DefinePK

Abstract

In this paper, a new approach for solving the system of coupled nonlinear partial differential equations that model fluid flow problems. The method, called the large parameter spectral perturbation method (LSPM) uses series expansion about a large parameter to decompose the system of partial differential equations (PDEs) into a sequence of ordinary differential equations (ODEs). The sequence of ODEs is then solved using the Chebyshev spectral collocation method. The LSPM is tested on a coupled three-equation system that models the problem of natural convection heat transfer flow through a magnetized vertical permeable plate for liquid metals. The accuracy of the LSPM is tested against the multi-domain bivariate spectral quasilinearisation method (MD-BSQLM) which is an approach that uses the quasilinearisation technique to linearise the nonlinear PDEs first and thereafter using the Chebyshev spectral collocation method to solve the governing equations on a sequence of smaller non-overlapping sub-intervals. The approximate numerical results indicate that the LSPM is an accurate and computationally efficient method for solving coupled nonlinear systems of PDEs defined over a large parameter interval. The numerical results obtained are presented graphically to show the effect of different parameters on the temperature, velocity profiles and transverse component field for different values of some of the parameters. Approximate numerical results for local skin friction, current density, and rate of heat transfer are presented in tabular forms. Residual error graphs are presented in order to further show the accuracy of the LSPM. We remark also that this paper aims at correcting the errors introduced by wrong transformations evident in the system of equations which have been chosen from literature for the numerical experiment.