Modeling slip flow of Bingham fluid induced by a porous revolving disk with viscous dissipation and Joule heating effects

Rotating-disk generated flows find potential applications in industry such as cooling of electronics, car-breaking system, wind turbine engineering and others. Current article formulates heat transfer in the steady revolving flow of viscoplastic fluid obeying Bingham model over a rotating disk. Simulations are conducted by applying partial slip wall conditions, which are Robbin-type and non-linear in velocity components. Contribution of viscous dissipation, representing the conversion of mechanical energy into thermal energy caused by internal friction, is added in the analysis. Furthermore, the phenomenon of Joule heating due to the consideration of magnetic field affected flow is accounted for. The self-similar problem that arises after implementing Von-K & aacute;rm & aacute;n variables is computationally addressed using the MATLAB tool bvp4c. Significance of yield stress on the Von-K & aacute;rm & aacute;n flow under slip boundary assumption is elucidated through graphical results. Additionally, the implications of frictional heating and Joule heating on the development of a thermal boundary layer in a Bingham fluid are clarified. As the yield stress tau y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tau }_{{\text{y}}}$$\end{document} increases, the velocity profiles meet their respective far field conditions at smaller vertical distances, and therefore a higher torque is required by the disk. Noticeably, considering the slip effect not only lowers the torque that the disk requires, but it also boosts disk's rate of cooling-a desirable outcome in practical applications. The reliability of the mathematical model is assessed by performing uncertainty analysis of the computational data.