Abstract
Fluid flow and heat transfer of water-based nanofluids over a stretching/shrinking permeable sheet with porous environment under velocity slip and temperature jump conditions is investigated. The flow phenomenon is instigated by a two-dimensional boundary layer flow. On exercising suitable similarity variables, the resulting physical system of nonlinear partial differential equations is transformed into a set of ordinary differential equations. The existence and nonexistence of multiple exact solutions in both the stretching and shrinking problems for various parameters domains is shown. The prominency of stretching or shrinking and velocity slip parameters in shaping the flow behavior and resulting in special exact solutions are reported under various parametric values. The shrinking surface flow exhibit different behavior than the stretching case problem and produces physically meaningful dual solutions. The solutions for the flow and temperature equations are obtained in the form of Kummers function, exponential integral and Eulers gamma function. Morover, results are shown for velocity and temperature profiles for inclusive graphical illustration that includes the influence of velocity slip parameter, temperature jump, permeability and Prandtl number. Moreover, the critical values and plotting curves for obtaining single or dual solution are successfully presented.