Rayleigh–Taylor instability in a Casson fluid layer with heat and mass transfer

Abstract

This study investigates the stability of the interface between two fluids, a Casson fluid on top and a viscous fluid below, with heat and mass transfer occurring between them. We used the potential flow theory, which simplifies the problem by ignoring tangential stresses and focusing on normal stress balance. We did not consider no-slip conditions at the boundaries, assuming zero normal velocity at these rigid boundaries instead. A second-order polynomial equation was developed to calculate the growth rate of instabilities and solved numerically using the Newton–Raphson method. The results showed that heat and mass transfer improved the stability of the interface, even though the Atwood number, a measure of instability, remained high.