An efficient and robust algorithm for incompressible flow and its application in heat transfer enhancement

AN EFFICIENT AND ROBUST ALGORITHM FOR INCOMPRESSIBLE FLOW AND ITS APPLICATION IN HEAT TRANSFER ENHANCEMENT CHENG YONGPAN NATIONAL UNIVERSITY OF SINGAPORE 2008 AN EFFICIENT AND ROBUST ALGORITHM FOR INCOMPRESSIBLE FLOW AND ITS APPLICATION IN HEAT TRANSFER ENHANCEMENT CHENG YONGPAN (B Eng., M Eng., Xian Jiaotong University, China) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2008 Acknowledgement I would like to express my deepest gratitude to my supervisors, Assoc Prof Lee Thong See and Assoc Prof Low Hong Tong for their continuous and invaluable support, supervision and encouragement Without their help, I cannot live through my Ph.D study and finish my thesis When I am going to finish my Ph.D thesis, I cannot help remembering my former supervisor in Xian Jiaotong University in China, the Academician of Chinese Academy of Science, Prof Tao Wen-quan, who led me to the field of Numerical Heat Transfer in 2001 His “hardworking, aggressive, practical and cooperative” attitude toward the research will benefit me for my whole life I would like to thank the kind colleagues in the Fluid Mechanics Laboratory, Shan Yongyuan, Sui Yi, Wu Jie, Chen Xiaobing, Wang Liping etc The discussion with them inspired me with many new ideas I would like to express my deepest love to my dear wife, Wang Wei, who gave me great love in my thesis preparation and defense; meanwhile, I would also like to express sincere thanks to my dear parents and sisters for their long-time love, support and understanding, which help me overcome the difficulty in the oversea life Finally, I would like to thank National University of Singapore for offering the research scholarship and valuable opportunity to pursue a Ph.D degree I Table of Contents Acknowledgement……………………………………………………………… I Table of Contents……………………………………………………………… II List of Figures……………………………………………………………….….VII List of Tables………………………………………………………………… XV Nomenclature……………………………………………………………… …XVI Abbreviations………………………………………………………………… XXI Summary………………………………………………………………… .XXIII Chapter Introduction and Literature Review……………………………… 1.1 Background………………………………………………………………… 1.2 Development in heat transfer enhancement in fin-and-tube heat exchangers 1.2.1 Recent development in experimental study…………………………… 1.2.1.1 Plain fin-and-tube heat exchanger…………………………………5 1.2.1.2 Wavy fin-and-tube heat exchanger………………………… ……8 1.2.2 Recent development in numerical study……………………………… 11 1.2.2.1 Plain fin-and-tube heat exchanger……………………………… 12 1.2.2.2 Wavy fin-and-tube heat exchanger……………………………….15 1.3 Development in numerical algorithms for incompressible flow…………… 16 1.3.1 Numerical algorithms on staggered grid……………………………….20 1.3.2 Numerical algorithms on collocated grid………………………………24 II 1.4 Objectives and significance of the study…………………………………… 29 1.5 Outline of the thesis………………………………………………………… 31 Chapter Grid Generation and Discretization of Governing Equations… 34 2.1 Requirement for grid…………………………………………………………34 2.2 Grid generation in two dimensions………………………………………… 37 2.3 Grid generation in three dimensions…………………………………………39 2.4 Discretization of governing equations……………………………………… 43 2.5 Implementation of high-order schemes………………………………………47 2.5.1 Normalized Variable and Space Formulation methodology…………… 47 2.5.2 Application of high-order schemes in equation discretization……… …49 Chapter CLEARER Algorithm on Staggered Grid……………………… 57 3.1 General review of SIMPLER algorithm on staggered grid……………………57 3.2 Mathematical formulation of CLEARER algorithm………………………… 61 3.3 Numerical