Effect of Joule Heating and Thermal Radiation of MHD Boundary Layer Oldroyd-B Nanofluid Flow with Heat Transfer over a Porous Stretching Sheet by Finite Element Method

Abstract

In this study, an incompressible two-dimensional Oldroyd-B nanofluid steady flow past a stretching sheet considering the outcomes of magneto-hydrodynamics (MHD) and porous medium with magnetic, electrical, and thermal radiation effects is investigated. Using a similarity transformation, the governing equations in the form of partial differential equations (PDEs) are converted into a nonlinear ordinary differential equations (ODEs) system. The acquired system is numerically solved by the finite element method (FEM). The effects of physical parameters like Deborah numbers “ ${\beta }_1$ ” and “ ${\beta }_2$ ”, Brownian motion “ $N_b$ ”, thermophoresis parameter “ $N_t$ ”, Prandtl parameter “ $\mathrm{Pr}$ ”, Lewis number “ $L_e$ ”, thermal conductivity “ $k$ ”, dynamic viscosity “μ”, magnetic and electric effects as “ $M$ ” and “ $E_1$ ”, and thermal radiation effect “ $\text{Rd}$ ” on the flow are studied in detail. For higher $N_b$ values, regional Nusselt numbers are increasing in magnitude. The local Sherwood number’s size rises for high $N_b$ numbers.