Thermal instability of three-dimensional boundary layer stagnation point flow towards a rotating disc

In this paper, the thermal instability of a three-dimensional boundary layer axisymmetric stagnation point flow towards a heated horizontal rotating disk is considered. A large number of works have been done on stability analysis. However, they did not check the thermal stability of the non-parallel-flow in the face of small disturbances that occur in the vicinity of the heated rotating disk. The governing equations of the basic flow are reduced to three coupled nonlinear partial differential equations, and solved numerically with the fourth-order Runge-Kutta method. Thermal stability is examined by making use of linear stability theory based on the decomposition of the normal mode of G & ouml;rtler-Hammerlin. The resulting eigenvalue problem is solved numerically using a pseudo-spectral method based on the expansion of Laguerre's polynomials. The obtained results are discussed in detail through multiple configurations. As the main result, for large Prandtl numbers (Pr), the rotation disk parameter (Omega) has a destabilizing effect while for small Pr (around the unity) it tends to stabilize the basic flow. It was found that as the disk radius r -> 0, the flow is linearly stable, and the disturbances grow rapidly away from the stagnation point. For low values of Pr, the flow becomes more stable, and strong thermal gradients are necessary to destabilize it. However, an increase in Pr leads to a significant expansion of the instability region.