**Abstract**

The present chapter aims at investigating the magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a non-Newtonian fluid over a stretching surface through a porous medium. Casson fluid model is utilized to describe the non-Newtonian fluid behavior. Two types of nanofluids, that is, Ag-water and Cuwater, are studied. The governing partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Keller box method. Numerical results are obtained for the velocity, temperature, skin friction coefficient and Nusselt number. The influence of the various governing parameters viz. Casson parameter, magnetic parameter, porosity parameter and Prandtl number on the flow and heat transfer characteristics of the nanofluids is plotted graphically and discussed in detail. The chapter shows that with an increase in the Casson parameter, the velocity field decreases whereas the temperature profile increases. A decrease in the momentum boundary layer thickness and an increase in the thermal boundary layer thickness are noted with an increase in the magnetic parameter.

**Keywords:** magnetohydrodynamic, Casson fluid, porous medium, stretching sheet
