Transient solution of temperature field of conjugate laminar forced convection heat transfer in functionally graded hollow cylinder

In this study, the numerical analysis of conjugate heat transfer of laminar flow in a functionally graded hollow cylinder (FGHC) made of metal/ceramic for a two‐dimensional fluid and wall conduction subject to Newton boundary condition is considered. The fluid and FGHC energy equations are coupled through the continuity of temperature and heat flux at the inner wall‐fluid interface while the outer surface is subject to convective heat transfer. The continuity, momentum, and energy equations of the fluid are discretized using the finite volume approach. The effects of fluid and functionally graded material parameters, such as volume fraction index, volume composition, time history, wall‐to‐fluid thermal diffusivity ratio, wall‐to‐fluid thermal conductivity ratio, Biot number, Peclet number, and Prandtl number are investigated on the temperature field in the FGHC. The result shows that on account of the inhomogeneity of the material property, the volume fraction index has a significant effect on the other parameters and the temperature variation along the thickness. The lower the volume fraction index, the higher the inner wall (metal side) temperature, and the temperature gradient along the thickness. However, except for the variation in the wall‐to‐fluid thermal conductivity ratio, the lower the volumetric fraction, the lower the outer wall (ceramic side) temperature distribution.     

Investigation of conjugate heat transfer in a photovoltaic wall

In this paper, the results of an experimental and theoretical investigation of combined heat transfer in a photovoltaic wall have been reported. The photovoltaic wall is a prototype, which is composed of two pieces of BP PV panels and a Styrofoam board, and part of the light of radiation energy from the indoor lamps can be converted into electricity. Through experiments, the performance of such a photovoltaic wall has been studied. For the convenience of the treatment of heat radiation, a model in terms of the integration of the absolute temperature has been proposed for the numerical simulation of the combined heat transfer in the test wall. By comparison, it is found that with regard to the thermal radiation of lamp surface, good agreement between the results of simulation and experimental data is obtained. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(2): 117–128, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10136     

Momentum and heat transfer in laminar boundary layer behind shock wave

Analytical and numerical solutions are established for momentum and energy laminar boundary layer induced by a shock wave. The results indicated that skin friction σ decreases with increasing in velocity ratio ξ(1≤ξ< 6). For each specified ξ(1≤ξ< 6), temperature w(t) increases with increasing of Tw but decreases with Te , and for a range of t ∈[1,ξ], w(t) decreases with the increasing of t. Thermal diffusion increases with increasing of uw but decreases with increasing Ue.     

Exact and analytical solutions for self-similar thermal boundary layer flows over a moving wedge

This article aims to achieve exact and analytical solutions for the classical Falkner–Skan equation with heat transfer (FSE-HT). Specifically, when the pressure gradient parameter , there already exists a closed-form solution in the literature for the Falkner–Skan flow equation. The main purpose here is to extend this case to obtain a closed-form solution to the heat transport equation with the solubility condition . An algorithm is presented and is found to be new to the literature that enriches the physical properties of FSE-HT. It is shown that for the moving wedge parameter $$, the momentum and temperature equations show multiple solutions analytically. The skin friction coefficient and the heat transfer rate are also obtained in analytical form. The thus-obtained solution is then adapted to derive an analytical solution applicable to a wide range of pressure gradient parameters $$ and Prandtl numbers $$. Furthermore, an asymptotic analysis is conducted, focusing on scenarios where the moving wedge parameter becomes significantly large ( $$). Nevertheless, in all the above-mentioned cases, the skin friction coefficient ( $$) and the heat transfer rate ( $$) are compared with the direct numerical solutions of the boundary layer equations, and it is found that the results are in good agreement. These solutions provide a benchmark and shed light on further studies on the families of FSE-HT.     

