Implementing the spectral relaxation method for MHD Casson and Williamson model under the effects of heat generation and viscous dissipation

Abstract

The nonlinear system of ordinary differential equations (ODEs) that represents the model of non‐Newtonian Casson and Williamson fluid flow and heat mass transfer on the slendering stretched surface immersed in a porous medium is solved and successfully treated by using the spectral relaxation method (SRM). In this physical model, which is dependent linearly on temperature, we investigate the impact of thermal conductivity viscous dissipation. The primary purpose of this research is to look at how the physical elements affecting the problem affect velocity, temperature, and concentration profiles. The Gauss–Seidel principle is also used in the SRM to break down the resulting nonlinear system of ODEs into smaller linear systems. We utilize this approach because it solves the problem accurately, quickly, and with little programming effort. We give particular focus on demonstrating the SRM's stability and convergence rate. The findings reveal that the skin friction coefficient grows as the magnetic number increases, whereas the Casson and local Williamson parameters behave oppositely. Additionally, the Nusselt number is further enhanced by improving the local Williamson parameter contrary to the decreasing trend with the thermal conductivity parameter and Eckert number. The numerical results show that the suggested methodology enhances the method's computing speed and gives improved accuracy, which we can confirm. Additionally, the SRM speeds up convergence to the necessary solution.