Homotopy and sensitivity analysis on hybrid nanofluid transient flow past a spinning sphere considering heat source and nonlinear thermal radiation: An optimization study

The current numerical exploration is aimed to study the Homotopy analysis on hydromagnetic hybrid nanofluid transient stream considering non-linear radiative heat flux and variable heat source with a special emphasis on improvement in heat exchange efficiency at the proximity of the spinning sphere's stagnation domain. The relevant transformations of similarity are applied to convert the flow representing partial differential equations (PDEs) to describe the flow phenomena into nonlinear coupled ordinary differential equations. The semi-analytical approach solves the resultant dimensionless Boundary Value Problem (BVP). Convective heat transfer coefficient optimisation is explored using Response Surface Methodology (RSM). The full quadratic regression model is used for the sensitivity analysis. The flow characteristics for the nanofluids with water as the base liquid and silver and alumina as metals, are presented in tabular and graphical form. In a limited sense, the calculated findings are confirmed by previously published literature, and it is discovered that there are strong correlations. The significant results observed that for both assisting and hindering flows, the presence of a variable heat source and thermal radiation greatly raises the temperature of the boundary layer. The rate of heat transfer has a maximum sensitivity of 1.084790 towards thermal radiation and the heat transmission rate has a lower sensitivity value of 0.078210 towards internal variable heat source. The significant impacts of numerous physical quantities are scrutinized and discussed meticulously in terms of friction factor and heat transfer coefficient.