Effect of rotation on the onset of thermal convection in a sparsely packed porous layer using a thermal non-equilibrium model. (English) Zbl 1194.80050
Summary: Linear and nonlinear stability of a rotating fluid-saturated sparsely packed porous layer heated from below and cooled from above is studied when the fluid and solid phases are not in local thermal equilibrium. The extended Darcy-Brinkman model that includes the time derivative and Coriolis terms is employed as a momentum equation. A two-field model that represents the fluid and solid phase temperature fields separately is used for energy equation. The onset criterion for both stationary and oscillatory convection is derived analytically. It is found that small inter-phase heat transfer coefficient has significant effect on the stability of the system. There is a competition between the processes of rotation and thermal diffusion that causes the convection to set in through oscillatory mode rather than stationary. The rotation inhibits the onset of convection in both stationary and oscillatory mode. The Darcy number stabilizes the system towards the oscillatory mode, while it has dual effect on stationary convection. Besides, the effect of porosity modified conductivity ratio, Darcy-Prandtl number and the ratio of diffusivities on the stability of the system is investigated. The nonlinear theory is based on the truncated representation of Fourier series method. The effect of thermal non-equilibrium on heat transfer is brought out. The transient behavior of the Nusselt number is investigated by using the Runge-Kutta method. Some of the convection systems previously reported in the literature is shown to be special cases of the system presented in this study.
MSC:
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 76S05 | Flows in porous media; filtration; seepage |
| 76U05 | General theory of rotating fluids |
| 76T99 | Multiphase and multicomponent flows |
| 76E07 | Rotation in hydrodynamic stability |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
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