The flow of a Reiner-Rivlin hydromagnetic nanoliquid due to rotating disk in the presence of Joule heating and a non-uniform heat source is investigated. To control the volume fraction of nanoparticles on the surface of a disk, a realistic passive control strategy is used, taking the thermal jump condition into account. Nonlinear governing differential equations are solved numerically using the Bulirsch-Stoer technique and a parametric analysis is performed using graphical representations. Using the Response Surface Methodology (RSM), the interaction effects of the influential parameters on the rate of heat transfer are visualized via three-dimensional surface graphs and contours. Further, the optimum rate of the heat transfer is estimated through the RSM analysis. It is found that the surface drag demotes due to enhancement in the cross-viscosity coefficient. A rise in the space-dependent heat source augments the temperature profile. The heat transfer rate is negatively influenced by the Eckert number. Further, when thermal slip is augmented, the sensitivity of the heat transfer towards the Hartmann number decreases at the rate of 0.2267%, and the sensitivity towards the Reiner-Rivlin fluid parameter decrements at the rate of 0.0554%.