Heat Transport in an Anisotropic Porous Medium Saturated with Variable Viscosity Liquid Under Temperature Modulation

• Published in: Transport in porous media Vol. 100; no. 2; pp. 279 - 295
• Main Authors: Bhadauria, B. S., Kiran, Palle
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.11.2013; Springer; Springer Nature B.V
• Subjects: Amplitudes; Anisotropy; Civil Engineering; Classical and Continuum Physics; Convection modes; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Exact sciences and technology; Fluid dynamics; Fluid flow; Geotechnical Engineering & Applied Earth Sciences; Heat; Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; Landau-Ginzburg equations; Marine and continental quaternary; Mathematical analysis; Modulation; Nonlinear analysis; Parameters; Porous media; Power series; Rheological properties; Rheology; Stability analysis; Surficial geology; Thermal instability; Transport; Viscosity; Viscous fluids; Non-linear stability; Temperature-dependent variable viscosity; Ginzburg–Landau model; Anisotropic Porous media; Temperature modulation; models; Ginzburg―Landau model; anisotropy; transport; frequency; convection; amplitude; viscosity; instability; temperature; porous media; heat transfer; stability
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-013-0216-0

Thermal instability in a horizontal porous medium saturated with temperature-dependant viscous fluid has been considered, and the effect of time-periodic temperature modulation has been investigated. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weak non-linear stability analysis has been performed for the stationary mode of convection, and heat transport in terms of the Nusselt number, which is governed by the non-autonomous Ginzburg–Landau equation, is calculated. The effects of thermo-rheological parameter, amplitude and frequency of modulation, thermo-mechanical anisotropies, and Vadasz number on heat transport have been analyzed and depicted graphically. It is found that an increment in the value of thermo-rheological parameter results in the enhancement of heat transport in the system. Further, the study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system.