Joule heating effects on MHD mixed convection of a Jeffrey fluid over a stretching sheet with power law heat flux: A numerical study

• The non-linear coupled ordinary differential equations are solved numerically using fourth order Runge–Kutta method along with shooting technique.
• The Deborah number ββ has opposite effects on skin friction and Nusselt numbers.
• The Nusselt number decreases in view of increase in Ec.
• Larger values of magnetic field parameter M has opposite effect on velocity and temperature profiles.

An analysis has been carried out to study the Joule heating effect on MHD heat transfer of an incompressible Jeffrey fluid due to a stretching porous sheet with power law heat flux and heat source. A constant magnetic field is applied normal to the stretching surface. The basic governing equations are reduced into the coupled nonlinear ordinary differential equations by using similarity transformations. The resulting equations are then solved numerically by shooting method with fourth order Runge–Kutta scheme. The effects of various physical parameters entering into the problem on dimensionless velocity and temperature distribution are discussed through graphs and tables. The results reveal that the momentum and thermal boundary layer thickness are significantly influenced by Deborah number (β), ratio of relaxation and retardation times parameter (λ  ), heat generation parameter (β*β*), Eckert number (EcEc) and magnetic field parameter (M). A comparison with the previously published works shows excellent agreement.