validation and comparison with SIMPLER algorithm………… 65 3.3.1 Lid-driven flow in a square cavity…………………………………… 66 3.3.2 Lid-driven flow in a polar cavity…………………………………… ….68 3.4 Concluding remarks…………………………………………………… …….69 Chapter CLEARER Algorithm on Collocated Grid ……………………….81 4.1 General review of SIMPLER algorithm on collocated grid………………….81 III 4.2 Mathematical formulation of CLEARER algorithm…………………………87 4.2.1 Discussion on SIMPLER algorithm……………………………………87 4.2.2 Improved SIMPLER algorithm……………………………………… 88 4.2.3 Discussion on the second relaxation factor…………………………….90 4.2.4 Treatment of solid region in computational domain………………… 91 4.2.4.1 Treatment of temperature field………………………………… 92 4.2.4.2 Treatment of flow field………………………………………… 93 4.3 Numerical validation and comparison with SIMPLER algorithm………… 94 4.3.1 Lid-driven flow in a square cavity…………………………………… 96 4.3.2 Natural convection in a square cavity………………………………….97 4.3.3 Lid-driven flow in a polar cavity……………………………………….97 4.3.4 Natural convection in an annular enclosure……………………………98 4.4 Concluding remarks………………………………………………………….99 Chapter CLEARER Algorithm on Curvilinear Non-orthogonal Coordinates ………………………………………………………… 111 5.1 General review of SIMPLE algorithm on curvilinear non-orthogonal coordinates…………………………………………………………………….111 5.2 Mathematical formulation of CLEARER algorithm……………………… 116 5.2.1 The predictor step of CLEARER algorithm………………………… 116 5.2.2 The corrector step of CLEARER algorithm………………………… 122 5.2.3 Solution procedure of CLEARER algorithm…………………………123 IV 5.2.4 Discussion on the second relaxation factor ………………………….124 5.3 Numerical validation and comparison with SIMPLERM algorithm……… 126 5.3.1 Lid-driven flow in an inclined cavity…………………………………128 5.3.1.1 Lid-driven flow at Re=100…………………………………… 129 5.3.1.2 Lid-driven flow at Re=1000…………………………………….130 5.3.1.3 Lid-driven flow at Re=5000………………………………… …131 5.3.2 Natural convection in an inclined cavity…………………………… 132 5.3.3 Natural convection in an enclosure with eccentric cylinder and square duct………………………………………………………………………….133 5.4 Investigation of minimum intersection angle among grid lines to guarantee convergence…………………………………………………………………… 135 5.5 Concluding remarks……………………………………………………… 137 Chapter Extension of CLEARER Algorithm to 3D Curvilinear Non-orthogonal Coordinates……………………………………………… 158 6.1 Discretization of governing equations………………………………………158 6.2 Implementation of CLEARER algorithm………………………………… 162 6.2.1 The predictor step of CLEARER algorithm………………………… 162 6.2.2 The corrector step of CLEARER algorithm………………………… 167 6.3 Validation of CLEARER algorithm…………………………………………172 6.4 Concluding remarks……………………………………………………… 173 V Chapter Application of CLEARER Algorithm to Triangular Wavy Fin-and-Tube Heat Exchanger……………………………………………… 176 7.1 Physical model…………………………………………………………… 176 7.2 Mathematic description…………………………………………………… 177 7.2.1 Computational domain……………………………………………… 177 7.2.2 Boundary condition………………………………………………… 177 7.3 Brief introduction of field synergy principle……………………………… 178 7.4 Results and discussion………………………………………………………180 7.4.1 Mesh independence study…………………………………………….180 7.4.2 Influence of wavy angle………………………………………………181 7.4.3 Influence of fin pitch………………………………………………….182 7.4.4 Influence of tube diameter…………………………………………….184 7.4.5 Influence of wavy density…………………………………………….185 7.5 Concluding remarks……………………………………………………… 186 Chapter Conclusions and Recommendations………………………… … 196 8.1 Conclusions……………………………………………………………… …196 8.2 Recommendations for future work………………………………………… 198 References………………………………………………………….