Approximate solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient

A new algorithm based on differential transform method for solving multi-point boundary value problems

“…The interested readers are referred to some recent Refs. [15,39,41,42,52,53]. To our best knowledge, this is the first work concerning the DTM to solve the multi-point BVPs.…”

Heat transfer study in a convective-radiative fin with temperature-dependent thermal conductivity and magnetic field using variation parameters method

“…Hosseini et al [16] applied the homotopy analysis method to provide approximate but accurate solution of heat transfer in a fin with temperature-dependent internal heat generation and thermal conductivity. Joneidi et al [17], Moradi and Ahmadikia [18] Moradi [19], Mosayebidorcheh et al [20], Ghasemi et al [21], Sandri et al [22], Ganji and Dogonchi [23] presented analytical solution for a fin with temperature dependent thermal coefficient using the differential transform method (DTM). Method of weighted residual are applied by Lederi et al [24] and Sobamowo [25] to the problem.…”

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

“…Fins are used to increase the heat transfer of heating systems such as, cooling electric transformers, cooling of computer processor, IC engines, air conditioning and refrigeration. In the heat transfer problems in high-temperature environments or if large temperature differences exists within a fin the assumption of the temperature dependence of the thermal conductivity is necessary [3][4][5][6][7][8][9][10]. This assumption leads to nonlinearity of governing equation.…”

“…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].…”