Stability analysis of MHD stagnation flow over a permeable heated rotating disk with heat generation/absorption

Abstract

The stagnation point flow of an incompressible viscous electrically conducting fluid impacting orthogonally on a heated rotating disk is studied with internal volumetric heat generation/absorption in the presence of a uniform magnetic field. A uniform suction or injection is applied through the surface of the disk. Appropriate similarity transformations are used to reduce the governing differential equations of the problem into a system of nonlinear ordinary differential equations and then solved numerically using the fourth-order Runge–Kutta method. In the second step, the work is oriented towards linear stability analysis by considering infinitesimally small disturbances within the boundary layer. Using normal mode decomposition in the Görtler–Hammerlin framework, the resulting eigenvalue problem is then solved numerically by means of the pseudo-spectral method using Laguerre’s polynomials. As a result, the critical conditions for the onset of thermal instability are described and discussed in detail using multiple configurations. It is found that the presence of a magnetic field and suction/injection act to increase the stability of the basic flow. However, the rotation parameter and the internal heat generation/absorption contribute significantly to destabilizing the basic flow.