Temperature-dependent Heat Transfer Coefficient Research Articles

A series solution of the non-linear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient

An extension of a series solution of the non-linear fin problem with temperature-dependent thermal conductivity [Kim and Huang 2006 J. Phys. D: Appl. Phys. 39 4894–901] is done to include a temperature-dependent heat transfer coefficient as well. It is assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. The algorithm is based on the Taylor series solution. The proposed approximate solution is successfully compared with the solutions for the Adomian decomposition method (ADM) and numerical algorithm. Also, it has been shown that the Adomian decomposition solution is just an approximation of the series solution given in this work, and therefore the present algorithm is better than ADM.

최적화 기법을 활용한 열전달계수의 측정

New method for evaluation of heat transfer coefficient is proposed. In general, many researchers have been studied about inverse problem in order to calculate the heat transfer coefficient on three-dimensional heat conduction problem. But they can get the time-dependent heat transfer coefficient only through inverse problem. In order to acquire temperature-dependent heat transfer coefficient, it requires much time for numerous repetitive calculation and inconvenient manual modification. In order to solve these problems, we are using the SQP(Sequential Quadratic Programming) as an optimization algorithm. When the temperature history is given by experiment, the optimization algorithm can evaluate the temperature-dependent heat transfer coefficient with automatic repetitive calculation until difference between calculated temperature history and experimental ones is minimized. Finally, temperature-dependent heat transfer coefficient evaluated by developed program can used on various heat transfer problem.

Inverse heat conduction analysis of quenching process using finite-element and optimization method

The calculation of surface heat transfer coefficient during quenching process is one of the inverse heat conduction problems, and it is a nonlinear and ill-posed problem. A new method to calculate the temperature-dependent surface heat transfer coefficient during quenching process is presented, which applies finite-element method (FEM), advance–retreat method and golden section method to the inverse heat conduction problem, and can calculate the surface heat transfer coefficient according to the temperature curve gained by experiment. In order to apply the advance–retreat method to the inverse heat conduction problem during quenching process, the arithmetic is improved, so that the searching interval of optimization can be gained by the improved advance–retreat method. The optimum values of surface heat transfer coefficient can be easily obtained in the searching interval by golden section method. During the calculation process, the phase-transformation volume and phase-transformation latent heat of every element in every time interval can be calculated easily by FEM. The temperature and phase-transformation volume of every element are calculated with the coupling calculation of phase-transformation latent heat.

Transient temperature fields with general nonlinear boundary conditions in electronic systems

Green's function representations of the solution of the heat conduction equation for general boundary conditions are generalized for the nonlinear, i.e., temperature dependent case. Temperature dependent heat transfer coefficients lead to additional terms in the Green's function representation of the temperature field. For a rectangular structure with averaged homogeneous material parameters several types of Green's functions can be chosen especially simple, because of the new representation with the possibility of differing types of boundary conditions for the temperature field and the Green's function. Exact finite closed form expressions for three-dimensional-Green's functions in the time domain using elliptic theta functions are presented. The temperature field is a solution of a nonlinear integral equation which is solved numerically by iteration. The resulting algorithm is very robust, stable and accurate with reliable convergence properties and avoids matrix inversions completely. The algorithm can deal with all sizes of volume heat sources without additional grid generation. Large and small size volume heat sources are treated simultaneously in the calculations that will be presented. Heat transfer coefficients are chosen representing radiative and convective boundary conditions. An extension of the solution algorithm to composed multilayer systems of arbitrary geometry is outlined.

A DECOMPOSITION METHOD FOR POWER-LAW FIN-TYPE PROBLEMS

The Adomian decomposition method is applied to determine the temperature distribution within a single fin with a temperature dependent heat transfer coefficient

Modelling of heat transfer in hot strip mill runout table cooling

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Analytical solutions of the 1-D heat conduction problem for a single fin with temperature dependent heat transfer coefficient – II. Recurrent direct solution

The recurrent direct solution of the 1-D heat conduction problem for a single straight fin and spine with power-law-type temperature dependent heat transfer coefficient has been derived using inversion of the closed-form solution obtained in the first part of the study. The expression with improving convergence to calculate accurately the dimensionless temperature excess T e at the fin tip for a given values of the fin parameter N and exponent n in heat transfer equation has been obtained by a linearization method. Equation for the temperature excess distribution throughout the fin has also been derived. The obtained formula for T e allows to calculate the fin base thermal conductance and augmentation factor. Obtained expressions are seen to be simple and convenient for the engineering design of the fins and finned surfaces.

