The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell
fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential
equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical
technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing
non-linear boundary value problem is based on applying the fourth-order Runge–Kutta method coupled with the shooting
technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter,
thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl
number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number
are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting
cases.