Computational Analysis of Thermal Radiative Mixed Convection Nanofluid Flow Past a Deformable Sheet With Convective Boundary Conditions: Quadruple Solutions

The objective of this research is to acquire multiple branch solutions for the two-dimensional (2D) mixed convective flow of magnesium oxide (MgO)/water and titanium dioxide (TiO2)/water nanofluids over an exponentially vertical shrinking/stretching sheet with thermal radiation effect. Similarity transformations are applied to transform partial differential equations (PDEs) into ordinary differential equations (ODEs). For numerical findings, the shooting method is used via Maple software. Tremendously, four distinct branches of solutions are found in the case of opposing and assisting flows for each using influential parameters and nanoparticle volume fractions. In addition, stability analysis is also conducted that shows the first branch of the obtained solution in each case is physically stable (reliable) and acceptable, while the other three branches are unstable and considered as extraneous. Some of the key findings reveal that, for the stretching case, the skin friction reduces, but enhances the shrinking case of the surface when the rate of suction is increased. Moreover, the Nusselt number enhances for stretching case and reduces for shrinking case of sheet by increasing rate of the suction. The velocity profile increases with increasing rate of buoyancy or mixed convection parameter. Whereas, the profile of temperature decreases with larger values of the suction parameter, but enhances with higher nanoparticle volume fractions, the thermal radiation parameter, and the Biot number. However, TiO2 nanoparticles provide a greater rate of heat transfer and skin friction coefficient as compared to MgO nanoparticles. These findings provide novel physical insights for advanced thermal engineering applications.