………… 199 List of Publications……………………………………………… …………….223 VI List of Figures Figure 1.1Heat transfer surface area density spectrum of heat exchanger surface33 Figure 1.2 Various enhanced heat transfer fins………………………………… 33 Figure 2.1 The relation between the physical domain and computational domain54 Figure 2.2 Grid generated in 2D complex enclosure…………………………… 54 Figure 2.3 Grid generated in 3D wavy fin-and-tube heat exchanger………… 54 Figure 2.4 Computational grid and the definition of parameters……………… 55 Figure 2.5 Original and normalized variable and profiles……………………… 56 Figure 2.6 Control volumes for two-dimensional problem………………………56 Figure 2.7 Treatment of boundary condition…………………………………… 56 Figure 3.1 Control volumes of staggered grid in 2D Cartesian coordinates…… 71 Figure 3.2 Lid-driven flow in a square cavity……………………………………71 Figure 3.3 Convergence histories of SIMPLER, CLEARER, CLEAR1 and CLEAR2………………………………………………………… 72 Figure 3.4 Accuracy test with fully developed flow in straight channel…… ……72 Figure 3.5 Comparison between predicted velocity distributions and benchmark solutions at Re=100…………………………………………………73 Figure 3.6 Comparison between predicted velocity distributions and benchmark solutions at Re=1000……………………………………………….73 Figure 3.7 Comparison between predicted velocity distributions and benchmark solutions at Re=5000…………………………………………………74 VII Figure 3.8 Comparison of iteration numbers among SIMPLER, CLEARER, CLEAR1 and CLEAR2 at Re=100…………………………………74 Figure 3.9 Comparison of iteration numbers among SIMPLER, CLEARER, CLEAR1 and CLEAR2 at Re=1000……………………………… 75 Figure 3.10 Comparison of iteration numbers among SIMPLER, CLEARER at Re=5000…………………………………………………………… 75 Figure 3.11 Comparison of iteration number ratio of CLEARER, CLEAR1, and CLEAR2 over SIMPLER at Re=100……………………………….76 Figure 3.12 Comparison of iteration number ratio of CLEARER, CLEAR1 and CLEAR2 over SIMPLER at Re=1000…………………………… 76 Figure 3.13 Comparison of iteration number ratio of CLEARER over SIMPLER at Re=5000……………………………………………….………….77 Figure 3.14 Lid-driven flow in polar cavity…………………………………… 77 Figure 3.15 Comparison of streamlines at Re=350………………………………78 Figure 3.16 Comparison of streamlines at Re=1000…………………………….78 Figure 3.17 Comparison of iteration numbers among SIMPLER, CLEARER, CLEAR1 and CLEAR2 at Re=350……………………………… 78 Figure 3.18 Comparison of iteration numbers among SIMPLER, CLEARER, CLEAR1 and CLEAR2 at Re=1000………………………………79 Figure 3.19 Comparison of iteration number ratio of CLEARER, CLEAR1 and CLEAR2 over SIMPLER at Re=350…………………………… 79 Figure 3.20 Comparison of iteration number ratio of CLEARER, CLEAR1 and VIII References Numerical Heat Transfer, Part B, vol.17, pp.63-82, 1990 Pirompugd W., Wongwises S and Wang C.C., Simultaneous heat and mass transfer characteristics for wavy fin-and-tube heat exchangers under dehumidifying conditions, Int J Heat Mass Transfer, vol.49, pp.132-143, 2006 Prakash C., A finite element method for predicting flow through ducts with arbitrary cross sections, Ph.D thesis, University of Minnesota, 1981 Prakash C., Patankar S.V., Combined free and forced convection in vertical tube with radial internal fin ASME J Heat Transfer, vol.7, pp.566-572, 1981 Qu Z.G., Tao W.Q and He Y.L., Three-dimensional numerical simulation on laminar heat transfer and fluid flow characteristics of strip fin surface with X-arrangement of strips, ASME J Heat Transfer, vol.126, pp.697-707 Qu Z G., Tao W Q and He Y L., Implementation of CLEAR algorithm on collocated grid system and application examples, Numerical Heat Transfer, Part B, vol.46, pp.65-96, 2005 Qu Z G., Tao W Q., and He Y L., An improved numerical scheme for SIMPLER method on non-orthogonal