Application of the variational iteration method to nonlinear non‐Fourier conduction heat transfer equation with variable coefficient

Abstract

In this paper, a variational iteration method (VIM) has been applied to nonlinear non-Fourier conduction heat transfer equation with variable specific heat coefficient. The concept of the variational iteration method is introduced briefly for applying this method for problem solving. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. The results of VIM 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 VIM is very effective and convenient in predicting the solution of such problems, and it is predicted that VIM can find a wide application in new engineering problems.

Two dominant analytical methods for thermal analysis of convective step fin with variable thermal conductivity

“…The primary purpose of the present paper is to demonstrate the usefulness of DTM and VIM to solve problem of convective heat transfer from a step fin with temperature dependent thermal conductivity. Thermal analysis of step fins is a new application for DTM and VIM which were used for other engineering applications [20][21][22][23]. The results to be presented will highlight the effects of the thickness ratio, a, dimensionless fin semi thickness, d, length ratio, l, thermal conductivity parameter, b, and Biot number, Bi, on the temperature distribution.…”

Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

“…Torabi et al [29] applied the homotopy perturbation method (HPM) to solve a non-linear convective-radiative non-Fourier conduction heat transfer equation with variable specific heat coefficient. Saedodin et al [30] used the variational iteration method (VIM) to solve the same problem. Differential transformation method (DTM) was applied to analysis of non-linear convective-radiative hyperbolic lumped systems with simultaneous variation of temperature-dependent specific heat and surface emissivity by Torabi et al [31].…”

Assesment of New Analytical Method for Solving the Foam Drainage Equation

“…In recent years, several such techniques have drawn special attention, such as inverse scattering method [19], Adomian decomposition method [20,21], Hamiltonian approach [22], variational iteration method [23][24][25], homotopy analysis method [26,27], variational approach [28], and homotopy perturbation method [29][30][31][32][33][34][35][36][37][38].…”