Non-similar Cross fluid flow with modified Darcy's law

•Dissipative flow of rheological material by Riga plate is addressed.•Modified Darcy's law concept is discussed.•Flow is induced by the linear stretching velocity.•Heat transfer by dissipation is accounted. This research investigates rheological material flow by Riga plate. Non-Newtonian material through Cross model is considered. Unlike traditional concept, a revised version of Darcy's law is employed to predict the fluid flow filling porous space. Flow is induced by the linear stretching velocity. Heat transfer by dissipation is accounted. Appropriate transformations yield the governing problems for computations. Series solutions are computed by Optimal homotopy analysis method (OHAM). Convergence of solutions is analyzed. Velocity, temperature and entropy rate are analyzed. Major findings are included in final remarks.