On dual solutions of the unsteady MHD flow on a stretchable rotating disk with heat transfer and a linear temporal stability analysis

Abstract The present paper is an extension of the work done by Fang and Tao (2012) in the presence of a magnetic field. The external magnetic field is applied normal to a stretchable disk surface and heat is transferred from the disk surface to the ambient fluid which gives a new family of unsteady viscous flow over a stretchable rotating disk with deceleration. The Navier–Stokes equations and the energy equation admit similarity solutions depending on unsteadiness parameter. The resulting set of highly nonlinear ordinary differential equations are solved numerically. Two solution branches are found due to the effect of unsteadiness parameter for several values of magnetic parameter and stretching parameter. The effects of pertinent flow parameters on the shear stresses on radial and tangential directions, Nusselt numbers, torque, dimensionless velocity and temperature profiles are shown graphically for both the solution branches and their physical interpretation are discussed in detail. Emphasis has been laid to check the stability of dual solution branches. The stability is tested by the sign of the smallest eigenvalue, and our analysis reveals that the lower solution branches are unstable.