scholarly journals Thermal performance of porous fins with temperature-dependent heat generation via the homotopy perturbation method and collocation method

2015 ◽  
Vol 14 (4) ◽  
pp. 53-65 ◽  
Author(s):  
Hossein Ali Hoshyar ◽  
◽  
Iman Rahimipetroudi ◽  
Davood Domiri Ganji ◽  
Ali Reza Majidian ◽  
...  
Keyword(s):  
Perturbation Method ◽  
Collocation Method ◽  
Heat Generation ◽  
Thermal Performance ◽  
Homotopy Perturbation Method ◽  
Temperature Dependent ◽  
Homotopy Perturbation ◽  
Porous Fins

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

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.

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.

Homotopy perturbation method for temperature distribution, fin efficiency and fin effectiveness of convective straight fins with temperature-dependent thermal conductivity

2012 ◽  
Vol 227 (8) ◽  
pp. 1754-1760 ◽  
Author(s):  
Erdem Cuce ◽  
Pinar Mert Cuce
Keyword(s):  
Thermal Conductivity ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Rapid Assessment ◽  
Thermal Design ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Homotopy Perturbation ◽  
Infinite Power ◽  
Temperature Dependent Thermal Conductivity

Homotopy perturbation method is a novel approach that provides an approximate analytical solution to differential equations in the form of an infinite power series. In our previous work, homotopy perturbation method has been used to evaluate thermal performance of straight fins with constant thermal conductivity. A dimensionless analytical expression has been developed for fin effectiveness. In this study, homotopy perturbation method has been applied to convective straight fins considering thermal conductivity of the fin material is a function of the fin temperature. Former expression for fin effectiveness has been rearranged. The fin efficiency and the fin effectiveness have been obtained as a function of thermo-geometric fin parameter. The results have revealed that homotopy perturbation method is a very effective and practical approach for a rapid assessment of physical systems even if the energy balance equations include terms with strong nonlinearities. The resulting correlation equations can assist thermal design engineers for designing of straight fins with both constant and temperature-dependent thermal conductivity.

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