Analytical solutions of 1-D heat conduction problem for a single fin with temperature dependent heat transfer coefficient – I. Closed-form inverse solution

Closed-form solution of 1-D heat conduction problem for a single straight fin and spine of constant cross-section has been obtained. The local heat transfer coefficient is assumed to vary as a power function of temperature excess. The dependence of the fin parameter N on the dimensionless temperature difference T e at the fin tip for a given exponent n was derived in a form N/ N 0= T e − μn (where N 0 is a well-known N expression for n=0). Coefficient μ was found to be equal to 5/12 according to the exact solution at T e→1 or to 0.4 according to the fitting procedure for the data of the numerical integration. Obtained formula serves as a basis for the derivation of the direct expressions for T e vs N at given n, fin base thermal conductance and augmentation factor presented in the second part of the study.

Hydromechanical Deep-Drawing of Aluminium-Alloys at Elevated Temperatures

This paper presents a technology that combines the different effects used in hydromechanical and warm deep drawing to reduce the drawing force and to increase the transmittable drawing force in the deep drawing process of aluminium sheets by flange heating and by using a counter pressure. Adequate process parameters and an optimised tool design are discussed in thermo-mechanically coupled Finite Element Simulations. The required system parameters, such as temperature and strain rate dependent flow curves, temperature dependent friction coefficients and heat transfer coefficients, were detected in different model experiments for the numerical simulations. Experimental results are presented to highlight the possibilities and limitations of this forming method.

Étude des transferts de chaleur non linéaires dans les ailettes longitudinales

This work aims to quantify the effects of non-simplified situations on longitudinal fins efficiency. For this purpose a more realistic model, which has been developed here, is based on variable profile and temperature-dependent thermophysical properties in transient two-dimensional fin with internal non-uniform heat generation. An explicit exponential finite-difference method, conditionally stable, is extended in this study for the discretization of the governing equations. The numerical procedure consists in solving series of nodal temperature distribution according to the type of node, in order to reach the steady-state heat exchange. Then, the numerical simulation is used to present the sensitivity of some parameters on efficiency. Numerical results of interest are illustrated for a direct comparison with the traditional solutions. Extensive numerical experiments were conducted and showed that temperature-dependent heat transfer coefficient and generation lead to a significant reduction of fin-efficiency. The simultaneous effects of parameters for this non-linear problem are not negligible.

An analytical study of the optimum dimensions of rectangular fins and cylindrical pin fins

Considering temperature dependent heat transfer coefficients and heat transfer from the fin tip, the optimum dimensions of rectangular fins and cylindrical pin fins are investigated analytically. In this work, the fin volume is fixed to obtain the aspect ratios of the uniform area cross-section fins with maximum heat transfer rates. The characteristic length that has been determined empirically is taken into consideration in heat transfer coefficient. The analysis shows that an optimum aspect ratio of a fin is not found for a fin with heat transfer from the tip at a large fin volume or a large heat transfer coefficient at the fin base. However, there always exists an optimum aspect ratio for an insulated-tip fin. The optimum aspect ratio of a fin is highest for a fin with an insulated tip and decreases with increasing rate of heat transfer from the tip.

Analysis of thermally optimized fin array in boiling liquids

Abstract Considering temperature dependent heat transfer coefficient, an optimum longitudinal fin array is investigated. The heat transfer coefficient is assumed to vary with a power-law-type formula. The heat transfer from tips of an array fins is taken into consideration. For convenience of design, two approaches in the optimization of array system are given. The system is optimized by maximizing the heat dissipation of the fin array at a fixed total fin volume. It shows that the aspect ratios of fins for an optimized array is larger than that of a single optimum fin. The results of this work are all presented in dimensionless form for the convenience of design analysis. In addition, results from this study are compared with the experimental data of previous works.

