Heat transfer from hollow cylinder using optimal homotopy asymptotic method

Optimal homotopy asymptotic method (OHAM) is employed to investigate steady‐state heat conduction with temperature dependent thermal conductivity and uniform heat generation in a hollow cylinder. Analytical models are developed for dimensionless temperature distribution and heat transfer for two cases using mixed boundary conditions (Dirichlet, Neumann, and Robin). The inner cylinder is assumed to be insulated in both cases. In the first case, the outer cylinder is assumed to be isothermal whereas in the second case, the outer cylinder is convectively cooled by a fluid of temperature T₂ through a uniform heat transfer coefficient h. The effects of Biot number, dimensionless heat generation, and thermal conductivity parameters on the temperature distribution and heat transfer are determined analytically and validated numerically using MAPLE 14. In both cases, the results obtained by OHAM are found to be in good agreement with the numerical results. It is found that as the Biot number increases, the results approach that of the isothermal case. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20407     

边界点法在传热问题数值分析中的应用

将一种新的数值分析方法-边界点法应用于传热问题的研究，对无内热源稳态热传导问题，通过传统边界元法将边界积分方程离散化，发现可以不直接求解影响系数矩阵，而是通过对偶关系，由域外虚源构造方程组的特解场形成边界已知和未知温度，热流密度的系数矩阵，而且域内温度和热流密度的求解将不依赖于边界未知参数的求解，对于有内热源的问题，可以将非齐次方程的解转换为齐次方程的解和某一确定解的叠加，对于非线性问题，可以通过基尔霍夫变换，将非线性问题转化为线性问题求解，这种边界点方法不但具有边界元法降维的优势，而且不须求解奇异积分，大大节约了计算时间，计算精度极高，以有内热源非线性稳态热传导问题的实例印证了这种方法的高效性。     

Reverse computation of forced convection heat transfer for optimal control of thermal boundary conditions

A reverse computation based on adjoint formulation of forced convection heat transfer is proposed to obtain the optimal thermal boundary conditions for heat transfer characteristics; for example, a total heat transfer rate or a temperature at a specific location. In the reverse analysis via adjoint formulation, the heat flow is reversed in both time and space. Thus, using the numerical solution of the adjoint problem, we can inversely predict the boundary condition effects on the heat transfer characteristics. As a result, we can obtain the optimal thermal boundary conditions in both time and space to control the heat transfer at any given time. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(3): 161–174, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20002     

DNS of turbulent heat transfer in a channel flow with a varying streamwise thermal boundary condition

Direct numerical simulation (DNS) was performed for the turbulent heat transfer in a channel flow. In the present study, the effect of the thermal boundary condition was examined. DNS was carried out for varying streamwise thermal boundary conditions (Re_τ = 180) with Pr = 0.71 to obtain statistical mean temperatures, temperature variances, budget terms, and time scale ratios. The results obtained indicate that the time scale ratio varies along the stream direction. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(4): 265–278, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20114     

Thermal boundary condition effects on forced convection heat transfer

We propose a numerical solution of an adjoint problem of forced convection heat transfer to evaluate the mean heat transfer characteristics under arbitrary thermal boundary conditions. Using the numerical solution of the adjoint problem under the Dirichlet condition, which can be computed by slightly modifying a conventional heat transfer code, we obtain an influence function of local surface temperature on total heat transfer. As a result, the total heat transfer for arbitrary surface temperature distributions can be calculated by the influence function. Similarly, using the numerical solution of the adjoint problem under the Neumann condition, we can also obtain an influence function of the local heat flux on the mean surface temperature. The influence functions for a circular cylinder and for an in-line square rod array are presented to illustrate the capability of this method. © 1999 Scripta Technica, Heat Trans Asian Res, 28(3): 227–238, 1999     

Application of Optimal Homotopy Asymptotic Method for solving nonlinear equations arising in heat transfer

We consider one of the newest analytical methods, the Optimal Homotopy Asymptotic Method (OHAM), to solve nonlinear equations arising in heat transfer. Two specific applications are considered: cooling of a lumped system with variable specific heat and the temperature distribution equation in a thick rectangular fin radiation to free space. Results obtained by OHAM, which does not need small parameters are compared with numerical results and a very good agreement was found. This method provides us with a convenient way to control the convergence of approximation series and adjust convergence regions when necessary. The results reveal that the proposed method is explicit, effective and easy to use.     

