Effect of Variable Thermal Conductivity on Heat Transfer From a Hollow Sphere With Heat Generation Using Homotopy Perturbation Method

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

Homotopy perturbation method (HPM) is employed to investigate steady-state heat conduction with temperature dependent thermal conductivity and heat generation in a hollow sphere. Analytical models are developed for dimensionless temperature distribution and heat transfer using mixed boundary conditions (Dirichlet, Neumann and Robin). The effects of dimensionless heat generation parameter and temperature dependent thermal conductivity on temperature distribution and heat transfer from hollow spheres are analyzed graphically. It is demonstrated that the heat transfer is strongly dependent on the dimensionless heat generation parameter and temperature dependent thermal conductivity. Finally the HPM results are compared with Kirchhoff Transformation results.

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

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.

Exact solution of a nonlinear fin problem of temperature-dependent thermal conductivity and heat transfer coefficient

2020 ◽  
Vol 98 (7) ◽  
pp. 700-712 ◽  
Author(s):  
Sheng-Wei Sun ◽  
Xian-Fang Li
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Temperature Distribution ◽  
Transfer Coefficient ◽  
Power Law ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Special Cases ◽  
Temperature Dependent Thermal Conductivity

This paper studies a class of nonlinear problems of convective longitudinal fins with temperature-dependent thermal conductivity and heat transfer coefficient. For thermal conductivity and heat transfer coefficient dominated by power-law nonlinearity, the exact temperature distribution is obtained analytically in an implicit form. In particular, the explicit expressions of the fin temperature distribution are derived explicitly for some special cases. An analytical expression for fin efficiency is given as a function of a thermogeometric parameter. The influences of the nonlinearity and the thermogeometric parameter on the temperature and thermal performance are analyzed. The temperature distribution and the fin efficiency exhibit completely different behaviors when the power-law exponent of the heat transfer coefficient is more or less than negative unity.

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.

scholarly journals A Study on Convective-Radial Fins with Temperature-dependent Thermal Conductivity and Internal Heat Generation

2019 ◽  
Vol 8 (1) ◽  
pp. 145-156
Author(s):  
Trushit Patel ◽  
Ramakanta Meher
Keyword(s):  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Fractional Order ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Temperature Dependent Thermal Conductivity

Abstract In this paper, the temperature distribution in a convective radial fins is analyzed through a fractional order energy balance equation with the consideration of internal heat generation and temperature dependent thermal conductivity. Adomian decomposition Sumudu transform method is used to study the influence of temperature distribution and the efficiency of radial fins for different values of thermal conductivity and to determine the role of thermal conductivity, thermo-geometric fin parameter as well as fractional order values in finding the temperature distribution and the fin efficiency of the convective radial fins. Finally, the efficiency of this proposed method has been studied by comparing the obtained results with the classical order results obtained by using numerical method and Variational Iteration Method (Coskun and Atay, 2007).

Performance of Asymmetrically Heated Extended Surface With Temperature Dependent Thermal Conductivity

2006 ◽  
Author(s):  
A. Aziz
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Heat Exchangers ◽  
Numerical Solutions ◽  
Temperature Dependent ◽  
Compact Heat Exchangers ◽  
Extended Surface ◽  
Temperature Dependent Thermal Conductivity ◽  
Perturbation Solutions

The effect of temperature dependent thermal conductivity on the performance of an asymmetrically heated extended surface which is commonly encountered in compact heat exchangers is studied both analytically and numerically. The surface is assumed to extend between two primary surfaces at different temperatures and to operate in a convective environment. The nonlinear differential equation governing the thermal performance of the extended surface is solved by carrying out a perturbation analysis in which the perturbation parameter is the dimensionless measure of thermal conductivity variation with temperature. Two-term analytical solutions for the temperature distribution and the convective heat dissipation are presented. The problem is also solved numerically for a range of conventional fin parameter, thermal asymmetry parameter, and thermal conductivity-temperature variation parameter to assess the accuracy of the perturbation solutions. Graphical results illustrating the effect of these parameters on the temperature distribution, heat transfer rates from the end primary surfaces, and the total heat transfer from the extended surface are provided and discussed. For the thermal conductivity variations encountered in compact heat exchangers, the two-term perturbation solutions are accurate with 2% of the numerical solutions.

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