Porous media forced convection

Bolton EW, Lasaga AC, Rye DM (1996) A model for the kinetic control of quartz dissolution and precipitation in porous media flow with spatially variable permeability Eormulation and examples of thermal convection. J Geophys Res 101 22,157-22,187 Bolton EW, Lasaga AC, Rye DM (1997) Dissolution and precipitation via forced-flux injection in the porous medium with spatially variable permeability Kinetic control in two dimensions. J Geophys Res 102 12,159-12,172... 

Eq. (10.34) together with Eqs. (10.11) to (10.14) constitutes the set of equations governing forced convective flow through a porous medium. As discussed in the previous section, the distribution of the velocity components is the same as would exist with potential flow in the same geometrical situation. This potential flow solution gives the values of u, v, and w which can then be used in Eq. (10.34) to give the temperature distribution. 

If the Darcy assumptions are used then with forced convective flow over a surface in a porous medium, because the velocity is not assumed to be 0 at the surface, there is no velocity change induced by viscosity near the surface and there is therefore no velocity boundary layer in the flow over the surface. There will, however, be a region adjacent to the surface in which heat transfer is important and in which there are significant temperature changes in the direction normal to the surface. Under many circumstances, the normal distance over which such significant temperature changes occur is relatively small, i.e., a thermal boundary layer can be assumed to exist around the surface as shown in Fig. 10.9, the ratio of the boundary layer thickness, 67, to the size of the body as measured by some dimension, L, being small [15],[16]. 

Natural convective flows in porous media occur in a number of important practical situations, e.g., in air-saturated fibrous insulation material surrounding a heated body and about pipes buried in water-saturated soils. To illustrate how such flows can be analyzed, e.g., see [20] to [22], attention will be given in this section to flow over the outer surface of a body in a porous medium, the flow being caused purely by the buoyancy forces resulting from the temperature differences in the flow. The simplest such situation is two-dimensional flow over an isothermal vertical flat surface imbedded in a porous medium, this situation being shown schematically in Fig. 10.25. 

Using the procedure outlined in this chapter for using the boundars laser equations to find the-forced convective heat transfer rate from a circular cylinder buried in a saturated porous medium, investigate the heat transfer rate from cylinders with an elliptical cross-section with their major axes aligned with the forced flow. The surface velocity distribution should be obtained from a suitable book on fluid mechanics. 

Oosthuizen, P.H. and Paul, J.T., Forced Convective Heat Transfer from a Flat Plate Embedded Near an Impermeable Surface in a Porous Medium , Symp. on Fundamentals of Forced Convection Heat Transfer, ASME HTD-Vol. 101. Am. Soc. Mech. Eng., New York, 1988, pp. 105-111. 

Nakayama, A., A Unified Theory for Non-Darcy Free, Forced, and Mixed Convection Problems Associated with a Horizontal Line Heat Source in a Porous Medium , J. Heat Transfer, Vol. 116, pp. 508-513, 1994. 

Chikh, S., Boumedien, A., Bouhadef, K., Lauriat, G., 1995. Analytical solution of non-Darcian forced convection in an annular duct partially filled with a porous medium. Int J. Heat Mass Transf. 38, 1543-1551. 

Kuznetsov, AV, Nield, DA., 2009. Thermally developing forced convection in a porous medium occupied by a rarefied gas parallel plate channel or circular tube with walls at constant heat flux. Transp. Porous Media 76, 345-362. 

Narasimhan, A., Lage, J.L., 2001. Forced convection of a fluid with temperature-dependent viscosity through a porous medium channel. Numer. Heat Transf. Part A Appl. 40, 801-820. 

Nield, D.A., Kuznetsov, A.V., 1999. Local thermal nonequilibrium effects in forced convection in a porous medium channel a conjugate problem. Int. J. Heat Mass Transf. 42, 3245-3252. 

A further complication arises in forced convection in fabric, which is a porous medium. There may be significant thermal dispersion, i.e., heat transfer due to hydrodynamic mixing of the fluid at the pore scale. In addition to the molecular diffusion of heat, there is mixing due to the nature of the fabric. 

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