Transient thermal analysis of longitudinal fins with internal heat generation considering temperature-dependent properties and different fin profiles

Variation of parameters method for optimizing annular fins with variable thermal properties

“…(15), an iterative approach is required to solve . The iterative solution begins with an initial guess of the temperature profile.…”

“…On the other hand, Torabi et al [14] worked on same problem by using differential transformation method. Mosayebidorcheh et al [15] studied the transient thermal analysis of longitudinal fins with variable cross section considering internal heat generation. In this study, it is assumed that both thermal conductivity and internal heat generation are as linear functions of temperature.…”

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].…”

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

“…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.…”