Thermally Developing Forced Convection in a Porous Medium: Circular Duct with Walls at Constant Temperature,with Longitudinal Conduction and Viscous Dissipation Effects

A modified Graetz methodology is applied to investigate the thermal development of forced convection in a circular duct filled by a saturated porous medium, with walls held at constant temperature, and with the effects of longitudinal conduction and viscous dissipation included. The Brinkman model is employed. The analysis leads to expressions for the local Nusselt number, as a function of the dimensionless longitudinal coordinate and other parameters (Darcy number, Péclet number, Brinkman number).     

The Effect of Vertical Throughflow on Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid

The effect of vertical throughflow on the onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The dependences of the critical Rayleigh number for the non-oscillatory and oscillatory modes of instability on the thermophoresis and Brownian motion parameters for the cases with and without throughflow are investigated.     

The Effect of Strong Heterogeneity on the Onset of Convection Induced by Internal Heating in a Porous Medium: A Layered Model

An analytical investigation of the onset of convection, induced by internal heating, in a composite porous medium consisting of two horizontal layers has been made. The two-layer model that we adopted makes it possible to investigate and compare the effects of both weak and strong heterogeneity. Both cases of constant heat flux and constant wall temperature boundary conditions have been treated. In general, we established that anything that aids convection in the upper portion of the layer is destabilizing. In agreement with this rule, we found that conductivity increasing upward leads to a more stable situation, permeability increasing upward leads to a less stable situation, and source strength increasing upward generally leads to a less stable situation.     

The Onset of Double-Diffusive Convection in a Vertical Cylinder Occupied by a Heterogeneous Porous Medium with Vertical Throughflow

This paper investigates the onset of convection in a vertical cylinder occupied by a saturated porous medium of vertically heterogeneous permeability. The flow is induced by an applied vertical temperature gradient and an imposed solute concentration gradient. The main interest of this paper is studying the effect of vertical throughflow on the onset of instability in this system. The study is performed using linear stability theory. The problem is of considerable interest for hydrological and geophysical situations.     

The Effect of Strong Heterogeneity on the Onset of Convection in a Porous Medium

The effect of strong heterogeneity on the onset of convection induced by a vertical density gradient in a saturated porous medium governed by Darcy’s law is discussed. The general case, where there is heterogeneity in both the vertical and horizontal directions, and where there is heterogeneity in permeability, thermal conductivity, and applied temperature gradient, is considered. A computer package has been developed to implement an algorithm giving a criterion for instability. This package is applied to the case of a cube partitioned into octants and to the cases where the permeability and thermal conductivity vary continuously across a cube in either a linear or a quadratic manner.     

Instability of Hadley–Prats Flow with Viscous Heating in a Horizontal Porous Layer

The onset of convective rolls instability in a horizontal porous layer subject to a basic temperature gradient inclined with respect to gravity is investigated. The basic velocity has a linear profile with a non-vanishing mass flow rate, i.e., it is the superposition of a Hadley-type flow and a uniform flow. The influence of the viscous heating contribution on the critical conditions for the onset of the instability is assessed. There are four governing parameters: a horizontal Rayleigh number and a vertical Rayleigh number defining the intensity of the inclined temperature gradient, a Péclet number associated with the basic horizontal flow rate, and a Gebhart number associated with the viscous dissipation effect. The critical wave number and the critical vertical Rayleigh number are evaluated for assigned values of the horizontal Rayleigh number, of the Péclet number, and of the Gebhart number. The linear stability analysis is performed with reference either to transverse or to longitudinal roll disturbances. It is shown that generally the longitudinal rolls represent the preferred mode of instability.     

Interaction of Transverse Heterogeneity and Thermal Development of Forced Convection in a Porous Medium

The classical Graetz methodology is applied to investigate the thermal development of forced convection in a parallel plate channel filled by a saturated porous medium whose permeability and thermal conductivity vary in the transverse direction. It was found that there is a significant interaction between heterogeneity and thermal development.     

Deep Saline Fluids in Geologic Basins: The Possible Role of the Soret Effect

The possible relevance of the Soret effect in geoscientific studies is discussed. In particular, the question is addressed of whether the observation that salinity generally increases with depth in geologic basins can be explained by this effect. We proceed from the fact that salinity increases with depth, in many cases almost precisely linearly at larger depths. This suggests that salinity may be interdependent with the geothermal gradient that behaves in precisely the same way. Our work on a transient analysis suggests that the timescales involved in establishing corresponding steady state salinity distributions in the presence of a temperature gradient could be on the order of 100 million years.     

Onset of Convection with Internal Heating in a Weakly Heterogeneous Porous Medium

Linear stability analysis is applied to the onset of convection due to internal heating in a porous medium with weak vertical and horizontal heterogeneity. It is found that the effect of horizontal heterogeneity of each of permeability and thermal conductivity is slightly destabilizing. Increase of permeability in the upward direction is destabilizing and increase in the downward direction is stabilizing, and the reverse is true for increase of conductivity.     

A Note on Modeling High Speed Flow in a Bidisperse Porous Medium

A model of a bidisperse porous medium is extended to the case where quadratic drag is significant. The extension may be significant in some geophysical situations as well as when transition to turbulence in this medium is investigated.