heat conduction in rectangular coordinates

... Review of Heat Conduction in 1D systems 1.3 14 Literature Review of Heat Conduction in 1D systems 1.3.1 Breakdown of Fourier’s law The starting point for the study of heat conduction in 1D lattice ... Normal Heat Conduction which obeys the Fourier’s heat conduction law These striking results bring the imminent challenge: what is the reason for 1D lattices to exhibit anomalous heat conduction in ... be size independent showing normal heat conduction [76–78] 1.3.2 Anomalous heat conduction The anomalous heat conduction was found in numerical simulations for the 1D momentum-conserving systems...

Ngày tải lên: 13/09/2015, 19:52

... complex non-linear relationship with heat conduction coefficient and is unsuitable for evaluating the change of heat conduction in NS It was found that the rate of heat conduction in unit area ... cooling plate were recorded by measuring the voltage in 30s interval until the temperature of the cooling plate was cooled to less than °C below T1 Finally, the cooling rate and the heat conduction ... the heat conduction equation can be written as follows: Q¼KÂ Sample (air) Cooling plate Z DT ÂA DZ In Eq 1, Q is the quantity of heat, K is heat conduction coefficient (refers to the conducting heat...

Ngày tải lên: 22/06/2014, 00:20

... stability is ensured by stopping the iterative process at the point where the errors in predicting the exact solution start increasing Thus, regularization is achieved by truncating the iterative process ... alternating iterative algorithm presented in Section 3.4 was given in Mera et al (2000) It was shown that a substantial improvement in the rate of convergence is obtained by relaxing the marching ... is achieved by truncating the iterative process at the point where the errors in predicting the exact solution start increasing Thus, a stable solution is achieved by matching the number of iterations...

Ngày tải lên: 16/06/2016, 01:11

... ESE heat engine at intermediate regime is also discussed Model of an ESE heat engine with filter heat conduction The schematic diagram of an ESE heat engine with filter heat transfer is shown in ... China in 2006 He is pursuing for his PhD in power engineering and engineering thermophysics from Naval University of Engineering, P R China His work covers topics in finite time thermodynamics ... diversity of topics in engineering thermodynamics, constructal theory, reliability engineering, and marine nuclear reactor engineering He is a Professor in the Department of Power Engineering, Naval University...

Ngày tải lên: 05/09/2013, 15:28

... highly specific peptidebinding domain found in poly(A)-binding protein and a HECT ubiquitin ligase EMBO J 23, 272–281 Craig A (1998) Interaction of polyadenylate-binding protein with the elF4G homologue ... to interact with eIF4G at a stoichiometry of more than : It should be noted here that, in addition to the C-terminal domain, PABP1 has another eIF4G-binding domain within its N-terminal RNA-binding ... bind the cap-binding complex involved in splicing [34] It is believed that the nuclear eIF4G may associate with pre-mRNA through its interaction with the polypeptide partners of the cap-binding...

Ngày tải lên: 18/02/2014, 12:20

... improving the industry’s knowledge of overheating The project, due to report in 2012, is gathering data from incidences of new homes in which overheating has been a problem and considering the ... were introduced in 1995 both in Finland (Classification of Indoor Climate, Construction and Finishing Materials) and in Denmark (Indoor Climate Label) and are quite widely applied in other Scandinavian ... alveolitis, chronic rhinosinusitis and allergic fungal sinusitis Toxicological evidence obtained in vivo and in vitro supports these findings, showing the occurrence of diverse inflammatory and toxic...

Ngày tải lên: 18/03/2014, 02:20

... determine the electrical features of a grain and to take into account the various mechanisms taking part in electric conduction Indeed, by supposing that the film consists of an homogeneous stacking ... Biographies Jacques Guerin was born in France in 1947 He received his engineering diploma in electronics and radio-communication at the Institut National Polytechnique of Grenoble (INPG) in 1972 and his ... Aix-Marseille III in 1996 with a thesis on shape memory alloys thin films He is specialized in thin films preparation and characterization for applications in microsystems Since 1997, he is interested in gas...