BEM/FDM conjugate heat transfer analysis of a two-dimensional air-cooled turbine blade boundary layer

A coupled boundary element method （BEM） and finite difference method （FDM） are applied to solve conjugate heat transfer problem of a two-dimensional air-cooled turbine blade boundary layer. A loosely coupled strategy is adopted, in which each set of field equations is solved to provide boundary conditions for the other. The Navier-Stokes equations are solved by HIT-NS code. In this code, the FDM is adopted and is used to resolve the convective heat transfer in the fluid region. The BEM code is used to resolve the conduction heat transfer in the solid region. An iterated convergence criterion is the continuity of temperature and heat flux at the fluid-solid interface. The numerical results from the BEM adopted in this paper are in good agreement with the results of analytical solution and the results of commercial code, such as Fluent 6.2. The BEM avoids the complicated mesh needed in other computation method and saves the computation time. The results prove that the BEM adopted in this paper can give the same precision in numerical results with less boundary points. Comparing the conjugate results with the numerical results of an adiabatic wall flow solution, it reveals a significant difference in the distribution of metal temperatures. The results from conjugate heat transfer analysis are more accurate and they are closer to realistic thermal environment of turbines.     

Improvement of the heat transfer quality by air cooling of three-heated obstacles in a horizontal channel using the lattice Boltzmann method

This study focuses on the cooling of three heated obstacles with different heights mounted on the bottom of the channel wall using different aspects that influence the enhancement of the heat exchange, as is known in the concept of cooling electronic devices. The lattice Boltzmann method associated with multiple relaxation times (LBM-MRT) was adopted to simulate the physical configurations of the studied system. In this context, the D2Q9 and D2Q5 models are applied to describe the fluid flow behavior and conjugate heat transfer, respectively. The evaluation of heat exchange between the cold fluid and three-heated obstacles has been accurately analyzed under the effect of several parameters such as Reynolds number, obstacle spacing, and thermal conductivity ratio. In addition, the setting of two and three fluids flow inlets were also studied. The results are presented in terms of streamlines, isotherms, and local Nusselt curves. The heat transfer increases with increasing solid-fluid thermal conductivity. It is also more pronounced for large Reynolds numbers. Moreover, the heat transfer significantly enhances for the second and third obstacles when obstacle spacing increases. The improvement of the heat transfer is performed by the implementation of several jet flows in the studied system.     

Modeling of thermal radiation in a participating media with conjugate heat transfer

Modeling a combination of thermal radiation and conjugate heat transfer in a three-dimensional rectangular domain which has a participating media CO₂ flowing through is done numerically in OpenFOAM. The rectangular duct has a vertical step (facing forward to the inlet) which is located at a distance from the inlet (the distance is same as the height of the inlet section). The domain is divided into two regions (namely solid and fluid). Carbon dioxide, a highly absorbing fluid with extinction, is used here as the participating medium. The ability of the code is verified to analyze the thermal radiation in a participating media with conjugate heat transfer. The study was carried out for a constant Reynolds number 250 and a contraction ratio of 0.5. The study focused primarily on the importance of adding thermal radiation on to thermal analysis and the reason behind the Nusselt number variation on different regions of solid–fluid interface. It also discussed the effect of radiative properties, such as optical thickness and linear scattering albedo, on the average convective Nusselt Number.     

Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet

Viscoelastic boundary layer flow and heat transfer over an exponential stretching continuous sheet have been examined in this paper. Approximate analytical similarity solution of the highly non-linear momentum equation and confluent hypergeometric similarity solution of the heat transfer equation are obtained. Accuracy of the analytical solution for stream function is verified by numerical solutions obtained by employing Runge-Kutta fourth order method with shooting. These solutions involve an exponential dependent of stretching velocity, prescribed boundary temperature and prescribed boundary heat flux on the flow directional coordinate. The effects of various physical parameters like viscoelastic parameter, Prandtl number, Reynolds number, Nusselt number and Eckert number on various momentum and heat transfer characteristics are discussed in detail in this work.     

