Series solution of convective radiative conduction equation of the nonlinear fin with temperature dependent thermal conductivity

The singular boundary method for steady-state nonlinear heat conduction problem with temperature-dependent thermal conductivity

“…Afterwards, the boundary value problem (15) or (16) can be solved in a collocation sense by satisfying the boundary conditions at the N points. More details about the SBM can be found in the literatures [34][35][36].…”

“…One-dimensional nonlinear heat conduction problem has been solved with some semi analytical methods, such as the perturbation method (PM) [11,12], the variational iteration method (VIM) [13], the homotopy analysis method (HAM) [14], the differential transform method (DTM) [3][4][5][6]15,16] and the Adomian decomposition method (ADM) [8,17]. Two-dimensional boundary value problems have been the subject of several studies using the ADM [9], the finite element method (FEM) [18][19][20], the boundary element method (BEM) [21][22][23], the method of fundamental solutions (MFS) [24,25], the fundamental solution-based hybrid finite element method (HFS-FEM) [26], the hybrid Trefftz finite element method (HT-FEM) [27] or the boundary knot method (BKM) [28,29].…”

Investigation of the viscoelastic flow and species diffusion in a porous channel with high permeability

“…The residual vector can be obtained by substituting (a 1 , a 2 , a 3 ) n in Eq. (20). The components of the Jacobian matrix in Eq.…”

“…He used this method to derive the semi analytical solution for the electrical circuit analysis. A considerable amount of researches have been done using DTM to investigate the solution of linear differential algebraic equations [19], nonlinear ordinary differential equations [20][21][22][23][24], partial differential equations [25], fractional differential equations [26] and integral equations [27]. DTM is a powerful and simple technique which is well known as a high accurate technique for solving the differential equations.…”

Analytical solution of the steady state condensation film on the inclined rotating disk by a new hybrid method

“…This method was introduced by Zhou (1986) to solve initial value problems in analysis of the electrical circuits. After that, DTM applied to differential algebraic equation Liu and Song, 2007) partial differential equation (Ayaz, 2003Ravi-Kanth and Aruna, 2008;Yang et al, 2006;Chang and Chang, 2009), integral equation (Odibat, 2008;Ozkol, 2005, 2008), ordinary differential equation (Mosayebidorcheh, 2014;Mosayebidorcheh and Mosayebidorcheh, 2012;Torabi and Aziz, 2012;Joneidi et al, 2009) and fractional differential equation (Nazari and Shahmorad, 2010;Odibat et al, 2008;Erturk et al, 2008;Arikoglu and Ozkol, 2007). The method is an iterative technique to find the Taylor series solution of the problem.…”