Numerical treatment via the spectral collocation method for Casson–Williamson nanofluid flow due to a stretching sheet with slip conditions

Abstract

The main goal of the research is to investigate the effects of temperature and concentration slip on the MHD Casson–Williamson nanofluid flow through a porous sheet, with a focus on viscous dissipation. This research has a novel approach, as it seeks to incorporate various factors that have not been previously studied in this context. Moreover, an inclined magnetic field from the outside is applied to the stretched surface. Besides this, it is considered that the viscosity of nanofluids depends on temperature while all other physical characteristics are taken to be constant. It is hypothesized that the expanding surface that stretched exponentially is what caused the flow motions of the nanofluid. There are several engineering applications for this type of study, which is based on MHD non-Newtonian nanofluid flow across a stretched surface with heat generation and viscous dissipation. They include solar energy storage, energy distribution, chemical reactors, and the manufacturing of polymers. To examine the heat transmission and mass transfer rates, tools like thermophoresis and Brownian motion were implemented. The flow problem is formally represented as a set of nonlinear PDEs that are then, through the use of dimensionless variables, converted into a set of ODEs. To numerically obtain the solution to the problem, the shifted Chebyshev polynomials of the third-kind approximation along with the spectral collocation technique are utilized. This process transforms the existing model into an algebraic equation system that was created as a restricted optimization problem, which is then optimized to obtain the solution and the unknown coefficients. For a variety of pertinent parameter values, the graphic and tabular representations of the concentration, temperature, velocities, rate of heat mass transfer, and shear stresses of nano-fluids at the surface of the sheet are shown. Finally, there is a remarkable amount of agreement between the earlier investigation and the comparison research that was conducted. The findings suggest that higher values of the magnetic parameter, Casson parameter, viscosity parameter, and suction parameter lead to a decrease in both velocity and boundary layer thickness. Furthermore, an increase in the viscosity parameter, Casson parameter, and magnetic parameter results in elevated values for both temperature and concentration.