating the water temperature is also developed for this system and the detail of the program is shown in the next section The heat pump model used in this simulation program is modified from the models of Kiatsiriroat and Euakit [5] This heat pump uses R22/R124/R152a refrigerant blend as the working fluid It should be noted that the LPG is also a backup to keep the water temperature at 80◦ C before using the water in the nighttime in both cases SIMULATION PROGRAM Figure shows the detail of the simulation program in case of the normal solar water heater In this program, the heat transfer Figure Schematic of a solar water heater combined with a heat pump heat transfer engineering vol 31 no 2010 C CHAICHANA ET AL 421 If each collector is connected in series, the characteristics of the total unit in terms of FR (τα) and FR UL can be evaluated from [11] (FR (τα))total = (FR (τα))single unit (FR UL )total = (FR UL )single unit − (1 − K)N NK − (1 − K)N NK (3a) (3b) A (F U ) Figure roof The detail of a solar collector modified from a corrugated metal rate from the solar collector (Qc ) is calculated by ˙ wc Cpw Twc,o − Twc,i Qc = m (1) Qc = FR (τα)It Ac − FR UL Ac (Twc,i − Ta ) (2) R L single unit where K = c m ˙ wc Cpw The model for evaluating the temperature of water in the storage tank is applied from a lump model By assuming that there is no heat loss from the storage tank and the piping, the water temperature can be evaluated from Ms Cpw ˙ wc is the mass flow rate of water, Cpw is the specific where m heat of water, and Twc,i , Twc,o and Ta are the inlet and the outlet temperatures of water and the ambient air temperature, respectively From the experimental result of Sanguantrakarnkul [10], FR (τα) and FR UL are 0.802 and 10.37 W/m2 K, respectively dTs dt = Qc (4) where Ms is the mass of water in the storage tank, Ts is the temperature of water in the storage tank, and t is time Using the numerical method, the water temperature can be calculated from Tst+ t = Tst + Qc t , Ms Cpw (5) where Tst+ t is the temperature of water at time equal to t + t and Tst is the temperature of water at time t Notice that the calculation is carried out from a.m to p.m with the weather data of Chiang Mai, Thailand, given in the appendix Figure shows the simulation flow chart of the solar-boosted heat pump water heating The unglazed flat-plate solar collector is modified from a corrugated metal roof and its FR (τα) and FR UL are experimentally found to be 0.6475 and 12.098 W/m2 K, respectively [9] The heat pump models of Kiatsiriroat and Euakit [5] are applied with the models of the solar collector and the storage tank Notice that the composition of the refrigerant mixture in this work is R22/R124/R152a = 20/57/23% by volume The compressor in this work is a swash-plate automobile compressor driven with a 1300-cc engine The evaporator and the condenser are cross-flow heat exchangers It should be noted that the heat pump models of Kiatsiriroat and Euakit [5] can predict all of the experimental results within ±10% variation The pressure ratio of compressor can be written in term of the mass flow rate of refrigerant and the inlet temperature of compressor as Pcp,o ˙ r Tcp,i + 273.15 = 6.613351 + 6.752657 m Pcp,i ˙ r Tcp,i + 273.15 − 127.7766 m Figure Calculation steps for a normal solar water heater heat transfer engineering − 0.686263Ncp ˙ r Tcp,i + 273.15 Ncp + 0.00554Ncp + 6.371892 m vol 31 no 2010 422 C CHAICHANA ET AL Figure Calculation steps for the solar-boosted heat pump water heating heat transfer engineering vol 31 no 2010 C CHAICHANA ET AL ˙ r Tcp,i + 273.15 − 9.03919 m 423 The total heat transfer coefficient of the evaporator can be calculated from Ncp UAev = ˙ r Tcp,i + 273.15 Ncp − 0.056664 m ˙ r Tcp,i + 273.15 + 0.092339 m 2 Ncp (6) where Pcp,i and Pcp,o are the inlet and the outlet pressures of the ˙ r is the refrigerant mass flow rate, and compressor respectively, m Tcp,i is the inlet refrigerant temperature Note that this model is ˙ r ≤ 0.016 valid in the ranges of 10 ≤ Ncp ≤ 60 rps, 0.008 ≤ m kg/s, and 10 ≤ Tcp,i ≤ 25◦ C Moreover, the pressure ratio of the compressor can be expressed as Pcp,o = Pcp,i Tcp,o + 273.15 Tcp,i + 273.15 n n−1 (7) where Tcp,o is the outlet refrigerant