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2 Journal of Applied Mathematics and Computational Mechanics

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Thermal analysis of longitudinal a porous fin with temperature-dependent internal heat generation using the variation of parameters method

Güngör Osman, Arslantürk Cihat

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 3

5--16

The present study investigates the thermal performance of longitudinal a porous fin with temperature-dependent internal heat generation. The Darcy model is utilized to obtain the differential form of the governing equation that solves the nonlinear temperature distribution equation using the method of variation of parameters. Although this method is applied to solve both linear and nonlinear differential equations, there exist rare applications of this method to solve nonlinear heat transfer problems. In the present study, we applied the method to estimate the thermal analysis of the porous fin exposed to convection. The heat generation is assumed as a function of temperature. The effects of the convection parameter Nc, internal heat generation ɛ, porosity Sh, and generation number G parameter on the dimensionless temperature distribution are discussed in detail. The accuracy of the variation of parameters method is verified through comparison with homotopy perturbation method and the Matlab bvp4c solver (NUM). The results have disclosed that the variation of parameters method can be used as a very effective and practical approach for further studies of the porous medium.

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

Hoshyar H. A., Rahimipetroudi I., Ganji D. D., Majidian A. R.

Journal of Applied Mathematics and Computational Mechanics

2015

Vol. 14, nr 4

53--65

An analysis has been performed to study the problem of the thermal performance of a nonlinear problem of the porous fin with temperature-dependent internal heat generation. Highly accurate semi-analytical methods called the collocation method (CM) and the homotopy perturbation method (HPM) are introduced and then are used to obtain a nonlinear temperature distribution equation in a longitudinal porous fin. This study is performed using passage velocity from the Darcy’s model to formulate the heat transfer equation through porous media. The heat generation is assumed to be a function of temperature. The effects of the natural convection parameter Nc, internal heat generation εg, porosity Sh and generation number G parameter on the dimensionless temperature distribution are discussed. Also, numerical calculations called the fourth order Runge-Kutta method were carried out for the various parameters entering into the problem for validation. Results reveal that analytical approaches are very effective and convenient. Also it is found that these methods can achieve more suitable results compared to numerical methods.