Influence of radiative transfer on Rayleigh-Benard-Marangoni canvection in a couple-stress fluid saturated porous medium

Influence of radiative transfer on Rayleigh-Benard-Marangoni canvection in a couple-stress fluid saturated porous medium

The problem of Rayleigh-Benard-Marangoni convection in a couple-stress fluid saturated porous medium with thermal radiation is studied within the framework of linear stability analysis. Only infinitesimal disturbances are considered. The linear stability analysis is based on the normal mode technique. The Darcy law is used to model the momentum equation. The fluid between the boundaries absorbs and emits thermal radiation. The boundaries are treated as black bodies. The absorption coefficient of the fluid is assumed to be the same at all wavelengths and to be independent of the physical state. The principle of exchange of stabilities is valid and the existence of oscillatory instability is ruled out. The expression for the stationary Darcy-Rayleigh number is obtained as a function of the governing parameters, viz., the wave number, the couple-stress parameter, the conduction-radiation parameter, the absorptivity parameter, the Marangoni number and the Biot number. The Galerkin method is used to determine the eigenvalues. The effect of various parameters on the stability of the fluid layer is discussed through figures and tables.

SINGH NINGTHOUJAM SHIBIRAJ

Mathematics