Successive linearisation analysis of unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and thermal radiation effects

Abstract

In this study, we investigate the application of the new successive linearisation method (SLM) to the problem of unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and thermal radiation effects. The governing nonlinear momentum, energy and mass transfer equations are successfully solved numerically using the SLM approach coupled with the spectral collocation method for iteratively solving the governing linearised equations. Comparison of the SLM results for various flow parameters against numerical results and other published results, obtained using the homotopy analysis method (HAM) and Runge-Kutta methods, for related problems indicates that the SLM is a very powerful tool which is much more accurate and efficient than other methods. The SLM converges much faster than the traditional methods like the HAM and is very easy to implement.

Application of Successive Linearisation Method to Squeezing Flow with Bifurcation

“…where D = ((2/ )D) and D is the Chebyshev spectral differentiation matrix (see, e.g., [20,21]). Substituting (17)- (19) in (13) results in the matrix equation…”

“…Several approximation techniques have been developed to tackle this problem such as the homotopy analysis method [9][10][11], homotopy perturbation method [12,13], spectral homotopy analysis method [14,15], and variational iteration method [16]. In this paper, we employ the successive linearisation method [17][18][19] to tackle a fourth order nonlinear boundary value problem that governs the squeezing flow problem between parallel plates. In this work, we assess the applicability of the SLM approach in solving nonlinear problems with bifurcations.…”

Thermally Driven Steady MHD Mixed Convective Chemically Reacting Flow over a Hot Porous Linearly Stretching Sheet

“…Upon these imports, Vyas and Srivastava [16] investigated the radiation effects on the MHD flow over a non-isothermal stretching sheet in a porous medium. Motsa and Shateyi [17] studied the problem of unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and thermal radiation effects using successive linearization method, and showed that the results obtained are more accurate and efficient than those obtained by the homotopy method and Runge-Kutta numerical scheme. Vyas and Srivastava [18] studied the radiation effects on MHD boundary layer flow in a porous medium over a non-isothermal stretching sheet in presence of dissipation.…”

On the Comparison between Compact Finite Difference and Pseudospectral Approaches for Solving Similarity Boundary Layer Problems

“…In recent years Motsa and his coworkers [15][16][17][18] have developed successful methods based on the spectral method to solve nonlinear similarity boundary layer problems. The methods include, among others, the spectral relaxation method (SRM) [15,19,20], the spectral successive linearisation method [21][22][23], spectral homotopy analysis method [24][25][26][27], and the spectral quasilinearisation method (SQLM) [16]. The SRM is based on simple decoupling and rearrangement of the governing equations and numerically integrating the resulting equations using the Chebyshev spectral collocation method.…”