An Analytical Study on a Model Describing Heat Conduction in Rectangular Radial Fin with Temperature-Dependent Thermal Conductivity

Abstract

The coupling of the homotopy perturbation method (HPM) and the variational iteration method (VIM) is a strong technique for solving higher dimensional initial boundary value problems. In this article, after a brief explanation of the mentioned method, the coupled techniques are applied to one-dimensional heat transfer in a rectangular radial fin with a temperature-dependent thermal conductivity to show the effectiveness and accuracy of the method in comparison with other methods. The graphical results show the best agreement of the three methods; however, the amount of calculations of each iteration for the combination of HPM and VIM was reduced markedly for multiple iterations. It was found that the variation of the dimensionless temperature strongly depends on the dimensionless small parameter ε 1 . Moreover, as the dimensionless length increases, the thermal conductivity of the fin decreases along the fin.

A novel and developed approximation for motion of a spherical solid particle in plane coquette fluid flow

“…One of the recent analytical methods used in the literature, namely, the Homotopy Perturbation Method (HPM) which was firstly proposed by Chinese mathematician Ji-Huan He [1][2][3][4][5][6][7][8] has attracted special attention of researchers as it is flexible in applying and gives sufficiently accurate results with modest effort. This method is a powerful series-based analytical tool that has been used by many authors [9][10][11][12][13][14] however, the convergence region of the obtained truncated series approximation is limited and in the best case scenario, it needs some enhancements to enlarge the convergence region of the approximate solution. It is well known that Padé approximations which was presented by Padé in 1892 [15], have the advantage of manipulating the polynomial approximation into a rational function of polynomials.…”

Evaluation of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field by the differential transformation method

“…1 Nu 0 Re x x (19) Kuznetsov and Nield [31] referred to Re x -1/2 Nu x as the reduced Nusselt number. Applying the differential transformation on the equation (15) we get:…”

“…For computing its value, the problem is solved with initial conditions. Pade approximation [16][17][18][19][20] is used and then the third boundary condition is applied. When = 0.1 and M = 2 with [10,10] Pade approximation the obtained is: …”

Series solution of entropy generation toward an isothermal flat plate

“…Like -------------- , entropy generation is a non-linear equation which usually does not have an exact solution and there is a certain need to find a technique to solve it. To overcome this problem, in this paper we have employed homotopy perturbation method (HPM) [9] which was presented by He in 1998. The application of HPM has been raised exponentially in engineering which can be gauged from Ganji's studies [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In order to explain the physical interpretations, Bejan number is computed for different cases and the effects of Ec, Re, and Pr on entropy generation have been shown graphically.…”