curvilinear coordinates, SIMPLERM, Numerical Heat Transfer, vol.51, pp.43-66, 2007a Qu Z.G., He Y L., Zhao C Y and Tao W Q., Implementation of CLEAR algorithm on non-orthogonal curvilinear co-ordinates for solution of incompressible flow and heat transfer, Int J Numerical Methods in Fluids, vol.53, pp 1077-1105, 2007b 211 References Rahman M.M., Miettinen A and Siikonen T., Modified SIMPLE formulation on a collocated grid with an assessment of the simplified QUICK scheme, Numerical Heat Transfer, vol 30, pp 291-314, 1996 Raithby G.D and Schneider G.E., Elliptic system: Finite difference methodⅡ, in Minkowycz W J., Sparrow E M., Pletcher R.H and Schneider G.E.(eds.) Handbook of Numerical Heat Transfer, pp 241-289, Wiley, New York, 1988 Reggio M and Camarero R., Numerical solution procedure for viscous incompressible flows, Numerical Heat Transfer, vol.10, pp.131-146,1986 Rhie C.M., A numerical study of the flow past an isolated airfoil with separation, Ph.D thesis, University of Illinois at Urbana-Champaign, 1981 Rhie C.M and Chow W.L., A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation, AIAA J., vol.21, pp.1525-1532,1983 Rich D.G., The effect of fin spacing on the heat transfer and friction performance of multirow, smooth plate fin-and-tube heat exchangers, ASHRAE Trans., vol.79, pp 135-145, 1973 Rich D.G., The effect of the number of tubes rows on heat transfer performance of smooth plate fin-and-tube heat exchangers, ASHRAE Trans., vol 81, pp 307-317, 1975 Rodi W., Majumdar S and Schonung B., Finite volume methods for two-dimensional incompressible flows with complex boundaries, Comput Meth Appl Mech Eng., vol.75, pp.369-392,1989 212 References Rogers S.E., Kwak D and Kiris C., Steady and unsteady solutions of the incompressible Navier-Strokes equations, AIAA Journal, pp.603-610, 1991 Romero-Mendez R., Sen M., Yang K.T and McClain R., Effect of fin spacing on convection in a plate fin and tube heat exchanger, Int J Heat Mass Transfer, vol 43, pp.39-51, 2000 Saboya F.E.M and Sparrow E.M., Local and average transfer coefficients for one-row plate fin and tube heat exchanger configurations, ASME J Heat Transfer, vol 96, pp 265-272, 1974 Saboya F.E.M and Sparrow E.M., Transfer characteristics of two-row plate fin and tube heat exchanger configurations Int J Heat Mass Transfer, vol.19, pp 41-49, 1976a Saboya F.E.M and Sparrow E.M., Experiments on a three-row fin and tube heat exchanger, ASME J Heat Transfer, vol.98, pp 520-522, 1976b Sahin B, Akkoca A, Ozturk N.A and Akilli H., Investigation of flow characteristics in a plate fin and tube heat exchanger model composed of single cylinder Int J Heat Fluid Flow, vol.27, pp 522-530, 2006 Sahin H.M., Dal A.R and Baysal E., 3-D numerical study on the correlation between variable inclined fin angles and thermal behavior in plate fin-tube heat exchanger, Applied Thermal Engineering, vol.27, pp.1806-1816, 2007 Seker D., Karatas H and Egrican N., Frost formation on fin-and-tube heat exchangers Part Ⅰ -Modeling of frost formation on fin-and-tube heat exchangers, Int J Refrigeration, vol.27, pp.367-374, 2004 213 References Seshimo Y and Fujii M., An experimental study of the performance of plate fin and tube heat exchangers at low Reynolds number, proceeding of the 3rd ASME/JSME Thermal Engineering Joint Conference, vol 4, pp 449-454, 1991 Shah R K., Classification of heat exchangers, in Heat Exchangers: Thermal-Hydraulic Fundamentals and Design, Kakac S, Bergles A E and Mayinger F eds., Hemisphere Publishing, Washington, DC, pp.9-46, 1981 Shah R.K., Heikal M.R., Thonon B and Tochon P., Progress in the numerical analysis of compact heat exchanger