Performance and optimum dimensions of different cooling fins with a temperature-dependent heat transfer coefficient

This paper presents a theoretical-numerical analysis of longitudinal and annular fins and spines. We examine rectangular, triangular and parabolic profiles for the fins and cylindrical, conical and parabolic spines. In order to reach an understanding of the performance of these odd-shaped, but real world fins, the situation examined here is the case of fins subject to a temperature-dependent heat transfer coefficient. Figures as well as numerical correlations of performance and optimum dimensions of these fins are presented.

Optimum dimensions of longitudinal rectangular fins and cylindrical pin fins with variable heat transfer coefficient

AbstractConsidering a temperature dependent heat transfer coefficient, the optimum dimensions of longitudinal rectangular fins and cylindrical pin fins have been investigated analytically. Employing the parameters of fin thickness or fin diameter and tip temperatures, the optimum dimensions, heat dissipation, and efficiency of fins are obtained by Lagrange's multiplier method. It is shown that the fin efficiency of an optimum cylindrical pin fin is higher than that of an optimum rectangular fin. To facilitate the thermal design of the heat transfer components, very simple mathematical expressions for the optimum dimensions of fins are presented in this study.

On optimum spines

This article presents the optimum dimensions and heat transfer characteristics of spines for cylindrical, convex parabolic, conical, and concave parabolic profiles. With a derived solution form, the optimum base diameter, length, heat dissipation, temperature profile, and efficiency of spines are obtained by fin parameter and tip temperature. The temperature-dependent heat transfer coefficient is assumed to be a power-law type. It is found that the optimum dimensions of a spine are functions of fin volume, heat transfer coefficient at fin base, and thermal conductivity. For a fin with least material, the optimum conditions are also obtained. It shows that the results are solely related to the heat transfer mode on the fin surface. To facilitate the thermal design of heat transfer components, simple mathematical expressions as well as design charts are presented. 15 refs.

Analysis of a thermally enhanced ball grid array package

A thermally enhanced ball grid array package (SuperBGA package) has been developed. Its thermal performance has been analyzed using a nonlinear, lumped parameter model. This model uses a temperature-dependent heat transfer coefficient which accounts for the natural, mixed, and forced convection regimes and radiative heat transfer. The accuracy of the model is verified experimentally using one package size. The model is then used to predict the thermal performance of other package sizes and to rationalize the high level of thermal performance exhibited by the package.

Influence of heat transfer on the development of residual stresses in quenched steel cylinders

In this paper results of systematic FE-calculations about the influence of characteristic points of the temperature dependent heat transfer coefficient, especially the Leidenfrost point and the point of maximum heat transfer coefficient on the development of residual stresses are discussed. The numerical investigations were carried out for SAE 1045 and 4140 steel cylinders with 10 and 20 mm O quenched in water and oil, respectively. In this work experimentally determined h, T-curves are linearly approximated in the successive stages of heat transfer. Changes of the Leidenfrost-temperature do not influence the middle plane residual stresses of the cylinders investigated

Generalized thermoelastic waves in a layer with a boundary condition that is nonlinear with respect to temperature

A solution for the unsteady, generalized problem of thermoelasticity is constructed and investigated for a plane layer on one of whose surfaces there is given a generalized boundary condition of the third kind with a temperature-dependent heat-transfer coefficient.

Transient performance of a high temperature solar distillation system

The transient performance of a solar still coupled to a flat-plate solar collector and operating in the thermosiphon mode is presented. Performance of the system has been evaluated considering the heat transfer coefficient as a function of the water temperature within the still. The effect of water depth on the performance of the proposed system is also addressed. The study reveals that it is worthwhile to consider a temperature dependent evaporative heat transfer coefficient when evaluating the performance of a high-temperature solar distillation system.

Thermal evaluation of high temperature distillation under an active mode of operation

The thermal analysis of a double effect distillation unit in active operation is presented, taking into account the system as well as climatic parameters. Analytical expressions for hourly yield from the upper and lower basin and daily efficiency have been derived by using temperature-dependent internal heat transfer coefficients. Numerical calculations have been carried out for the same set of parameters as before [1] for comparison purposes. On the basis of numerical results, it is observed that there is an increase of 20% and 30% in efficiency of a solar distillation unit working under active and passive modes, respectively.