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

Abstract

Abstract. 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.

Optimum Design and Performance Analyses of Convective-Radiative Cooling Fin under the Influence of Magnetic Field Using Finite Element Method

“…The development of exact analytical solutions for such nonlinear models is very difficult. Consequently, some of the past studies have developed approximate analytical solution in terms of series solutions for the thermal analyses of fins using different approximate 2 Journal of Optimization analytical methods [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Nevertheless, the series solutions involve large number of terms.…”

Heat transfer analysis of non-Newtonian natural convective fluid flow using homotopy perturbation and Daftardar-Gejiji & Jafari methods

“…It is an exact analytical tool that does not require any approximation. Various studies have been done with the Homotopy Perturbation Method (HPM) such as use of the Homotopy Perturbation Method for the analysis of heat transfer in longitudinal fins [18], the use of the Homotopy Perturbation Method (HPM) and collocation method (CM) for analysis of thermal performances of porous fin with temperature-dependent heat generation [19] and the Homotopy perturbation method for a three dimensional problem of condensation film on an inclined rotating disk [20]. Another method used in this study for solving the problem of heat transfer of a non-Newtonian natural convective fluid flow between two vertical infinite flat plates is a new iterative method called the Daftardar-Jafari method (DJM).…”

Application of Approximate Analytical Technique Using the Homotopy Perturbation Method to Study the Inclination Effect on the Thermal Behavior of Porous Fin Heat Sink

“…a combination of two or more methods to investigate the thermal behaviour of fin under different operating conditions. Example of these methods include: Runge-Kutta [4][5][6], Galerkin's method of weighted residual [7,8], least squares method [9], and various collocation methods, including Haar wavelet [10,11], spectral [12], Chebychev [13][14][15], spectral element [16], Legendre [17], Adomian decomposition method [18,19], differential transform method [20][21][22], variational iteration method [23], homotopy analysis method [24], and hybrid methods [25][26][27]. Furthermore, in the quest to enhance the performance of fins, especially porous fins, different authors are investigating various thermal characteristics of porous fin including material, geometry, orientation, and composition are investigated to achieve heat transfer enhancement and augmentation.…”