surfaces, Advances in Heat Transfer, vol.34, pp.363-442, 2000 Sheng Y., Shoukri M., Sheng G and Wood P., A modification to the SIMPLE method for buoyancy-driven flows, Numerical Heat Transfer, Part B, vol 33, pp.65-78, 1998 Shieh C.F., Three-dimensional grid generation using Poisson equations, Proceedings of the symposium on numerical generation of curvilinear coordinate systems and their use in the numerical solution of partial differential equations, Nashville, TN, U.S.A., pp.687-694, 1982 Shyy W and Vu T.C., On the adoption of velocity variable grid system for fluid flow computation in curvilinear coordinates, J Computational Physics, vol.92, pp 82-105, 1991 Shyy W., Element of pressure-based computational algorithms for complex fluid flow and heat transfer, In: Advances in heat transfer, pp 191-275, San Diego: 214 References Academic Press, 1994 Shyy W and Mittal R., Solution methods for the incompressible Navier-Stokes equations, in Johnson R.W (ed.), Handbook of Fluid Dynamics, pp.31.1-31.33, CRC Press, Boca Raton, 1998 Spalding D B., A general purpose computer program for multi-dimensional one-and-two phase flow Math Comput Simulation, vol.23, pp.267-276, 1981 Tao W Q., Recent advances in computational heat transfer, Science Press, Beijing, 2000 Tao W.Q., Numerical Heat Transfer, 2nd ed., Xi’an Jiaotong University Press, Xi’an, China, 2001 Tao W.Q., Guo Z Y and Wang B.X., Field synergy principle for enhancing convective heat transfer-Its extension and numerical verifications, Int J Heat Mass Transfer, vol.45, pp 3849-3856, 2002a Tao W.Q., He Y.L., Wang Q.W., Qu Z.G and Song F.Q., A unified analysis on enhancing convective heat transfer with field synergy principle, Int J Heat Mass Transfer, vol.45, pp.4871-4879, 2002b Tao W.Q., Qu Z G and He Y L., A novel segregated algorithm for incompressible fluid flow and heat transfer problems -CLEAR (Coupled and Linked Equations Algorithm Revised) Part Ⅰ : Mathematical formulation and solution procedure, Numerical Heat Transfer, Part B, vol.45, pp 1-17, 2004a Tao W.Q., Qu Z G and He Y L., A novel segregated algorithm for incompressible 215 References fluid flow and heat transfer problems -CLEAR (Coupled and Linked Equations Algorithm Revised) PartⅡ: Application examples, Numerical Heat Transfer, Part B, vol.45, pp 19-48, 2004b Tao Y.B., He Y L., Huang J., Wu Z.G and Tao W.Q., Numerical study of local heat transfer coefficient and fin efficiency of wavy fin-and-tube heat exchangers Int J Thermal Science, vol.46, pp.768-778, 2007a Tao Y.B., He Y L., Huang J., Wu Z G., and Tao W.Q., Three-dimensional numerical study of wavy fin-and-tube heat exchangers and field synergy principle analysis, Int J Heat Mass Transfer, vol 50, pp.1163-1175, 2007b Tao Y.B., He Y.L., Wu Z.G and Tao W Q., Three-dimensional numerical study and field synergy principle analysis of wavy fin heat exchangers with elliptic tubes, Int J Heat and Fluid Flow, in press, 2007c Thiart G.D., Finite difference scheme for the numerical solution of fluid flow and heat transfer problems on nonstaggered grids, Numerical Heat Transfer, Part B, vol.17, pp.43-62, 1990a Thiart G.D., Improved finite-difference scheme for the solution of convection-diffusion problems with the SIMPLEN algorithm, Numerical Heat Transfer, Part B, vol 18, pp.81-95, 1990b Thomas P.D and Middlecoeff J.F., Direct control of the grid point distribution in meshes generated by elliptic equations, AIAA J., vol.18, pp.652-656, 1980 Thomas P.D., Numerical generation of composite three dimensional grids by quasilinear elliptic systems, Proceedings of the symposium on numerical 216 References generation of curvilinear coordinate systems