Similarity solution of fractional viscoelastic magnetohydrodynamic fluid flow over a permeable stretching sheet with suction/injection

A novel easy-to-use similarity technique for spatial fractional partial differential equations is introduced to solve the flow and heat transfer of fractional viscoelastic magnetohydrodynamic (MHD) fluid over a permeable stretching sheet. The proposed method represents a new technique for deriving similarity transformations, which allows the conversion of the fractional partial differential equations to fractional ordinary differential equations. Moreover, using the Grunwald-Letnikov formula, the fourth-order Runge-Kutta method is adopted here to solve the obtained similarity equations, using the shooting method. The transformed governing equations were found to be dependent on six physical parameters, namely, fractional parameter, magnetic field parameter, generalized local Reynolds number, generalized Prandtl number, the wall suction/injection parameter, and the wall stretching exponential. The results reveal that maximums of the skin friction coefficient and local Nusselt number are obtained for fractional-order derivative of about 0.5. Moreover, application of a magnetic field on electrically conducting fractional fluid thins the velocity boundary layer and thickens the thermal boundary layer; therefore, the skin friction coefficient increases whereas the local Nusselt number decreases. Furthermore, an increase in any parameters of the local Reynolds number, suction parameter, or the wall stretching exponential leads to thinner boundary layers and higher values of skin friction coefficient and local Nusselt number, whereas imposing injection has opposite effects. Finally, increasing the generalized Prandtl number leads to a thinner thermal boundary layer and higher local Nusselt number for the fractional viscoelastic fluid. It would be of interest to extend the proposed method to other practical problems in the same field.