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

2007 ◽  
Vol 364 (1) ◽  
pp. 33-37 ◽  
Author(s):  
A. Rajabi
Keyword(s):  
Thermal Conductivity ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Homotopy Perturbation ◽  
Temperature Dependent Thermal Conductivity

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.

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.

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.

Convective Fins Problem with Variable Thermal Conductivity: An Approach Based on Embedding Green’s Functions into Fixed Point Iterative Schemes

2016 ◽  
Vol 71 (12) ◽  
pp. 1105-1110
Author(s):  
H.Q. Kafri ◽  
S.A. Khuri ◽  
Ali Sayfy
Keyword(s):  
Thermal Conductivity ◽  
Fixed Point ◽  
Current Method ◽  
Numerical Approach ◽  
Variable Thermal Conductivity ◽  
Iteration Scheme ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Range Of Values ◽  
Temperature Dependent Thermal Conductivity

AbstractThis article introduces a new numerical approach to solve the equation that models a rectangular purely convecting fin with temperature-dependent thermal conductivity. The algorithm embeds an integral operator, defined in terms of Green’s function, into Krasnoselskii–Mann’s fixed point iteration scheme. The validity of the method is demonstrated by a number of examples that consist of a range of values of the parameters that appear in the model. In addition, the evaluation of the fin efficiency is presented. The residual error computations show that the current method provides highly accurate approximations.

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