Numerical solution of three dimensional unsteady biomagnetic flow and heat transfer through stretching/shrinking sheet using temperature dependent magnetization

The problem of biomagnetic fluid flow and heat transfer in the three-dimensional unsteady stretching/shrinking sheet is examined. Our model is the version of biomagnetic fluid dynamics (BFD) which is consistent with the principles of ferrohydrodynamics (FHD). Our main contribution is the study of the three dimensional time dependent BFD flow which has not been considered yet to our best knowledge. The physical problem is described by a coupled, nonlinear system of ordinary differential equations subject to appropriate boundary conditions. The solution is obtained numerically by applying an effcient numerical technique based on the fnite difference method. Computations are performed for a wide range of the governing parameters such as ferromagnetic interaction parameter, unsteadiness parameter, stretching parameter and other involved parameters. The effect of these parameters on the velocity and temperature fields are examined. We observed that for the decelerated flow, the velocity profile overlap with the increasing unsteadiness parameter and we also found that the skin friction coefficient is decreased for a shrinking sheet whereas, opposite behavior is shown for the stretching sheet. We also monitored the rate of the heat transfer coefficient with the ferromagnetic interaction parameter and showed opposite behavior for stretching and shrinking sheets. Our results are also compared for specific values of the parameters with others documented in literature.