Coupled effect of pressure corrections and heat-mass transfer on Rayleigh-Taylor instability in Casson fluid layer

This study explores the novel stability characteristics of the interface in a system composed of a viscous-Casson fluid, focusing on the coupled effects of heat and mass transfer. Extending the work of Awasthi et al. (Physics Fluids, 36 (2024) 102132), this investigation incorporates tangential viscous stresses into the interfacial dynamic condition, marking a departure from traditional potential flow theories. The model features a Casson fluid as the upper layer and a viscous fluid as the lower layer, with the analysis assuming no-slip conditions at rigid boundaries while the normal velocity is zero at these boundaries. A second-order polynomial equation is derived to characterize the growth rate, solved numerically using the Newton-Raphson method. Key findings demonstrate that heat and mass transfer enhance interface stability, with increased heat transport mitigating the destabilizing effects of the Atwood number. This theoretical advancement provides deeper insights into the dynamics of interfacial instability in complex fluid systems.