A numerical study for three-dimensional viscoelastic flow inspired by non-linear radiative heat flux

• Three-dimensional flow of upper-convected Maxwell fluid.
• Novel idea of non-linear radiative heat transfer is addressed.
• Comparative study with the previously published results is presented.
• Interesting S-shaped temperature profiles exist in a particular case.

Present article examines the three-dimensional flow of upper-convected Maxwell (UCM) fluid over a radiative bi-directional stretching surface. Novel non-linear Rosseland formula for thermal radiation is utilized in the formulation of energy equation. The conventional transformations lead to a strongly non-linear differential system which is treated numerically through Runge–Kutta integration procedure together with the shooting approach. We found that heat transfer rate from the sheet has inverse as well as non-linear relationship with wall to ambient temperature ratio. Moreover an increase in viscoelastic fluid parameter (Deborah number) corresponds to a decrease in the fluid velocity and the boundary layer thickness.