Heat Transfer From Solids With Variable Thermal Conductivity and Uniform Internal Heat Generation Using Homotopy Perturbation Method

2008 ◽  
Author(s):  
Rahim Gul ◽  
Zafar H. Khan ◽  
Waqar A. Khan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Perturbation Method ◽  
Heat Generation ◽  
Homotopy Perturbation Method ◽  
Outer Boundary ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Dimensionless Temperature ◽  
Homotopy Perturbation

Homotopy perturbation method (HPM) is employed to investigate the effects of temperature dependent thermal conductivity and internal heat generation on the dimensionless temperature distribution and heat transfer from solids of arbitrary shapes (rectangular, cylindrical and spherical). Dirichlet and Robin boundary conditions are applied at the outer boundary of the solids.

Finite element thermal analysis of a moving porous fin with temperature-variant thermal conductivity and internal heat generation

2020 ◽  
Vol 1 (1) ◽  
pp. 110
Author(s):  
Gbeminiyi Sobamowo ◽  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Finite Element ◽  
Heat Generation ◽  
Peclet Number ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Péclet Number ◽  
Porous Fin

This paper focuses on finite element analysis of the thermal behaviour of a moving porous fin with temperature-variant thermal conductivity and internal heat generation. The numerical solutions are used to investigate the effects of Peclet number, Hartmann number, porous and convective parameters on the temperature distribution, heat transfer and efficiency of the moving fin. The results show that when the convective and porous parameters increase, the adimensional fin temperature decreases. However, the value of the fin temperature is amplified as the value Peclet number is enlarged. Also, an increase in the thermal conductivity and the internal heat generation cause the fin temperature to fall and the rate of heat transfer from the fin to decrease. Therefore, the operational parameters of the fin must be carefully selected to avoid thermal instability in the fin.

scholarly journals INVERSE PREDICTION AND APPLICATION OF HOMOTOPY PERTURBATION METHOD FOR EFFICIENT DESIGN OF AN ANNULAR FIN WITH VARIABLE THERMAL CONDUCTIVITY AND HEAT GENERATION

2016 ◽  
Vol 21 (5) ◽  
pp. 699-717 ◽  
Author(s):  
Ashis Mallick ◽  
Rajiv Ranjan ◽  
Dilip K. Prasad ◽  
Ranjan Das
Keyword(s):  
Temperature Field ◽  
Heat Generation ◽  
Thermal Loading ◽  
Homotopy Perturbation Method ◽  
Internal Heat ◽  
Variable Thermal Conductivity ◽  
Internal Heat Generation ◽  
Tangential Stresses ◽  
Homotopy Perturbation ◽  
Annular Fin

In the present work, various thermal parameters of an annular fin subjected to thermal loading are inversely estimated using differential evolution (DE) method. In order to obtain the temperature field, the second order nonlinear differential equation for heat transfer with variable thermal conductivity and internal heat generation is solved using Homotopy Perturbation Method (HPM). Classical thermoelasticity approach coupled with an HPM solution for temperature field is employed for the forward solution of thermal stresses. It is interesting that the internal heat generation does not affect the radial stresses, while the temperature field and the tangential stresses are influenced by the heat generation parameters. As the tangential stresses are mainly responsible for mechanical failure due to thermal loading in an annular fin, the unknown thermal parameters are inversely estimated from a prescribed tangential stress field. The reconstructed stress fields obtained from the inverse parameters are found to be in good agreement with the actual solution.

scholarly journals Determination of temperature distribution for annular fins with temperature dependent thermal conductivity by HPM

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 111-115 ◽  
Author(s):  
Domiri Ganji ◽  
Ziabkhsh Ganji ◽  
Domiri Ganji
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Variable Thermal Conductivity ◽  
Temperature Dependent ◽  
Homotopy Perturbation ◽  
Annular Fin ◽  
Temperature Dependent Thermal Conductivity

In this paper, homotopy perturbation method has been used to evaluate the temperature distribution of annular fin with temperature-dependent thermal conductivity and to determine the temperature distribution within the fin. This method is useful and practical for solving the nonlinear heat transfer equation, which is associated with variable thermal conductivity condition. The homotopy perturbation method provides an approximate analytical solution in the form of an infinite power series. The annular fin heat transfer rate with temperature-dependent thermal conductivity has been obtained as a function of thermo-geometric fin parameter and the thermal conductivity parameter describing the variation of the thermal conductivity

