A third-order two-step numerical scheme for heat and mass transfer of chemically reactive radiative MHD power-law fluid

Abstract

A two-stage third-order numerical scheme is proposed for solving ordinary differential equations. The scheme is explicit and implicit type in two stages. First, the stability region of the scheme is found when it is applied to the linear equation. Further, the stability conditions of the scheme are found using a linearized homogenous set of differential equations. This set of equations is obtained by applying transformations on the governing equations of heat and mass transfer of incompressible, laminar, steady, two-dimensional, and non-Newtonian power-law fluid flows over a stretching sheet with effects of thermal radiations and chemical reaction. The proposed scheme with an iterative method is employed in two different forms called linearized and non-linearized. But it is found that the non-linearized approach performs better than the linearized one when residuals are compared through plots. Additionally, the proposed scheme is compared to the second-order central finite difference method for second-order non-linear differential equations and the Keller-Box/trapezoidal method for a linear differential equation. It is determined that the proposed scheme is more effective and computationally less expensive than the standard/classical finite difference methods. Moreover, the impact of magnetic parameter, radiation parameter, modified Prandtl and Schmidt numbers for power-law fluid, and chemical reaction rate parameter on velocity, temperature, and concentration profiles are displayed through graphs and discussed. The power-law fluid’s heat and mass transfer simulations are also carried out with varying flow behavior index, sheet velocity, and mass diffusivity. We hoped that this effort would serve as a guide for investigators tasked with resolving unresolved issues in the field of enclosures used in industry and engineering.

A new explicit numerical scheme for enhancement of heat transfer in Sakiadis flow of micro polar fluid using electric field

“…The proposal can address problems in various research and engineering fields in addition to existing methods. Following the completion of this work, it will be possible to propose other applications for the currently employed methodology if desired [ 47 , 48 , 49 ]. The proposed scheme can be further applied to solve different problems in science and engineering with high accuracy.…”

MHD viscoelastic nanofluid flow across an extended plate using mixed convection and thermal radiation

“…Shukla et al (2019) established a non-similar result for a non-Newtonian fluid by means of an indigenous non-similar way. Some more related literature studies can be seen (Nawaz et al, 2021;Nawaz et al, 2022a;.…”