temperature and n is the polytropic index From the report of Kiatsiriroat and Euakit [5] n is equal to 1.13 The power at the compressor (Wcp ) can be calculated from ˙ rR Wcp = m n n−1 Tcp,o − Tcp,i (8) For the case of the refrigerant mixture, the gas constant, R, can be evaluated from 8.314 R= (9) MR22 xR22 + MR124 xR124 + MR152a xR152a where x and M are the mass fraction and molecular weight of each component The heat transfer rate at the evaporator (Qev ) can be calculated from ˙ wc Cpw Twev,i − Twev,o = m ˙ r hev,o − hev,i (10) Qev = m ˙ wc is the water mass flow rate at the solar collector, where m Twev,i and Twev,o are the inlet and the outlet water temperatures at the evaporator, and hev,i and hev,o are the inlet and the outlet refrigerant enthalpies, respectively Moreover, the heat transfer rate at the evaporator can be modeled in terms of the inlet and the outlet refrigerant temperatures, the inlet water temperature, and the total heat transfer coefficient of the evaporator (U Aev ) as Tev,i = − 6.927948 − 8.738572Qev + 0.141635Qev Twev,i + 0.456279Twev,i (11) Twev,i − Tev,o U Aev = 0.66917 + 1.170973 ˙ wc Cpw Twev,o − Tev,i m (12) Note that the ranges of the parameters used in Eqs (11) and (12) are 0.5 ≤ Qev ≤ kW, 20 ≤ Twev,i ≤ 40◦ C, 0.3 ≤ ˙ wc = 0.03–0.05 kg/s U Aev ≤ 0.8 W/K, and m heat transfer engineering Qev LMTDev (13) where LMT Dev is the log mean temperature difference at the evaporator The heat transfer rate of the condenser (Qcd ) can be calculated from ˙ ws Cpw (Twcd,o − Twcd,i ) = m ˙ r (hcd,i − hcd,o ), (14) Qcd = m Qcd = Qev + Wcp (15) ˙ ws is the water mass flow rate at the storage tank, Twcd,i where m and Twcd,o are the inlet and the outlet water temperatures at the condenser, and hcd,i and hcd,o are the inlet and the outlet refrigerant enthalpies, respectively Similarly, the heat transfer rate at the condenser can be modeled in terms of the inlet water temperature and the outlet refrigerant temperature (Tcd,o ) as Tcd,o = 8.210528 + 3.730154Qcd + 0.102957Qcd Twcd,i + 0.751396Twcd,i (16) Note that the ranges of each parameter in Eq (16) are ≤ Qcd ≤ kW, 20 ≤ Twcd,i ≤ 70◦ C, 0.3 ≤ U Aev ≤ 0.8 W/K, ˙ wc = 0.03–0.05 kg/s and m The total heat transfer coefficient at the condenser can be calculated from UAcd = Qcd LMTDcd (17) where LMT Dcd is the log mean temperature difference at the condenser The process at the expansion valve is assumed to be throttling; therefore, hex,i = hex,o (18) where hex,i and hex,o are the inlet and the outlet refrigerant enthalpies The method for calculating the thermodynamic properties of the refrigerant mixtures is shown in the appendix Note that the conditions for running the simulation programs in case of the normal solar water heater and the solar-boosted heat pump water heating system are shown in Table RESULTS AND DISCUSSION Performance of Normal Solar Water Heating Figure shows the effect of number of collector units In this analysis, the number of collector units is between and in series connection, and each unit has m2 area The volume of water in the storage tank is kept constant at 300 L The solar radiation used for the simulation is the mean solar radiation vol 31 no 2010 424 C CHAICHANA ET AL Table The conditions for running the simulation program Parameter Value Normal solar water heating system Area of collector m2 /unit Number of collector 1–5 units Initial temperature of water in storage tank 25◦ C Water volume 300–1200 L Mass flow rate of water 0.04 kg/s Solar-boosted heat pump water heating system Area of collector m2 /unit Number of collector 1–5 units Initial temperature of water in storage tank 25◦ C Water volume 300–1200 L ˙ wc , m ˙ ws ) Mass flow rate of water (m 0.04 kg/s Mass flow rate of refrigerant 0.01 kg/s Speed of compressor 20 rps Refrigerant ratio R22/R124/R152a 20/57/23% by volume level of Chiang Mai, Thailand, as shown in the appendix The results show that the temperature of water increases with the number of collector units However, the rate of temperature increase reduces due to the higher heat loss with more collector area Notice that the highest water temperature is 69.7◦ C when units of collector are used After p.m the water temperature slightly decreases due to the low