Ngày tải lên: 20/03/2014, 13:04

... ,l, p , H ]〉 t (5) ∂t From Eq.(5), using Hamiltonian in Eq.(2) and realizing calculations, we obtain quantum kinetic equation for confined electrons in CQW Using the first order tautology approximation ... respectively Inserting Cq into Eq.(7) and using Bessel function, Fermi-Dirac distribution function for electron and energy spectrum of electron in RQW, we obtain the explicit expression of α in RQW ... system In our model, we consider a wire of GaAs with rectangular cross section ( Lx × Ly ) and length Lz , embedded in GaAlAs The carriers (electron gas) are assumed to be confined by an infinite...

Ngày tải lên: 22/03/2014, 11:20

... Equations in Rectangular Cartesian Coordinates S.6-2 Equations in Cylindrical Coordinates S.6-3 Equations in Spherical Coordinates Index ... this book for other titles in the Topics in Chemical Engineering series HYDRODYNAMICS, MASS AND HEAT TRANSFER IN CHEMICAL ENGINEERING A.D Polyanin lnstitute for Problems in Mechanics, Moscow, Russia ... S.1-3 Heat Equation in the Cylindrical Coordinates S.1-4 Heat Equation in Spherical Coordinates S.2 Formulas for Constructing Exact Solutions ...

Ngày tải lên: 02/04/2014, 15:52

... Laser Pulse Interactions with Metal Films, Numer Heat Transfer A, vol 40, pp 1–20, 2001 D Y Tzou and K S Chiu, Temperature-Dependent Thermal Lagging in Ultrafast Laser Heating, Int J Heat Mass ... melting temperature velocity velocity factor in Eq (11) spatial coordinate thermal diffusivity radiation penetration depth ballistic depth interface superheating Fermi energy of gold coefficient in ... include both melting and evaporation effects on irradiation of metal with much shorter pulses, of femtosecond duration Heating above the normal melting and boiling temperatures is allowed by including...

Ngày tải lên: 06/05/2014, 08:53

... femtosecond duration Heating above the normal melting and boiling temperatures is allowed by including the appropriate kinetic relations in the computation Therefore, the main difference between ... Laser Pulse Interactions with Metal Films, Numer Heat Transfer A, vol 40, pp 1–20, 2001 D Y Tzou and K S Chiu, Temperature-Dependent Thermal Lagging in Ultrafast Laser Heating, Int J Heat Mass ... in a pump-probe reflectivity experiment on thin gold films [2] Homogeneous heating was observed in thin films of thickness less than 100 nm At thicknesses greater than this, diffusive motion dominates...

Ngày tải lên: 06/05/2014, 08:55

... Belarus Part Inverse Heat Conduction Problems Inverse Heat Conduction Problems Krzysztof Grysa Kielce University of Technology Poland Introduction In the heat conduction problems if the heat flux ... determination inverse problems, Initial value determination inverse problems, Material properties determination inverse problems, Source determination inverse problems Shape determination inverse ... this book covers several up-to-date approaches in the heat conduction theory such as inverse heat conduction problems, non-linear and non-classic heat conduction equations, coupled thermal and electromagnetic...

Ngày tải lên: 18/06/2014, 22:20

... subintervals In each subinterval the domain  is divided into J subdomains (finite elements) and in each subdomain j , j=1, 2,…, J (with  i  i ) the temperature is approximated with the linear combination ... elements in the case of temperature discontinuous in the nodes  (c) Nodeless FEMT Again, T j  x , y , t  , is a linear combination of the T-functions The time interval is divided into subintervals ... the inverse heat conduction problems 5.1 Inverse problems for the cooled gas turbine blade Let us consider the following stationary problem concerning the gas turbine blade (Figure 4): find temperature...

