Stability of double-diffusive convection in a porous medium with temperature-dependent viscosity: Brinkman-Forchheimer model. (English) Zbl 1465.76037
The authors investigate the thermal instability in a fluid layer confined between two horizontal rigid walls using both the Floquet theory and a numerical method. The walls are infinitely extended and rigid. It is assumed that the temperature distribution between the walls consists of a steady part and an oscillatory time-dependent part. The time-dependent part of the temperature is approximated by some functions and is expressed as Fourier series which contains both sine and cosine terms. Disturbances are assumed to be only infinitesimal. Thus, by changing the values of the Fourier coefficients, the present analysis can be used for any type of periodic temperature profile. However, only even solutions are considered in the paper. Numerical results for the critical Rayleigh numbers and wave numbers are obtained using the fourth-order Runge-Kutta-Gill method to solve the obtained ordinary differential equations for various values of the governing parameters. Also the formation of convective cells in the fluid layer is studied analytically with the help of the Floquet theory. It is found that time modulation of the wall temperatures can significantly affect the onset of instability. It has been also found that the disturbances are either synchronous with the primary temperature field or have its frequency. Some comparisons with known results from the literature have also been made. Results are presented for different values of the governing parameters in 8 figures. A list of 22 references is also included. In the reviewer’s opinion, this is a well-done paper important to researchers working in thermal instability area.
Reviewer: Ioan Pop (Cluj-Napoca)
MSC:
| 76E06 | Convection in hydrodynamic stability |
| 76R50 | Diffusion |
| 76S05 | Flows in porous media; filtration; seepage |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
Keywords:
Floquet theory; Fourier expansion; critical Rayleigh number; Runge-Kutta-Gill method; thermal convectionReferences:
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