level of solar radiation and high heat loss at the collectors In Figure 7, the number of collector is kept constant at units (6 m2 ) and the size of the water storage is varied Clearly the results show that the temperature of water depends on the mass of water in the storage tank More water results in lower water temperatures Since the application of this solar hot water system is for a small slaughterhouse, the required water temperature is 80◦ C and the usage of hot water is 30 L/pig If any solar energy Figure Effect of volume of water on the water temperature in a storage tank (average solar radiation) The number of collector is kept constant at units (6 m2 ) system can not raise the water temperature to the required value, an auxiliary heater using LPG as fuel is used for boosting up the water temperature The efficiency of the LPG heater is also assumed to be 25% [1] To evaluate the energy supplied by the solar hot water system compared with the total energy needed to generate hot water at 80◦ C, the solar fraction is defined as Solar fraction = Energy from solar system Total energy for producing 80◦ C water (19) Figure shows the annual solar fraction by using the hourly radiation of each month It can be seen that smaller size of the storage tank and higher number of the collectors result in higher solar fraction Performance of the Solar-Boosted Heat Pump Water Heating Figure Effect of number of collector on the water temperature in a storage tank (average solar radiation) The storage tank is kept constant at 300 L heat transfer engineering The performance of the solar-boosted heat pump water heating is shown in Figure For protecting the heat pump from overheating, the maximum water temperature in the storage tank should not be over 60◦ C The result from Figure shows that the minimum volume should be 300 L of water for controlling the water temperature The effects of volume of water in the storage tank and number of collector units are similar to those for the normal solar water heating system from the previous section However, since the water temperature is controlled by the condenser temperature of the heat pump, which is slightly increased, the effect of number of solar collector on the water temperature is not significant compared with the previous system It is found that the water temperature from collector units is approximately 3% higher than that of unit vol 31 no 2010 C CHAICHANA ET AL Figure Solar fraction for a normal solar water heating system Unlike the effect of number of solar collector units, the volume of water plays an important role on the water temperature The water temperature is approximately decreased by 13% when the volume of water increases from 300 L to 600 L Figure also shows the COP of the heat pump system The COP of the heat pump is between 4.1 and 4.6, depending on the volume of water in the storage tank The higher volume of water gives a higher COP This result comes from the effect of the water temperature The water temperature decreases with increasing its volume, and the condenser temperature also decreases Figure 10 shows the solar fraction with various numbers of unglazed solar collectors and volumes of water Notice that the calculation of the solar fraction is similar to that of the normal solar water heating system but the power at the heat pump compressor is added as an energy input It is found that the solar fraction is tremendously decreased with the increasing of water volume, while the number of solar collectors gives a small effect Figure The water temperature and average COP of the solar-boosted heat pump water heating (average solar radiation) heat transfer engineering 425 Figure 10 Solar fraction for a solar water heating system combined with a heat pump on the solar fraction When compared with the previous result, it is found that when using the heat pump, the solar fraction is lower than for the normal solar water heater Economic Evaluation In this section, an economic evaluation is considered The solar water heating system is used for increasing water temperature during the day time and this hot water is used in the nighttime If the water temperature is less than 80◦ C before utilization, the conventional