两类边界条件下管外对流换热性能实验研究

采用实验研究的方法,分别对针翅管、平直翅片管和光管在同一风洞实验台上进行实验。采用管内电加热法模拟第二类边界条件,管内流体加热,管外空气横掠模拟第三类边界条件,实验的管外雷诺数范围为Re=5000—35000。实验结果表明：光管在第三类边界条件下的Nu是第二类边界条件下的1．048倍,翅片管在第三类边界条件下的Nu是第二类边界条件下的1．073倍,针翅管第三类边界条件下的Nu是第二类边界条件下的1．1倍,且这个比例关系与Re的变化无关。     

Freezing of Water in a Slab with Boundary Conditions of the Third Kind

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Suitable Heat Transfer Model for Self-Similar Laminar Boundary Layer in Power Law Fluids

The classical power law non-Newtonian fluids energy boundary layer equation is proved improper to describe the self-similar heat transfer. A theoretical analysis for momentum and energy boundary layer transfer behavior is made and the full similarity heat boundary layer equation is developed, which may be characterized by a power law relationship between shear stress and velocity gradient with the Falkner-Skan equation as a special case. Both analytical and numerical solutions are presented for momentum and energy boundary layer equations by using the similarity transformation and shooting technique and the associated transfer characteristics are discussed.     

Effects of an unsteady thermal boundary condition on forced convection heat transfer

A numerical analysis based on adjoint formulation of unsteady forced convection heat transfer is proposed to generally evaluate effects of the thermal boundary condition on the heat transfer characteristics. A numerical solution of the adjoint problem enables us to predict the heat transfer characteristics, such as the total heat transfer rate or the temperature at a specific location, when the thermal boundary conditions change arbitrarily with time. Moreover, using the numerical solution of the adjoint problem, we can obtain the optimal thermal boundary conditions in both time and space to maximize the heat transfer at any arbitrary time. Numerical solutions of the adjoint problem in a lid‐driven cavity are presented to illustrate the capability of the present method. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(3): 237–247, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10032     

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.     

Periodic heat transfer through inhomogeneous media part 3: Hollow sphere

The paper presents the exact analytical solutions for periodic radial heat conduction through an inhomogeneous hollow sphere for a certain class of thermal-conductivity profile. The exact analytical solutions for some of these profiles, (including linear and quadratic) have been compared with those obtained by considering the spherical medium to be made up of a number of homogeneous layers with different thermal conductivities, varying from layer to layer, and using the layered-structure (or matrix-multiplication) method. The numerical results arrived at by the layered-structure method converge rapidly (with increasing number of layers considered) to the values obtained from the exact analytical solutions. It strengthens the confidence in applying the layered-structure method to the case of periodic heat conduction through an inhomogeneous hollow cylinder. Considering the inhomogeneous conducting medium to be made up of a number of spherical layers with a linear profile of thermal conductivity has been shown to be a more effective alternative method of accounting for any type of inhomogeniety; and it saves computation time, as the rate of convergence is much higher than for the homogeneous-layered structure method. The numerical results have been presented in the form of elements of a 2 × 2 matrix, relating the sinusoidal steady-state temperature and heat flux of the two surfaces of the hollow sphere.     

