Application of homotopy analysis method for natural convection of Darcian fluid about a vertical full cone embedded in pours media prescribed surface heat flux

Convection from an inverted cone in a porous medium with cross-diffusion effects

“…Cheng [14] studied the Dufour and Soret effects on the steady boundary layer flow due to natural convection heat and mass transfer over a downward-pointing vertical cone embedded in a porous medium saturated with Newtonian fluids with constant wall temperature and concentration. The study extends the earlier work by Sohouli et al [24] to include Dufour and Soret effects.…”

“…Thermal-diffusion and diffusion-thermo effects on mixed free and forced convection in boundary layer flow in clear fluids with temperature dependent viscosity have been studied by among others, Kafoussias and Williams [20], Chamkha and Ben-Nakhi [21], Sovran et al [22] and Postelnicu [23]. Sohouli et al [24] applied the homotopy analysis method to study natural convection of Darcian fluid about a vertical cone embedded in porous media with a prescribed surface heat flux to get the analytical solutions of the governing nonlinear equations.…”

Analytical expressions of concentration of nitrate pertaining to the electrocatalytic reduction of nitrate ion

“…Liao [36,37] proposed a powerful analytical method for solving nonlinear problems, namely the homotopy analysis method (see Appendix A). Different from all reported perturbation and nonperturbative techniques, the homotopy analysis method [38][39][40][41][42][43] itself provides us with a convenient way to control and adjust the convergence region and rate of approximation series, when necessary. Briefly speaking, the homotopy analysis method has the following advantages: It is valid even if a given nonlinear problem does not contain any small/large parameters at all; It can be employed to efficiently approximate a nonlinear problem by choosing different sets of base functions.…”

Implementation of Homotopy Analysis Method on circular permeable slider containing of incompressible Newtonian fluid

“…Recently, several new techniques have been presented to overcome the mentioned difficulties. Some of these techniques include Variational Iteration Method (VIM) [9][10], decomposition method [11], Homotopy Perturbation Method (HPM) [12] [13] and Homotopy Analysis Method [14,15,16,17,18,19,20,21,22] etc. The Homotopy Analysis method (HAM) has been introduced by Liao in 1992.…”