and their use in the numerical solution of partial differential equations, Nashville, TN, U.S.A., pp.667-686, 1982 Thompson J.F., General curvilinear coordinate systems, Proceedings of the symposium on numerical generation of curvilinear coordinate systems and their use in the numerical solution of partial differential equations, Nashville, TN, U.S.A., pp.1-30, 1982 Tsai S.F and Sheu T.W.H., Some physical insights into a two-row finned tube heat transfer, Computers & Fluids, vol.27(1), pp.29-46, 1998 Tso C.P., Cheng Y.C and Lai A.C.K., An improved model for predicting performance of finned tube heat exchanger under frosting condition, with frost thickness variation along fin, Applied Thermal Engineering, vol.26, pp.111-120, 2006 Tutar M and Akkoca A., Numerical analysis of fluid flow and heat transfer characteristics in three-dimensional plate fin-and-tube heat exchangers, Numerical Heat Transfer, Part A, vol.46, pp.301-321, 2004 van Doormaal J P and Raithby G.D., Enhancement of SIMPLE method for predicting incompressible fluid flows, Numerical Heat Transfer, vol 7, pp 147-163, 1984 van Doormaal J P and Raithby G.D., An evaluation of the segregated approach for predicting incompressible fluid flow, ASME Paper 85-HT-9, 1985 van Leer B., Towards the ultimate conservation difference scheme A second order 217 References sequel to Godunov's method J Computational Physics, vol 23, pp 101-136, 1977 Wang C.C Hsieh Y.C Chang Y.J and Lin Y.T., Sensible heat and friction characteristics of plate fin-and-tube heat exchangers having plane fins Int J Refrigeration, vol 19, pp 223-230, 1996 Wang C.C., Hsieh Y.C and Lin Y T., Performance of plate finned tube heat exchangers under dehumidifying conditions ASME J Heat transfer, vol.119, pp 109-117, 1997a Wang C.C., Fu W L and Chang C.T., Heat transfer and friction characteristics of typical wavy fin-and-tube heat exchangers, Experimental Thermal and Fluid Science, vol 14, pp 174-186, 1997b Wang C.C., Tsai Y M and Lu D.C., Comprehensive study of convex-louver and wavy fin-and-tube heat exchangers, Journal of Thermophysics and Heat Transfer, vol.12(3), pp.423-430, 1998a Wang Q.W., Wei J.G and Tao W Q., An improved numerical algorithm for solution of convective heat transfer problems on nonstaggered grid system, Heat and Mass Transfer, vol.33, pp.273-280, 1998b Wang S., Li Z.X and Guo Z.Y., Novel concept and devices of heat transfer augmentation Proceedings of 11th International Conference of Heat Transfer Taylor & Francis, vol.5, pp.405-408, 1998c Wang C.C., Lin Y.T and Lee C.J., Investigation of wavy fin-and-tube heat exchangers: A contribution to databank, Experimental Heat Transfer, vol.12, 218 References pp.73-89, 1999a Wang C.C., Chang J.Y and Chiou N.F., Effects of waffle height on the air-side performance of wavy fin-and-tube heat exchangers, Heat Transfer Engineering, vol.20(3), pp.45-56, 1999b Wang C.C., Jang J.Y and Chiou N.F., A heat transfer and friction correlation for wavy fin-and-tube heat exchangers, Int J Heat Mass Transfer, vol.42, pp.1919-1924, 1999c Wang C.C and Chi K.Y., Heat transfer and friction characteristics of plain fin-and-tube heat exchangers, partⅠ: New experimental data, Int J Heat Mass Transfer, vol 43, pp 2681-2691, 2000a Wang C.C Chi K Y and Chang C.J., Heat transfer and friction characteristics of plain fin-and-tube heat exchangers, partⅡ: Correlation Int J Heat Mass Transfer, vol 43, pp 2693-2700, 2000b Wang C.C., Lin Y.T and Lee C.J., An airside correlation for plain fin-and-tube heat exchangers in wet conditions Int J Heat Mass Transfer, vol 43, pp 1869-1872, 2000c Wang C.C., Lo J., Lin Y T and Wei C.S., Flow visualization of