EFFECT OF INTERNAL HEAT SOURCE ON DARCY-BRINKMAN CONVECTION IN A NON-NEWTONIAN CASSON NANOFLUID LAYER
Mamta Devi, Jyoti Sharma, Urvashi Gupta
Abstract
The Darcy-Brinkman convective instability of a non-Newtonian nanofluid layer saturating porous medium is investigated. Internal heat source effects are also considered to frame the conservation equations for the system, and non-Newtonian fluid behavior is characterized by the Casson model. The phenomenon is explored both analytically and numerically for free-free, rigid-free, and rigid-rigid boundaries. The normal mode technique is used to simplify the governing equations and linear stability theory is employed. Steady-state solutions are found to be the nonlinear functions of internal heat source strength, and an incremental rise in internal heat source raises the energy supply to the fluid, leading to large deviations in the solutions. Out of all three boundaries, the rigid-rigid makes the fluid layer most stable. To get complete insight into the problem, both bottom- and top-heavy arrangements of nanoparticles in the fluid layer are considered and the results are compared using the software Wolfram Mathematica. The analytical expressions and numerical results are also validated with the earlier findings as special cases of the present study by neglecting some of the parameters. The impact of nanofluid parameters is found to be destabilizing/stabilizing for top-/bottom-heavy configurations of nanoparticles in the layer. Non-Newtonian parameters and internal heat source strength largely show a destabilizing effect on the system irrespective of the arrangement of nanoparticles in the layer. Porosity delays the instability of the top-heavy layer while it hastens the onset of convection currents for the bottom-heavy case.