Effect of rotation on thermal instability under Hele-Shaw cell saturated by Casson nanofluid

Abstract

This paper examines the effect of rotation on thermal instability under Hele-Shaw cell saturated by Casson nanofluid using both linear and nonlinear ways. The nanofluid model incorporates Brownian and thermophoresis diffusion. While conducting an analysis of nonlinear stability numerically using the truncated Fourier series method, analysis of linear stability is performed analytically using the normal mode methodology. The outcomes are all displayed graphically. The results demonstrate that the rotation has dual effect on Hele-Shaw parameter as well as Casson parameter, for higher value of rotation it has destabilizing effect and it stabilizing  the system for lower values of rotation. Lewis number and concentration Rayleigh number promote the onset of convective motion within the system. On the other hand, rotation stabilize the system. Understanding the behavior of heat and mass transportation, the concentration of nanoparticles and fluid phase, utilize the Nusselt number when Nusselt numbers are assessed as a function of time, it is found that the variation of the rotation, Hele-Shaw and Casson parameter has a major influence on the heat and mass transfer. Both steady and unsteady weakly nonlinear analyses are performed to understand the heat transport in the system. It is concluded that the Casson nanofluid parameter has both stabilizing and destabilizing impact depending upon the rate of rotation and therefore this work can be possibly utilized in both places, where heat removal and heat conservation are required.