THROUGHFLOW AND GRAVITY MODULATION EFFECT ON THERMAL INSTABILITY IN A HELE-SHAWCELL SATURATED BY NANOFLUID

In this paper, throughflow effect on thermal instability in a Hele-Shaw cell filled with nanofluid has been studied under gravity modulation, and by performing linear and nonlinear stability analyses. For linear stability analysis, normal mode technique has been used, while double Fourier series technique has been used for nonlinear stability analysis. The Brinkman model for nanofluid has been considered, which incorporates the effect of Brownian motion along with thermophoresis. In linear analysis, it is observed that some parameters are having dual effect due to throughflow. In nonlinear analysis, effects of throughflow, gravity modulation, and Hele-Shaw number play important roles in heat and mass transfer. An increment in the value of Hele-Shaw number decreases heat transfer but increases mass transfer in the system. Heat and mass transfer both increase on increasing throughflow.