LAUSR

This research article presents the unsteady natural convection of Maxwell viscoelastic fluid based on boundary layer heat transfer. The stretching sheet on lower wall of fluid with exponential time dependent viscosity is implemented. The fractional derivative based governing equations of Maxwell fluid model are derived. These governing equations are used to derive nonlinear coupled partial differential equations (PDEs) which involves space and time derivatives in convection terms. By employing the Finite Difference Method with L1-algorithm, to solve system of nonlinear coupled PDEs and presented via graphically. The effects of fractional and physical parameters on velocity, temperature and particular fractional parameters effect on average skin friction coefficient $$\bar{Cf}$$ and average Nusselt number $$\bar{Nu}$$ are discussed in details. For instance, the thickness of velocity boundary layer increases in response to increase in fractional parameter $$\alpha $$ , whereas heat conduction reduces in response to increase in fractional parameter $$\gamma $$ .