MHD Carreau fluid slip flow over a porous stretching sheet with viscous dissipation and variable thermal conductivity

Abstract The aim of this article is to investigate MHD Carreau fluid slip flow with viscous dissipation and heat transfer by taking the effect of thermal radiation over a stretching sheet embedded in a porous medium with variable thickness and variable thermal conductivity. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The constitutive equations of Carreau fluid are modeled in the form of partial differential equations (PDEs). Concerning boundary conditions available, the PDEs are converted to ordinary differential equations (ODEs) by means of similarity transformation. The homotopy analysis method (HAM) is used for solution of the system of nonlinear problems. The effects of various parameters such as Weissenberg number We 2 $\mathit{We}^{2}$ , magnetic parameter M 2 $M^{2}$ , power law index n, porosity parameter D, wall thickness parameter α, power index parameter m, slip parameter λ, thermal conductivity parameter ε, radiation parameter R and Prandtl number on velocity and temperature profiles are analyzed and studied graphically.