Assessment of homotopy analysis method and homotopy perturbation method in non-linear heat transfer equation

Two new analytical methods to solve nonlinear heat transfer equations are homotopy perturbation method and homotopy analysis method. Here, homotopy analysis method, which gives us a vast freedom to choose the answer type, is applied to solve nonlinear heat transfer differential equations and analytical results are compared with those of HPM and the numerical results. In this study, the procedure of HAM is applied to two cases in different ways according to the physics of the target problem. Comparing the two methods, our attention is focused on the results accuracy; and applicability of different methods in many cases with different limitation is studied. In the two examples of this paper, the effect of small parameter increaser on the accuracy of the analytical results of two methods also has been studied. The first differential equation is the modeling equation of a cooling lumped system with combined convection and radiation. The second one is the modeling equation of heat transfer with conduction in a slab of thermal dependent conductivity.     

Direct numerical simulation of convective heat transfer in a zero-pressure- gradient boundary layer with supercritical water

Experimental research has long shown that forced-convective heat transfer in wall-bounded turbulent flows of fluids in the supercritical thermodynamic state is not accurately predicted by correlations that have been developed for single-phase fluids in the subcritical thermodynamic state. In the present computational study, the statistical properties of turbulent flow as well as the development of coherent flow structures in a zero-pressuregradient flat-plate boundary layer are investigated in the absence of body forces, where the working fluid is in the supercritical thermodynamic state. The simulated boundary layers are developed to a friction Reynolds number of 250 for two heat-flux to mass-flux ratios corresponding to cases where normal heat transfer and improved heat transfer are observed. In the case where improved heat transfer is observed, spanwise spacing of the near-wall coherent flow structures is reduced due to a relatively less stable flow environment resulting from the lower magnitudes of the wall-normal viscosity-gradient profile.     

Numerical modeling of conjugate heat transfer through concrete hollow bricks

The purpose of this study is to determine the thermal conductance of concrete hollow bricks, which is necessary for the evaluation of the energy efficiency of a building. The three varieties of hollow concrete bricks that are often used to build walls in Morocco are the subject of this study. A computational model created using the finite volume method is used to evaluate the conjugate heat transfer through concrete hollow bricks. According to the results, the use of hollow brick type A_h3 reduces the heat flux by approximately 86% compared with type A_h1. It is undeniable that hollow bricks type A_h3 with a thermal conductivity of 1 W/m K can improve the thermal characteristics of building walls.     

Application of Hermite wavelet method for heat transfer in a porous media

In this article, the flow and heat transfer for non-Newtonian viscoelastic fluid in an axisymmetric channel with a porous wall is investigated. Convective boundary conditions have been used in the problem formulation. We obtain coupled, highly nonlinear ordinary differential equations from the fundamental governing equations via appropriate similarity variables. The solution for velocity and temperature are computed by applying the Hermite wavelet method (HWM). The comparison between the results from the HWM, differential transform method, and numerical method are well in agreement which proves the capacity of HWM for solving such problems. The effects of Reynolds number and Prandtl number on the velocity and temperature are illustrated through graphs and tables for different values of an independent variable.     

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.     

Heat transfer of couple stress fluid from a vertical funnel: Impedance boundary conditions

The present level of literature on the subject matter indicates that nothing is known on the heat transfer across the couple stress rheological fluid flowing over a vertical avenue with Robin (mixed) wall conditions. The obtained conservation equations of the model are solved through DTM (differential transform method) and RPM (regular perturbation method). The nondimensional parameters obtained are a couple stress parameter, Brinkman number, mixed convection parameter, and Biot number. The computations reveal that flow acceleration and thermal enhancement is induced with increasing mixed convection parameter and Brinkman number for symmetric and asymmetric conditions. Increasing couple stress parameters dwindle the velocity and temperature for symmetric and asymmetric cases. The large values of the mixed convection parameter and Brinkman number increase the Nusselt values at the left wall and reduces at the right wall. The mass flow rate is augmented with the mixed convection parameter and Brinkman number but it is reduced with the couple stress parameter. The DTM, RKSM, and RPM solutions are in good agreement.