Exact solutions for MHD axisymmetric hybrid nanofluid flow and heat transfer over a permeable non-linear radially shrinking/stretching surface with mutual impacts of thermal radiation

Recently, the hybrid nanofluid has been extensively utilized to improve the capabilities of heat transfer fluids that are widely employed in modern industrialized applications. In this article, the features of heat transfer of axisymmetric flow over a nonlinear shrinking or stretching surface induced by hybrid (TiO₂–Ag) nanofluid are scrutinized analytically. A radiation impact is incorporated in the energy equation. The nonlinear leading PDEs (partial differential equations) are improved into a form of dimensionless ODEs (ordinary differential equations) by operating nonlinear similarity variables. The outcome is obtained in a closed-form equation. The physical parameters are retrieved by the use of nonlinear transformations, which are then determined analytically to produce the exact dual solutions. The impact of these obtained physical parameters on the velocity, the friction factor as well as the temperature distribution, and the Nusselt number are scrutinized in detail. The dual solutions are obtained as a result of the shrinking surface, which has an impact on the temperature distribution. The exploration specifies that the inclusion of nanoparticles volume fractions in the convectional fluid provides a great potential in enhancing the performance of heat transfer fluids.