An analytical study of nonlinear double-diffusive convection in a porous medium under temperature/gravity modulation

• Published in: Transport in porous media Vol. 91; no. 2; pp. 585 - 604
• Main Authors: Siddheshwar, P. G., Bhadauria, B. S., Srivastava, Alok
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2012; Springer; Springer Nature B.V
• Subjects: Amplitudes; Civil Engineering; Classical and Continuum Physics; Convection; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Engineering and environment geology. Geothermics; Exact sciences and technology; Fluid dynamics; Fluid flow; Geotechnical Engineering & Applied Earth Sciences; Gravitational effects; Gravitational fields; Hydrocarbons; Hydrogeology; Hydrology. Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; Modulation; Nonlinear analysis; Pollution, environment geology; Porous media; Power series; Sedimentary rocks; Series expansion; Temperature dependence; Temperature effects; Temperature gradients; Thermal instability; Time dependence; Gravity modulation; Ginzburg–Landau equation; Double-diffusive Convection; Temperature modulation; Non-linear stability analysis; Ginzburg-Landau equation; gravity field; transport; convection; amplitude; instability; temperature; porous media; stability
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-011-9861-3

The article deals with nonlinear thermal instability problem of double-diffusive convection in a porous medium subjected to temperature/gravity modulation. Three types of imposed time-periodic boundary temperature (ITBT) are considered. The effect of imposed time-periodic gravity modulation (ITGM) is also studied in this problem. In the case of ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent periodic part. The temperature of both walls is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally imposed time-periodic part. Using power series expansion in terms of the amplitude of modulation, which is assumed to be small, the problem has been studied using the Ginzburg–Landau amplitude equation. The individual effects of temperature and gravity modulation on heat and mass transports have been investigated in terms of Nusselt number and Sherwood number, respectively. Further the effects of various parameters on heat and mass transports have been analyzed and depicted graphically.