STABILITY ANALYSIS OF A COUPLE-STRESS FLUID WITH VARIABLE GRAVITY IN A POROUS MEDIUM FOR DIFFERENT CONDUCTING BOUNDARIES

Abstract

Models with higher order gradient terms are of considerable interest in modeling the transporting of biofluids in biological systems. A horizontal layer of couple stress fluid is considered to model a system with a variable gravity field and conducting boundaries. The stability of the nonlinear model is analyzed by applying the energy technique and calculating the values of Rayleigh numbers (critical) numerically using the Galerkin technique for rigid-rigid, rigid-free, and free-free boundary conditions. It is observed that the increase in values of Brinkman number and couple stress parameter stabilizes the model. However, the critical values of the Rayleigh number are greatly influenced by the gravity variation models. The results suggests that the stability of the fluids with higher order stress contribution is highly influenced by varying gravity conditions, such as in space.