annular and delta winglet vortex generators in fin-and-tube heat exchanger application Int J Heat Mass Transfer, vol.45, pp.3803-3815, 2002a Wang C.C., Lee W.S., Sheu W J and Chang Y.J., A comparison of the airside performance of the fin-and-tube heat exchangers in wet conditions;with and without hydrophilic coating Applied Thermal Engineering, vol 22, pp 219 References 267-278, 2002b Wang C.C Hwang Y.M and Lin Y.T., Empirical correlations for heat transfer and flow friction characteristics of herringbone wavy fin-and-tube heat exchangers, Int J Refrigeration, vol.25, pp.673-680, 2002c Webb R.L., Air-side heat transfer correlations for flat and wavy plate fin-and-tube geometries, ASHARE Trans., vol.96, pp 445-449, 1990 Wierbowski M and Stasiek J., Liquid crystal technique for heat transfer investigation in a fin-tube heat exchanger element, Experimental Thermal and Fluid Sicience, vol 26, pp 319-323, 2002 Wongwises S and Chokeman Y., Effect of fin pitch and number of tube rows on the air side performance of herringbone wavy fin and tube heat exchangers, Energy Conversion and Management, vol.46, pp.2216-2231, 2005 Xia Y P and Jacobi A M., Air-side data interpretation and performance analysis for heat transfers with simultaneous heat and mass transfer: Wet and frosted surfaces, Int J Heat Mass Transfer, vol.48, pp.5089-5102, 2005 Xiao Q and Tao W.Q., Effect of fin spacing on heat transfer and pressure drop of two-row corrugated-fin and tube heat exchangers, Int Comm Heat Mass Transfer, vol 17, pp 577-586, 1990 Yan W.M and Sheen P.J., Heat Transfer and friction characteristics of fin-and-tube heat exchangers, Int J Heat Mass Transfer, vol.43, pp.1651-1659, 2000 Yan W M., Li H.Y., Wu Y J., Lin J Y and Chang W R., Performance of finned tube heat exchangers operating under frosting conditions Int J Heat Mass 220 References Transfer, vol 46, pp 871-877, 2003 Yang D.K., Lee K.S and Song S., Modeling for predicting frosting behavior of a fin-tube heat exchanger, Int J Heat Mass Transfer, vol.49, pp.1472-1479, 2006a Yang D.K., Lee K.S and Song S., Fin spacing optimization of a fin-tube heat exchanger under frosting conditions, Int J Heat Mass Transfer, vol.49, pp.2619-2625, 2006b Yang M and Tao W Q., Numerical study of natural convection heat transfer in a cylindrical envelope with internal concentric slotted hollow cylinder, Numerical Heat Transfer, Part A, vol.22, pp.289-305, 1992 Yen R H and Liu C H., Enhancement of the SIMPLER algorithm by an additional explicit corrector step, Numerical Heat Transfer, Part B, vol 24, pp 127-141, 1993 Yu B., Ozoe H and Tao W Q., A modified pressure-correction scheme for the SIMPLER method, MSIMPLER, Numerical Heat Transfer, Part B, vol.39, pp 439-449, 2001a Yu B., Tao W Q., Zhang D S and Wang Q W., Discussion on numerical stability and boundedness of convective discretized scheme Numerical Heat Transfer, part B, vol.40, pp 343-365, 2001b Yu B., Kawaguchi Y., Tao W Q and Ozoe H., Checkerboard pressure prediction due to the underrelaxation factor and time step size for a nonstaggered grid with momentum interpolation method, Numerical Heat Transfer, Part B, 221 References vol.41, pp.85-94, 2002a Yu B., Tao W Q., Wei J.J., Kawaguchi Y., Tagawa T and Ozoe H., Discussion on momentum interpolation method for collocated grids of incompressible flow, Numerical Heat Transfer, Part B, vol.42, pp 141-166, 2002b Zhu J and Rodi W., A low-dispersion and bounded convection scheme, Comput Meth Appl Mech Eng, vol.92, pp 87-96, 1991 222 List of Publications Conference papers Wu L., Cheng Y P., Lee T.S and Shu C Fluid flow and heat transfer in a closed-ended horizontal concentric annulus with rotating inner heated wall The 4th International Conference on Computational Heat and Mass Transfer, Paris, France, pp.171-175, May 17-20, 2005 [P.N 0214944] Cheng Y.P., Lee T.S and Low H.T., The influence of strip arrangement on the performance of slit fin The Eleventh Asian Congress of Fluid Mechanics, Kuala Lumpur, Malaysia, pp.815-818, May 22-25, 2006.