Numerical Analysis Of The Bivariate Local Linearization Method (BLLM) For Partial Differential Equations In Casson Fluid Flow

Abstract

The double diffusion convection Casson fluid flow along a vertical plate incorporating Soret effect and viscous heating with thermal and solutal dispersion was studied. A well-known system of non-similar partial differential equations was solved using the bivariate local linearization method (BLLM). The solution procedure uses an approximation by a bivariate Lagrange interpolation polynomial. Older methods considered collocations along the non-dimensional boundary layer axis η only. In this paper collocations in both the (η, ζ) directions are considered. The numerical method is compared to the results obtained by the quasi-linearization method (QLM) and those previously published in the literature for the case (ζ = 0). This work also analyse the efficiency and robustness of the numerical method used as compared to traditional methods such as finite differences widely used in the literature. The increase in thermal stratification parameter decrease heat transfer coefficient and increase mass transfer coefficient. The increase in the non-Newtonian parameter result in the increase velocity profiles, skin friction coefficient and reduce both temperature and concentration profiles. Increasing the Biot number decrease temperature trends.