Computational fluid dynamics (CFD) modeling of heat transfer in a polymeric membrane using finite volume method

The efficiency, robustness and reliability of recent numerical methods for finding solutions to flow problems have given rise to the implementation of computational fluid dynamics (CFD) as a broadly used analysis method for engineering problems like membrane separation system. The CFD modeling in this study observes steady and unsteady (transient) heat flux and temperature profiles in a polymeric (cellulose acetate) membrane. This study is novel due to the implementation of user defined scalar (UDS) diffusion equation by using user-defined functions (UDFs) infinite volume method (FVM). Some details of the FVM used by the solver are carefully discussed when implementing terms in the governing equation and boundary conditions (BC). The contours of temperature due to high-temperature gradient are reported for steady and unsteady problems.     

Investigation of heat transfer in a geometry with variable cross section

In this paper, the thermal conductivity that plays an important role in heat transfer efficiency is investigated. He's homotopy perturbation method (HPM) and Adomian decomposition method (ADM) are applied to the nonlinear heat transfer equations and the comparison between results is illustrated within several plots. Here, thermal conductivity has been considered as a function of temperature. Also the variable heat generation has been taken into account. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20266 Copyright © 2009 Wiley Periodicals, Inc.     

Numerical simulation of vortex structures and heat transfer behind a hill in a laminar boundary layer

The present study examines a three‐dimensional numerical simulation of vortex structures and heat transfer behind a hill mounted in a laminar boundary layer. A vortex pair is formed symmetrically in the separation bubble behind the hill, and a hairpin vortex is periodically shed in the wake. The hairpin vortex moves downstream with time, and the gradient of the head of the hairpin vortex increases. Further downstream, the hairpin vortex is deformed to an Ω‐shaped structure. In the growth process of the hairpin vortex, horn‐shaped secondary vortices grow near the wall. The dissipation rate of the temperature fluctuation around the hairpin vortex increases because the heated fluid near the wall is removed to the free stream by Q2 ejection. Heat transfer increases due to the legs of the hairpin vortex and secondary vortices. These vortices generate high turbulence in the flow field and also contribute to an increase in Reynolds shear stress and turbulent heat flux. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(7): 398–411, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20217     

基于有限元方法的横掠错排光滑管束传热与流动特性研究

使用有限元方法对横掠不同型式措排光滑管束进行了计算分析，绘制了速度场和温度场的色差梯度图，比较了它们的传热与流动性能。有限元分析方法作为热分析和流动分析研究的有力工具，可以与实验研究相结合作为研究管束传热与流动性能的一种新方法。研究结果对于横掠光滑管束的优化设计具有一定的指导意义。     

Numerical simulation of coupled radiation‐convection heat transfer of high‐temperature developing flow in tube

By combining the discrete ordinate method with the control volume method, the coupled radiation‐convection heat transfer of high‐temperature developing laminar flow in a tube is investigated numerically. The radiative transfer is solved by the discrete ordinate method and its contribution to thermal balance is dealt with as a source term in the energy equation, which is solved, as well as the momentum equation, by the control volume method. The effects of medium optical thickness and tube wall temperature on the temperature distribution in medium as well as the heat flux and local Nusselt number on wall are analyzed. The results show that the radiation heat transfer of high‐temperature medium influences the temperature distribution and convection heat transfer greatly, and plays an important role in the heat transfer of developing laminar flow in a tube. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 53–63, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10135     

Enhanced heat transfer using oscillatory flows in solar collectors

In this work, we propose the use of oscillatory laminar flows to enhance the transfer of heat from solar collectors. The idea is to explore the possibility of transferring the heat collected from a solar device to a storage tank by means of a zero-mean oscillating fluid contained in a tube. This method takes advantage of the fact that the effective thermal diffusivity of a fluid in oscillatory motion is several orders of magnitude higher than the fluid molecular diffusivity. Therefore, the axial transport of heat along the tube is substantially higher when the fluid oscillates than when the fluid is static. Also, preliminary estimations show a dramatic heat transfer enhancement using oscillatory flows compared with the forced convection of heat by standard unidirectional flows. We explore the behavior of the effective thermal diffusivity using both Newtonian and viscoelastic fluids. For the Newtonian fluid a single maximum value of this quantity is exhibited for a given oscillation frequency. In contrast, several maxima for different resonant frequencies are observed for the viscoelastic fluid. Further, the absolute maximum of the enhanced thermal diffusivity for the viscoelastic fluid is several orders of magnitude larger than that of the Newtonian fluid.     

