Rotating porous convection with prescribed heat flux. (English) Zbl 1213.76193
Summary: The problem of thermal convection in a rotating horizontal layer of porous medium is considered. The porous medium is described by the equations of Darcy. A novel aspect of this work is to consider boundary conditions for the temperature of Newton-Robin type with heat flux prescribed as a limiting case. The effect of rotation is found to be crucial. For the Taylor number small enough the critical wave number is zero but we find a threshold such that for Taylor numbers beyond this non-zero critical wave numbers are found. The threshold is verified via a weakly nonlinear analysis. Finally, a sharp global nonlinear stability analysis is given.
MSC:
| 76S05 | Flows in porous media; filtration; seepage |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 76R05 | Forced convection |
| 76U05 | General theory of rotating fluids |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
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