In this paper, the unsteady motion of Casson liquid over a half‐infinite penetrable vertical plate with MHD, thermal radiation, Soret, and Dufour contributions have been explored numerically. In the physical geometry, the Casson liquid flows to the layer from the penetrable vertical plate. At the layer, Casson liquid is set into motion and the flow equations are illustrated using coupled partial differential equations (PDEs). This set of PDEs is simplified to form dimensionless PDEs with the use of normal nondimensional transformation. The controlling parameters' effects on the working fluid are extensively discussed on velocity, concentration, and temperature and presented graphically. Computational values of Nusselt plus Sherwood number and skin friction for controlling parameters are depicted in a tabular form. Our outcomes show that a raise in the Casson term depreciates the velocity because of the magnetic parameter influence on the fluid flow. The Soret parameter was found to accelerate the skin friction along with the Sherwood number coefficients. An incremental value of the Dufour parameter was detected to hike the skin friction alongside the Nusselt number. Results of this study were found to be in conformity with previously published work.

In this analysis, the effect of Catteneo–Christov model on heat alongside mass transport magnetohydrodynamics of a Casson nanoliquid with thermal radiation and Soret–Dufour mechanism is considered. The fluid flow is considered through porous media as the thermophysical attributes such as viscosity along with thermal conductivity are considered to be constant. Suitable similarity transformations were employed on the governing coupled flow equation to yield total differential equations (ODE). An accurate and newly developed spectral method called spectral homotopy analysis method (SHAM) was employed to provide solution to the simplified equations. The numerical method of homotopy analysis method (HAM) is SHAM. SHAM portrays the division of nonlinear equations into linear as well as nonlinear parts. The findings in this study show that an increment in the Casson parameter is seen to elevate the velocity plot at the wall and lessen the velocity far away from the plate. An increase in the Brownian motion and thermophoresis term is observed to speed up the local skin friction coefficient.

The primary goal of this research is to study the Cattaneo-Christov heat flux model on the impacts of mass and energy transit of MHD Casson-Carreu nanofluid through a permeable vertical accelerating plate with Soret and Dufour mechanism. The non-Newtonian fluids flowed over the porous vertical plate to reach the boundary layer in this investigation. In order to understand the physical model, partial differential equations (PDEs) are used. To get a linked nonlinear set of ordinary differential equations (ODEs), we reduced this set of PDEs by using similarity variables. SHAM, a spectrum basis technique, was utilized to solve these modified equations to understand the physical significance. A good method is to utilize SHAM to decouple the coupled nonlinear ODE systems and divide them into linear and nonlinear equation sets since this helps to separate the systems. As a result, the two non-Newtonian fluids (Carreu and Cassin) flow together through the vertical wall and into the boundary layer, where different parameters’ impacts are scrutinized. The current results showed that an upturn in the Casson parameter (β) degenerates the boundary layer velocity and the total thickness. Upturn in the Weissenberg number (We) on the other hand, raises the velocities and temperatures in both directions. Additionally, increasing the Soret and Dufour parameters sped up the velocity graph.