Ngày tải lên: 18/06/2014, 22:20

... trained much faster However, in order to have a good performance, the training set should be available in the beginning of the process Fig An RBF network topology 5.3 Implementation in inverse heat ... step in our study of these techniques, we investigate their capability in solving a general inverse heat conduction problem We start by applying the artificial neural networks to the inverse heat ... Various Methods in Solving Inverse Heat Conduction Problems As can be seen in Fig 15 (for α = 10-10), increasing the value of the self-confidence parameter results in better handling of the noisy...

Ngày tải lên: 18/06/2014, 22:20

... point of discontinuity x1 , and its values a1 and a2 are known beforehand, then the discontinuity point x1 can be determined from just one measurement of the heat conduction process 76 Heat Conduction ... al 2006) combined to the images processing In this method, liquid impinging the heat exchange surface is illuminated by a laser sheet in the axial direction as shown by Figure Rhodamine B with ... conductivities a ∈ A N ⊂ Aad having at most N − discontinuity points on the interval [0, 1] (ii) Use Powell’s minimization method in K = 2N − variables (N − discontinuity points and N conductivity values)...

Ngày tải lên: 18/06/2014, 22:20

... local heat transfer for impinging miniature jet, Heat Transfer Engineering, Vol 29, N° 2, pp.782-792 Louahlia-Gualous H & El Omari, L (2006) Local heat transfer for the evaporation of a laminar ... for solving nonlinear partial differential equations (NPDEs) in terms of accuracy and efficiency This is important, since systems of NPDEs have many applications in engineering 112 Heat Conduction ... J Heat and Mass Transfer, Vol 45, pp 4033-4043 Chen, H.T., Lin, S.Y and Fang, L.Ch., (2001) Estimation of surface temperature in two dimensional inverse heat conduction problems, Int J of Heat...

Ngày tải lên: 18/06/2014, 22:20

... and Mathematics, Ukrainian National Academy of Sciences Ukraine Introduction To provide efficient investigations for engineering problems related to heating/cooling process in solids, the effect ... (3.22) and substituting the result into (3.3), we obtain the following exact solution of Eq (1.1): Exact Travelling Wave Solutions for Generalized Forms of the Nonlinear Heat Conduction Equation ... non-linear heat conductivity problem (1)–(4), which is presented below, consists in the step-by-step linearization involving the Kirchhoff transformation along with linearization of the nonlinear...

Ngày tải lên: 18/06/2014, 22:20

... ; to determine the temperature using the obtained Kirchhoff’s variable The main feature of the method of linearizing parameters consists in a possibility to obtain the solution of linearized boundary ... thermosensitive bodies due to the internal heat sources In this case increasing of the temperature is unbounded Conclusion In this chapter, the formulations of non-linear heat conduction problems for the ... temperature-dependent heat conduction coefficients are in the ideal thermal contact The cylindrical coordinate system r , , z is chosen with z -axis coinciding with the axis of pipe The temperature field in this...

Ngày tải lên: 18/06/2014, 22:20

... scales Fourier’s laws not work in their initial forms In the next sections some interesting problems involving time varying heat sources will be discussed assuming that the conditions for the ... Comparing with Eq (1) we see that the parameter hcond has been incorporated in Eq (6) as the conduction heat transfer coefficient Using H=hconv+hrad=1/R (7) 180 Heat Conduction – Basic Research heat ... to explain heat transport phenomena appearing often in daily life, engineering applications and scientific research In terms of the heat flux density (q=/A) it lauds: =− ∇ (9) When combined with...

Ngày tải lên: 18/06/2014, 22:20

... analyzed, i.e the limit of infinitely long times Introducing the Biot Number defined in Eq (8) and taking t after a straightforward calculation the following results are obtained: At x=0: Δ ↑ (0, ... is a handicap in other techniques because the difficulties for their experimental quantification Conclusion Heat conduction in solids under time varying heating is a very interesting and important ... magnetic field lines is very restricted For instance, the mass loading of magnetic field lines 10 As discussed in LV99 and in more details in Eyink et al (2011) the magnetic field wandering, turbulence...

Ngày tải lên: 18/06/2014, 22:20