Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

The linear stability of Walters B viscoelastic fluid-saturated horizontal porous layer is examined theoretically when the walls of the porous layer are subjected to time-periodic temperature modulation. Three types of boundary temperature modulations are considered namely, symmetric, asymmetric, and only the lower wall temperature is modulated while the upper wall is held at constant temperature. A regular perturbation method based on small amplitude of applied temperature field is used to compute the critical values of Rayleigh number and the corresponding wave number. The shift in critical Rayleigh number is calculated as a function of modulation frequency, viscoelastic parameter, and Prandtl number. The effect of all three types of modulations is found to be destabilizing as compared to the unmodulated system. This result is in contrast to the system with other types of fluids. Besides, the influence of physical parameters on the control of convective instability of the system is discussed

Oberbeck convection through vertical porous stratum

Natural convection through a vertical porous stratum is investigated both analytically and numerically. Analytical solutions are obtained using a perturbation method valid for small values of buoyancy parameter N and the numerical solutions are obtained using Runge-Kutta-Gill method. It is shown that analytical solutions are valid for N < 1 and several features of the effect of large values of N are reported. The combined effects of increase in the values of temperature difference between the plates and the permeability parameter on velocity, temperature, mass flow rate and the rate of heat transfer are reported. It is shown that higher temperature difference is required to achieve the mass flow rate in a porous medium equivalent to that of viscous flow

An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients

This paper explores an operative technique for deriving nonlinear stability by studying double-diffusive porous convection with a concentration-based internal heat source. Previous stability analyses on this problem have yielded regions of potential subcritical instabilities where the linear instability and nonlinear stability thresholds do not coincide. It is shown in this paper that the operative technique yields sharp conditional nonlinear stability in regions where the instability is found to be monotonic. This is the first instance, in the present literature, where this technique has been shown to generate sharp thresholds for a system with spatially dependent coefficients, which strongly advocates its wider use

Effect of modulation on the onset of convection in a sparsely packed porous layer

The stability of a Boussinesq fluid-saturated horizontal porous layer heated from below is examined when the applied temperature gradient is the sum of a steady component and a time-dependent sinusoidal component. The Brinkman model is employed and only infinitesimal disturbances are considered. A perturbation solution as a function of the applied field is obtained. The critical Rayleigh number is obtained for several cases depending on the frequency of oscillations and it is found that it is possible to advance or delay the onset of convection by thermal modulation of the wall temperature. The Darcy limit and viscous flow limit are obtained as degenerate cases

Effect of thermal modulation on the onset of convection in a viscoelastic fluid saturated porous layer

The effect of thermal modulation on the onset of convection in a horizontal, anisotropic porous layer saturated by a viscoelastic fluid is investigated by a linear stability analysis. Darcy's law with viscoelastic correction is used to describe the fluid motion. The perturbation method is used to find the critical Rayleigh number and the corresponding wavenumber for small amplitude thermal modulation. The stability of the system characterized by a correction Rayleigh number is calculated as a function of the thermal and mechanical anisotropy parameters, the viscoelastic parameters and the frequency of modulation. It is found that the onset of convection can be delayed or advanced by the factors represented by these parameters. The results of the problem have possible implications in mantle convection. © Springer 2006