heater using LPG as fuel is used for controlling the temperature In this part, the efficiency of the LPG stove is kept constant at 25% and the LPG cost is 17 Baht/kg (1 Baht is about 0.0286 USD) The economic evaluation is based on the average monthly solar irradiation of Chiang Mai Thailand as shown in Figure 11 Figure 11 The average solar radiation of Chiang Mai, Thailand vol 31 no 2010 426 C CHAICHANA ET AL Table Cost of hot water production from the solar-boosted heat pump water heating system with LPG auxiliary Cost Item unit units units Investment cost (Baht) Vs = 300 L 42,295 46,695 51,095 45,320 49,720 54,120 Vs = 600 L Vs = 900 L 47,762 52,162 56,562 49,500 53,900 58,300 Vs = 1, 200 L Operating and maintenance cost (Baht/yr) Vs = 300 L 21,820 22,325 22,845 Vs = 600 L 49,228 48,452 48,490 Vs = 900 L 85,758 84,878 84,883 122,716 121,761 121,732 Vs = 1, 200 L Figure 12 Payback period for normal solar water heating Tables and show the cost for producing hot water for various numbers of solar collector units and varied mass of water in a storage tank Notice that the operating cost covers the labor cost, the maintenance cost, the electrical cost (3 Baht/kWh), and the LPG cost The labor and the maintenance costs per year are approximately 12% of the investment cost From these tables, it is found that the investment cost of the normal solar water heating system is lower than for the solar heat pump system in the case of one collector unit However, the investment cost of the normal solar water heating system is higher than that of the solar heat pump system when more collector units are used This result comes from the cost of the normal flat-plate solar collector, which is rather high compared to that of the modified collector In terms of operating and maintenance costs, it is found that the solar-boosted heat pump system gives lower cost than the normal solar water heating system for 1–2 units of collectors But when the collector area is higher, the solar heat pump system gives a lower advantage To protect the heat pump, the system units units 55,495 58,520 60,962 62,700 59,895 62,920 65,362 67,100 23,369 48,767 85,118 121,979 23,894 49,141 85,485 122,339 shuts off when the water temperature reaches 60◦ C The LPG consumption to raise the water temperature is nearly the same for any number of solar collectors This is unlike the case of the normal solar water heater, where by increasing the number of collectors, the water temperature is increased and the LPG consumption is decreased The payback periods of both systems are shown in Figures 12 and 13 The payback period is defined as Pb = CI CS − CO&M (20) where Pb is payback period, CI is investment cost, CS is total energy cost saving, and CO&M is operating and maintenance cost The total cost saving, CS , is calculated from CS = CLP G − CLP G,solar − CElec , (21) where CLP G is cost when using only LPG for producing hot water (80◦ C), CLP G,solar is LPG consumption cost to raise the hot water temperature that was produced by the solar water Table Cost of hot water production from the normal solar water heating system with LPG auxiliary Cost Item unit units units Investment cost (Baht) Vs = 300 L 31,680 52,866 74,052 Vs = 600 L 34,606 55,792 76,978 Vs = 900 L 37,048 58,234 79,420 Vs = 1, 200 L 38,786 59,972 81,158 Operating and maintenance cost (Baht/yr) Vs = 300 L 28,514 23,722 21,476 Vs = 600 L 64,372 56,594 51,321 Vs = 900 L 101,216 92,015 85,089 Vs = 1, 200 L 138,286 128,259 120,290 units units 95,238 98,164 100,606 102,344 116,424 119,350 121,792 123,530 20,700 47,741 79,830 113,920 20,831 45,380 75,830 108,824 heat transfer engineering Figure 13 Payback period for solar-boosted heat pump water heating vol 31 no 2010 C CHAICHANA ET AL 427 Table Average maximum–minimum temperatures in past 10-yr period (1986–1997) (◦ C) Tmax Tmin (◦ C) January February March April May June July August September October November December 29.7 13.7 32.1 14.9 35.1 19.0 36.2 21.9 34.4 23.6 32.2 23.9 31.8 23.7 31.2 23.4 31.5 23.0 30.9 21.7 29.5 18.5 28.2 14.8 heating system or solar heat pump system to 80◦ C, and CElec is electrical cost From Figure 12, it is found that the suitable number of collector units for 300 L water is unit, while