Multiple solutions for nanofluids flow and heat transfer in porous medium with velocity slip and temperature jump

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.

Automated summary

This study investigates the 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. By transforming the nonlinear partial differential equations into a set of ordinary differential equations, multiple exact solutions are found for both stretching and shrinking problems. The influence of stretching or shrinking and velocity slip parameters in shaping the flow behavior is reported, along with the presentation of velocity and temperature profiles under various parametric values.