Analysis of Nonlinear Heat Transfer in Solids of Various Geometries with Variable Thermal Conductivity and Heat Source

2017 ◽  
Vol 377 ◽  
pp. 1-16
Author(s):  
Raseelo Joel Moitsheki ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Exact Solutions ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Variable Thermal Conductivity ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Power Law Function

In this paper we consider heat transfer in a hot body with different geometries. Here, the thermal conductivity and internal heat generation are both temperature-dependent. This assumption rendered the model considered to be nonlinear. We assume that thermal conductivity is given by a power law function. We employ the preliminary group classification to determine the cases of internal heat generation for which the principal Lie algebra extends by one. Exact solutions are constructed for the case when thermal conductivity is a differential consequence of internal heat generation term. We derive the approximate numerical solutions for the cases where exact solutions are difficult to construct or are nonexistent. The effects of parameters appearing in the model on temperature profile are studied.

Homotopy Perturbation Method for the Analysis of Heat Transfer in an Annular Fin With Temperature-Dependent Thermal Conductivity

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Rishi Roy ◽  
Sujit Ghosal
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Differential Equations ◽  
Base Temperature ◽  
Temperature Dependent ◽  
Homotopy Perturbation ◽  
Annular Fin ◽  
Temperature Dependent Thermal Conductivity

A recent mathematical technique of homotopy perturbation method (HPM) for solving nonlinear differential equations has been applied in this paper for the analysis of steady-state heat transfer in an annular fin with temperature-dependent thermal conductivity and with the variation of thermogeometric fin parameters. Excellent benchmark agreement indicates that this method is a very simple but powerful technique and practical for solving nonlinear heat transfer equations and does not require large memory space that arises out of discretization of equations in numerical computations, particularly for multidimensional problems. Three conditions of heat transfer, namely, convection, radiation, and combined convection and radiation, are considered. Dimensionless parameters pertinent to design optimization are identified and their effects on fin heat transfer and efficiency are studied. Results indicate that the heat dissipation under combined mode from the fin surface is a convection-dominant phenomenon. However, it is also found that, at relatively high base temperature, radiation heat transfer becomes comparable to pure convection. It is worth noting that, for pure radiation condition, the dimensionless parameter of aspect ratio (AR) of a fin is a more desirable controlling parameter compared to other parameters in augmenting heat transfer rate without much compromise on fin efficiency.

Finite Volume Method for Analysis of Convective Longitudinal Fin with Temperature-Dependent Thermal Conductivity and Internal Heat Generation

2017 ◽  
Vol 374 ◽  
pp. 106-120 ◽  
Author(s):  
Gbeminiyi M. Sobamowo ◽  
Bayo Y. Ogunmola ◽  
Gaius Nzebuka
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Volume Method

In this study, heat transfer in a longitudinal rectangular fin with temperature-dependent thermal properties and internal heat generation has been analyzed using finite volume method. The numerical solution was validated with the exact solution for the linear problem. The developed heat transfer models were used to investigate the effects of thermo-geometric parameters, coefficient of heat transfer and thermal conductivity (non-linear) parameters on the temperature distribution, heat transfer and thermal performance of the longitudinal rectangular fin. From the results, it shows that the fin temperature distribution, the total heat transfer, and the fin efficiency are significantly affected by the thermo-geometric of the fin. Therefore, the results obtained in this analysis serve as basis for comparison of any other method of analysis of the problem and they also provide platform for improvement in the design of fin in heat transfer equipment.

Heat Transfer in Plane with Temperature Dependent Thermal Variables

2018 ◽  
Vol 387 ◽  
pp. 23-36 ◽  
Author(s):  
Marcio Lourenco ◽  
Raseelo Joel Moitsheki ◽  
Adewunmi Gideon Fareo ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Exact Solution ◽  
Exact Solutions ◽  
Heat Generation ◽  
Heat Conductivity ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Bench Mark ◽  
Temperature Dependent

In this paper we consider heat transfer in a wall with temperature dependent heat conductivity and internal heat generation. It turns out the model considered is non-linear. We employ the classical Lie point symmetry analysis to determine the exact solutions. A number of cases for thermal conductivity and internal heat generation are considered. In some cases the exact solutions are not possible to construct. However, we first use the obtained exact solution as a bench mark for the quasilinear method. Since confidence is established, we then use the quasilinear method to solve some other applicable problem.

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