for 600–900 L water, the system with collector units is more suitable In the case of 1200 L water, the system with collector units gives the shortest payback period The shortest payback periods for 300, 600, 900, and 1200 kg water are 3.63, 3.12, 2.95, and 2.82 yr, respectively, with 1, 2, 2, and collector units For the solar-boosted heat pump as shown in Figure 13, it is found that the payback periods are shorter than the previous case Notice that, in this case, the proper number of collectors is unit The payback periods for 300, 600, 900, and 1200 kg water are 2.74, 1.79, 1.83, and 1.88 yr, respectively Therefore, it can be concluded that the solar-boosted heat pump using one unit of a corrugated metal sheet roof as solar collector is the best choice for small slaughterhouse However, the suitable mass of water depends on the hot water consumption of the small slaughterhouse Actually, pig uses 30 L of hot water for cleaning; therefore, this result is valid for 10–40 killed pigs each day CONCLUSIONS From this research work, the following conclusions can be drawn: • The number of solar collectors and the mass of water in storage tank play an important role in the water temperature for normal solar water heating system For a solar-boosted heat pump system, only the water volume, not the number of solar collectors, has a strong effect on the temperature • In case of the normal solar water heating system, the shortest payback periods for 300, 600, 900, and 1200 kg water are 3.63, 3.12, 2.95, and 2.82 yr, respectively with 1, 2, 2, and collector units • In case of the solar-boosted heat pump system, the shortest payback periods for 300, 600, 900, and 1200 kg water are 2.74, 1.79, 1.83, and 1.88 yr, respectively In this case, one collector unit is the appropriate size for the small-scale slaughterhouse NOMENCLATURE A CElec CI area (m2 ) electrical cost (Baht) investment cost (Baht) heat transfer engineering CLP G CLP G,solar CO&M Cp Cs FR h It LMTD ˙ m M Ms n N Ncp P Pb Q R T t U V W x cost when using only LPG for producing hot water (80◦ C) (Baht) LPG consumption cost from solar water heating system (Baht) operation and maintenance costs (Baht/yr) specific heat (kJ/kg-K) cost saving (Baht/yr) heat removal factor enthalpy (kJ/kg) solar radiation (W/m2 ) log mean temperature difference mass flow rate (kg/s) molecular weight mass of water in storage tank (kg) polytropic index number of collector units speed of compressor (rps) pressure (kPa) payback period (yr) heat transfer rate (kW) gas constant (kJ/kg-K) temperature (◦ C) time (s) overall heat transfer coefficient (kW/m2 -K) volume (L) power (kW) mass fraction Greek Symbols η efficiency τα optical efficiency of collector Subscripts a amb c cd cp ev ex i L o r s w air ambient collector condenser compressor evaporator expansion valve inlet loss outlet refrigerant storage tank water vol 31 no 2010 428 C CHAICHANA ET AL for 20 ≤ PR152a ≤ 100 kPa and −20 ≤ T ≤ 20◦ C; and from REFERENCES [1] Dussadee, N., Khuntha, U., and Nuntaphan, A., Efficiency Analysis of Cooking Stoves for Household Industry, 16th Conference of Mechanical Engineering Network of Thailand, Phuket, Thailand, 2002 [2] Ito, S., Miura, N., and Wang, K., Performance of a Heat Pump Using Direct Expansion Solar Collectors, Solar Energy, vol 65, no 3, pp 189–196, 1999 [3] Huang, B J., Lee, J P., and Chyng, J P., Heat-Pipe Enhanced Solar-Assisted Heat Pump Water Heater, Solar Energy, vol 78, no 3, pp 375–381, 2005 [4] Hawlader, M N A., Chou, S K., and Ullah, M Z., The Performance of a Solar Assisted Heat Pump Water Heating System, Applied Thermal Engineering, vol 21, no 10, pp 1049–1065, 2001 [5] Kiatsiriroat, T., and Euakit, T., Performance Analysis of an Automobile Air-Conditioning System With R22/R124/R152a Refrigerant, Applied Thermal Engineering, vol 17, no 11, pp 1085– 1097, 1997 [6] Troxel, S O., and Braven, K R D., Method for Predicting the Performance of Non-Azeotropic Mixtures in Heat Pumps, ASHRAE Transactions, vol 95, no 1, pp 305–310, 1989 [7] He, X., Spindler, U C., and Jung, D S., Investigation of R22/R142b Mixture as a Substitute for R12 in Single Evaporator Domestic Refrigerators, ASHRAE Transactions, vol 98, no 1, pp 150–159, 1992 [8] Kiatsiriroat, T., and Na Thalang, K., Performance Analysis of Vapor Compression Refrigeration With R22/R124/R152a Refrigerant, International Journal of Energy Research, vol 21, pp 221– 232, 1997 [9] Nuntaphan, A., Chansena, C., and Kiatsiriroat, T., Performance Analysis of Solar Water Heating Using Solar Collector Modified From Corrugated Metal Roof, KKU Engineering Journal, vol 35, pp 71–80, 2008 [10] Sanguantrakarnkul, P., Sizing of a Solar Water Heating System for Abattoir, M.Eng thesis, Chiang Mai University, Thailand, 2006 [11] Oonk, R., and Jones, D E., Cole-Appel, B E., Calculation of Performance of N Collectors in Series From Test Data on a Single Collector, Solar Energy, vol 23, pp 535–536, 1979 APPENDIX Thermodynamic Properties of Refrigerant Mixtures The enthalpy of a refrigerant mixture at any state can be calculated from h = xR22 hR22 + xR124 hR124 + xR152a hR152a (22) Enthalpy before entering the compressor can be evaluated from hR22 = 410.7325103 + 0.0002058 ln (PR22 ) + 0.65T + 0.006875T + 0.7143275T + 0.0026908T (25) for 40 ≤ PR124 ≤ 200 kPa and −20 ≤ T ≤ 20◦ C Enthalpy leaving the compressor can be evaluated from hR22 = 409.8550847 + 0.0099661 ln(PR22 ) + 0.691643T + 0.0004018T (26) for 250 ≤ PR22 ≤ 1000 kPa and 40 ≤ T ≤ 120◦ C; from hR152a = 513.5822785 − 0.0037975 ln(PR152a ) + 0.955T + 0.00125T (27) ◦ for 200 ≤ PR152a ≤ 700 kPa and 40 ≤ T ≤ 120 C; and from hR124 = 300.3286264 + 0.0040197 ln(PR124 ) + 2.4416831T − 0.0104313T (28) for 400 ≤ PR124 ≤ 1200 kPa and 40 ≤ T ≤ 120◦ C Enthalpy of liquid-phase refrigerant leaving the condenser can be evaluated from hR22 = 193.2109395 + 1.579484T − 0.0072663T + 0.0000721T (29) for 34 ≤ T ≤ 75◦ C; from hR152a = 197.6898629 + 1.6039641T + 0.0010383T + 0.0000294T (30) ◦ for 34 ≤ T ≤ 75 C; and from hR124 = 199.1728295+1.09582T −0.0001501T +0.0000144T (31) for 34 ≤ T ≤ 75◦ C The total pressure of refrigerant can be estimated from Dalton’s law as MR22 XR22 +MR124 XR124 +MR152a XR152a Ptotal = (32) MR152a XR152a MR22 XR22 MR124 XR124 + + PR22 PR124 PR152a where PR22 = 694.16503090 + 4.9839493T + 0.3989612T (33) for −150 ≤ T ≤ 96◦ C; (23) for 30 ≤ PR22 ≤ 150 kPa and −20 ≤ T ≤ 20◦ C; from PR124 = 272.84860220 − 0.1948168T + 0.2045294T (34) for −118 ≤ T ≤ 113◦ C; and hR152a = 511.4104308 − 0.0201814 ln (PR152a ) + 0.975T + 0.00125T hR124 = 362.5673183 − 0.0323082 ln (PR124 ) PR152a = 420.7057830 + 0.3993661T + 0.2961888T (35) (24) heat transfer engineering for −60 ≤ T ≤ 112◦ C vol 31 no 2010 C CHAICHANA ET AL The Average Ambient Temperature Tanongkiat Kiatsiriroat is a professor in the Department of Mechanical Engineering, Chiang Mai University (CMU), Thailand He received his D.Eng in energy technology from the Asian Institute of Technology in 1987 He worked at King Mongkut’s Institute of Technology Thonburi, Bangkok, for 16 years before joining CMU in 1995 His research activities are in thermal system design, heat transfer enhancement, and eco-energy systems The ambient temperature of Chiang Mai could be calculated from the maximum and minimum temperatures in Table as Tamb = 2π (t − 9) (Tmax + Tmin ) + (Tmax − Tmin ) sin 24 Note that t is time in hours (for example at a.m., t = h) Atipoang Nuntaphan received the B.Eng and M.Eng in mechanical engineering from Chiang Mai University, Thailand, in 1993 and 1997 respectively, and a Ph.D in thermal technology from the School of Energy and Materials, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand, in 2000 Now he is an engineer with the Electricity Generating Authority of Thailand His research field covers thermodynamic systems and heat transfer enhancement Chatchawan Chaichana is an assistant professor in the Department of Mechanical Engineering, Chiang Mai University, Thailand He received his Ph.D in 2002 from the University of Melbourne, Australia His main research area is in renewable energy technologies, especially solar energy Currently, he is also a deputy director of Energy Research and Development Institute, Chiang Mai University heat transfer engineering 429 vol 31 no 2010 new products GEMS SENSORS & CONTROLS INTRODUCES HIGHLY ACCURATE FDA COMPLIANT FLOW SENSOR Gems R Sensors & ControlsTM (Gems) announces’ 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