DIFFERENTIAL TRANSFORMATION METHOD FOR SOLVING THE NONLINEAR HEAT TRANSFER EQUATION WITH A VARIABLE SPECIFIC HEAT COEFFICIENT

2012 ◽  
Vol 4 (3) ◽  
pp. 183-191
Author(s):  
Mohsen Torabi ◽  
Hessameddin Yaghoobi
Keyword(s):  
Heat Transfer ◽  
Specific Heat ◽  
Transfer Equation ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Heat Transfer Equation ◽  
Differential Transformation ◽  
Nonlinear Heat Transfer ◽  
Specific Heat Coefficient

A modified firefly algorithm to maximize heat dissipation of a rectangular porous fin in heat exchangers exposed to both convective and radiative environment

2019 ◽  
Vol 233 (6) ◽  
pp. 1203-1216 ◽  
Author(s):  
Tuhin Deshamukhya ◽  
Ratnadeep Nath ◽  
Saheera Azmi Hazarika ◽  
Dipankar Bhanja ◽  
Sujit Nath
Keyword(s):  
Heat Transfer ◽  
Particle Swarm Optimization ◽  
Firefly Algorithm ◽  
Particle Swarm ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Computational Time ◽  
Swarm Optimization ◽  
Differential Transformation ◽  
Porous Fins

The current study deals with the optimization of significant parameters of aluminium and copper rectangular porous fins using firefly algorithm with reflective boundary condition. The study has been done considering convective heat transfer, in the first case, as well as combined convective and radiative modes of heat transfer, in the second case. To solve the non-linear governing equation, a semi analytical technique, differential transformation method is adopted. The results obtained by differential transformation method are validated by the numerical solution obtained by the finite difference method. The performance of firefly algorithm is evaluated by comparing with the results obtained by particle swarm optimization where it is seen that for the current set of equations, firefly algorithm took lesser number of iterations and computational time to converge than particle swarm optimization for all the cases. The analysis has been done for three different fin volumes and the effect of important variables which directly influence the heat transfer rate through porous fins has been discussed.

Differential Transformation Method for the Flow and Heat Transfer Due to a Permeable Stretching Surface Embedded in a Porous Medium With a Second Order Slip and Viscous Dissipation

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
M. M. Khader ◽  
Ahmed M. Megahed
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Transformation Method ◽  
Second Order ◽  
Differential Transformation Method ◽  
Stretching Surface ◽  
Local Skin ◽  
Differential Transformation

This paper is devoted to introduce a numerical simulation using the differential transformation method (DTM) with a theoretical study for the effect of viscous dissipation on the steady flow with heat transfer of Newtonian fluid towards a permeable stretching surface embedded in a porous medium with a second order slip. The governing nonlinear partial differential equations are converted into a system of nonlinear ordinary differential equations (ODEs) by using similarity variables. The resulting ODEs are successfully solved numerically with the help of DTM. Graphic results are shown for nondimensional velocities and temperatures. The effects of the porous parameter, the suction (injection) parameter, Eckert number, first and second order velocity slip parameters and the Prandtl number on the flow and temperature profiles are given. Moreover, the local skin-friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.

scholarly journals Assessment of homotopy perturbation method in nonlinear convective-radiative non-Fourier conduction heat transfer equation with variable coefficient

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 263-274 ◽  
Author(s):  
Mohsen Torabi ◽  
Hessameddin Yaghoobi ◽  
Seyfolah Saedodin
Keyword(s):  
Heat Transfer ◽  
Perturbation Method ◽  
Transfer Equation ◽  
Homotopy Perturbation Method ◽  
Heat Transfer Equation ◽  
Conduction Heat Transfer ◽  
Homotopy Perturbation ◽  
Runge Kutta Method ◽  
Engineering Problems ◽  
Specific Heat Coefficient

Analytical solutions play a very important role in heat transfer. In this paper, the He's homotopy perturbation method (HPM) has been applied to nonlinear convective-radiative non-Fourier conduction heat transfer equation with variable specific heat coefficient. The concept of the He's homotopy perturbation method are introduced briefly for applying this method for problem solving. The results of HPM as an analytical solution are then compared with those derived from the established numerical solution obtained by the fourth order Runge-Kutta method in order to verify the accuracy of the proposed method. The results reveal that the HPM is very effective and convenient in predicting the solution of such problems, and it is predicted that HPM can find a wide application in new engineering problems.

Differential Transformation Method

2017 ◽  
pp. 140-172
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Nonlinear Equation ◽  
Nonlinear Differential Equation ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Differential Transformation

In this chapter, a new linearization procedure based on Differential Transformation Method (DTM) will be presented. The procedure begins with solving nonlinear differential equation by DTM. The effectiveness of the procedure is verified using a heat transfer nonlinear equation. The simulation result shows the significance of the proposed technique.

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