ψ - v Computation of steady-state conjugate heat transfer in backward-facing step flow

In this paper, we study steady-state conjugate heat transfer over a backward-facing step flow using a combination of a compact finite difference scheme for the $\psi$-$v$ form of the Navier–Stokes equations and a higher-order compact scheme for the temperature equations on nonuniform grids. We investigate the effect of Reynolds number ($200\le Re\le 800$), conductivity ratio ($1\le k\le 1000$), Prandtl number ($0.1\le Pr\le 15$), and slab thickness ($h\le b\le 6h$) on the heat transfer characteristics. Isotherms remain clustered near the reattachment point in the fluid, while the temperature in the solid decreases vertically, with the minima at the reattachment point. Heat transfer rate (HTR) increases with Re, the maximum at the reattachment point. The HTR increases with $k$ till $k=100$ after, which it becomes invariant as $k\to \infty$. Isotherms at the inlet become more disorderly with increasing Pr, and progressively clustered near the interface, indicating an increase in HTR, while the temperature in the solid region decreases with Pr. Increasing b decreases the HTR. In addition to obtaining an excellent match with results previously reported in the literature, we offer more comprehensive and previously unreported insights on flow physics.     

Flow and heat transfer over an unsteady stretching surface with non-uniform heat source

The non-uniform heat source/sink effect on the flow and heat transfer from an unsteady stretching sheet through a quiescent fluid medium extending to infinity is studied. The boundary layer equations are transformed by using similarity analysis to be a set of ordinary differential equations containing three parameters: unsteadiness parameter (S), space-dependent parameter (A?) and temperature-dependent parameter (B?) for heat source/sink. The velocity and temperature fields are solved using the Chebyshev finite difference method (ChFD). Results showed that the heat transfer rate, − θ′(0) and the skin friction, − f″(0) increase as the unsteadiness parameter increases whereas decrease as the space-dependent and temperature-dependent parameters for heat source/sink increase.     

Heat transfer characteristics of gaseous flows in microtube with constant heat flux

Heat transfer characteristics of gaseous flows in a microtube with constant heat flux whose value is positive or negative are investigated on two-dimensional compressible laminar flow for no-slip regime. The numerical methodology is based on the Arbitrary–Lagrangian–Eulerian (ALE) method. The computations are performed for tubes with constant heat flux ranging from −10⁴ to 10⁴ W m⁻². The tube diameter ranges from 10 to 100 μm and the aspect ratio of the length and diameter is 200. The stagnation pressure, p_stg is chosen in such away that the Mach number at the exit ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in microtubes with positive heat flux are compared with those of negative heat flux case and also compared with those of the incompressible flow in a conventional sized tube. In the case of fast flow, temperature profiles normalized by heat flux have different trends whether heat flux is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the microtube is proposed. Supplementary runs with slip boundary conditions for the case of D = 10 μm conducted and rarefaction effect is discussed. With increasing Ma number, the compressibility effect is more dominant and the rarefaction effect is relative insignificant where Kn number is less than Kn = 0.0096. And, the magnitudes of viscous dissipation term and compressibility term are investigated along the tube length.     

A simplified approach to solving conjugate heat transfer problems in annular and dissimilar parallel plate ducts

A simple perturbation technique is used to reformulate the energy equations which describe the treatment thermal behaviour of a radially lumped conjugate that transfer problem is annular and dissimilar parallel plate ducts of finite wall thickness. The simplified perturbation tecnique is used to eliminate the coupling between the fluid and the solid-wall energy equations when the temperature difference between the fluid and the solid-wall is a small perturbed quantity, which is true when the interface convective heat transfer coefficient between the fluid and the solid-wall is high. A mathematical criterion is derived to determine the conditions under which the fluid and the solid-wall are in thermal equilibrium. It is found that seven dimensionless parameters control the state of the thermal equilibrium between the fluid and the solid domains. © 1998 John Wiley & Sons, Ltd.