Mathematical model for a thermal cooling system with variable viscosity and thermal conductivity over a rotating disk

Mathematical models involving rotation of the disks and the flow of fluid over these serve as a prototypical representation of electronic devices including rotational components. The rotation results in substantial heat generation and the excessive heat buildup can affect performance and reliability, and can cause failure. Therefore efficient cooling mechanisms are essential to dissipate the generated heat and maintain the devices' temperature within safe operating limits. In this research paper, the focus is on investigating the magnetohydrodynamic (MHD) slip flow and heat transfer of power-law nanofluid over an infinite rotating disk. The study incorporates numerical methods to analyze the system, considering the variable thermal conductivity and viscosity as a function of velocity gradients, and employing velocity slip conditions at the boundary. To facilitate the analysis, the similarity transformation technique is applied, which effectively reduces the governing boundary value problem to a set of nonlinear ordinary differential equations (ODEs). The research explores the dependence of the velocity and temperature profiles on various parameters, including the nanofluid volume concentration parameter, power-law index, magnetic parameter, and velocity slip parameters. Through the numerical results, the influence of these parameters on the flow and heat transfer characteristics is presented and thoroughly discussed. The outcomes of the study are presented in the form of graphs and tables, providing valuable insights into the behavior of the power-law nanofluid flow and heat transfer over the rotating disk.