On multiple solutions of an unsteady MHD flow over a rotating and vertically moving disk with radiative heat transfer

The present study numerically explores an unsteady flow due to a rotating and vertically moving disk with the inclusion of an applied magnetic field and thermal radiation effects. Self-similar equations are obtained by utilizing the appropriate similarity transformations, and then the similarity solutions are evaluated in Matlab software using the “BVP4c” solver. First time in the literature, triple solutions are reported for this flow geometry. Although these solutions are mathematically valid, the first solution branch is physically more reliable and describes the main flow dynamics. The calculated results of several flow fields like shear stresses, heat transfer rate, fluid velocity and temperature for the triple solution branches are apparently discussed through graphs and tabular forms. The results indicated that the shear stresses and heat transfer rate decreased in all three solution branches with an increase in magnetic parameter. As reported in the study, the influence of magnetic parameter leads to a decrease in radial and tangential fluid velocities near the disk surface in all three branches, whereas axial and temperature profiles depict opposite trends. It is observed that the intensity of temperature ratio and thermal radiation parameters enhance the fluid temperature in the first solution branch. The common feature is that both the momentum and thermal boundary layer thicknesses in the third solution branch are higher than the remaining two solution branches. In fact, they are found in ascending order.