[P.N.0368654] Cheng Y P., Lee T.S., Low H.T and Tao W.Q., An efficient and robust SIMPLER-like numerical algorithm and its application, The Asian Symposium on Computational Heat Transfer and Fluid Flow, Xi’an, China, October 18-21, 2007 [P.N.0368658] Journal papers 1.Cheng Y P., Lee T.S and Low H.T., Numerical analysis of mixed convection in three-dimensional rectangular channel with flush-mounted heat sources based on field synergy principle International Journal for Numerical Methods in Fluids, vol.52, pp 987-1003, 2006 [P.N.: 0305521] 2.Cheng Y P., Lee T S., Low H T and Tao W Q., An efficient and robust numerical scheme for SIMPLER algorithm on non-orthogonal curvilinear coordinates, CLEARER, Numerical Heat Transfer, Part B, vol.51(5), pp 223 433-461, 2007 [P.N.: 0345670] Cheng Y P., Lee T S., Low H T and Tao W.Q., Improvement of SIMPLER algorithm for incompressible flow on collocated grid system Numerical Heat Transfer, Part B, vol.51(5), pp 463-486, 2007 [P.N.: 0322007] Lee T.S.，Cheng Y P and Low H T., Improvement of SIMPLER algorithm for incompressible flow on staggered grid system International Journal of Modern Physics C, vol.18(7), pp.1149-1155, 2007 [P.N.: 0345607] 5.Tao W.Q., Cheng Y P and Lee T.S., 3D numerical simulation on fluid flow and heat transfer characteristics in multistage heat exchanger with slit fins, Heat and Mass Transfer, vol.44, pp.125-136, 2007 [P.N.0368667] Tao W.Q., Cheng Y P and Lee T.S., The influence of strip location on the pressure drop and heat transfer performance of slotted fin, Numerical Heat Transfer, Part A, vol.52, pp.463-480, 2007 [P.N.: 0352393] Cheng Y P., Lee T S and Low H T., Numerical analysis of conjugate heat transfer in electronic cooling based on field synergy principle, Applied Thermal Engineering, vol.28, pp.1826-1833, 2008 [P.N.0368672] Cheng Y P., Lee T S and Low H T., Numerical analysis of periodically developed fluid flow and heat transfer characteristics in the triangular wavy fin-and-tube heat exchanger based on field synergy principle Numerical Heat Transfer, Part A, vol.53(8), pp.821-842, 2008 [P.N.0368679] Cheng Y P., Lee T S., Low H T and Sui Y., Implementation of CLEARER 224 algorithm on three-dimensional non-orthogonal curvilinear coordinates and its application Numerical Heat Transfer, Part B, vol.54(1), pp.62-83, 2008 10 Cheng Y P., Lee T S and Low H T., Numerical prediction of periodically developed fluid flow and heat transfer characteristics in the sinusoid wavy fin-and-tube heat exchanger Int J Numerical Methods for Heat and Fluid Flow, in press 11 Sui Y., Chew Y T., Roy P., Cheng Y P and Low H T., Dynamic motion of red blood cells in simple shear flow Physics of Fluids, in press 225 .. .AN EFFICIENT AND ROBUST ALGORITHM FOR INCOMPRESSIBLE FLOW AND ITS APPLICATION IN HEAT TRANSFER ENHANCEMENT CHENG YONGPAN (B Eng., M Eng., Xian Jiaotong University, China) A THESIS SUBMITTED FOR. .. airside convective heat transfer coefficient for the wet and frosted surfaces in heat exchangers with simultaneous heat and mass transfer 1.2.2.2 Wavy fin -and- tube heat exchanger Jang and Chen (1997)... performance for plain fin -and- tube heat exchanger in wet conditions Niederer (1986) performed experiments to investigate the frosting and defrosting effects on the heat transfer in heat exchangers