MHD 3D nanofluid flow over nonlinearly stretching/shrinking sheet with nonlinear thermal radiation: Novel approximation via Chebyshev polynomials’ derivative pseudo-Galerkin method

Abstract

This research work aims to theoretically examine the influence of various factors on the three-dimensional nanofluid flow. The study includes parameters such as temperature ratio coefficient, Prandtl numbers, Schmidt, Soret, Dufour, Biot, expansion ratio coefficient, Power index, and nanoparticle volume fraction parameter, as well as the effect of non-linear thermal radiation and magnetic parameter on the behavior of the nanofluid. These characteristics significantly impact the flow of the three-dimensional boundary layer in the presence of an expansion plate. To facilitate the investigation, we have selected nanofluids that contain water-based copper and aluminum oxide for this study. We have developed a model of a system of partial differential equations (SYS-PDEs) with non-linear terms. Based on selected similarity equations, the SYS-PDEs with non-linear terms has been transformed into a system of ordinary differential equations (SYS-ODEs) whose terms are non-linear. To approximate and solve the obtained SYS-ODEs, we utilized a modified spectral Chebyshev polynomials’ first derivative pseudo-Galerkin spectral method. Additionally, we conducted an error analysis discussion to ensure the credibility of our results. We presented our analysis in graphical form and provided comments on each figure along with the effects of the various parameters studied. Consequently, we concluded that the power low is an essential factor affecting the flow’s behavior, such as the nanofluid’s velocity, temperature, and concentration.

Keywords

• MHD
• Nanofluid
• Magnetic field
• Boundary layer flow
• Pseudo-Galerkin method
• Chebyshev polynomials’ first derivative