451 words - 2 pages

BENSON KILONZO MBITHI

MECHANISMS OF HEAT TRANSFER IN ROCKS

THERMAL CONDUCTIVITY OF ROCKS

Thermal conductivity of a rock (������) is defined as the heat flow across a surface per unit area per unit time when a particular temperature difference exists in a unit length perpendicular to the surface. It depends on following factors:-

Chemical composition of the rocks (rocks are aggregates of minerals)

1. Water content of the rock

2. Temperature

3. Pressure

4. Radioactive decay (if any) etc.

Thermal conductivity has units of W/(m℃)

Heat is transported through a saturated porous medium in a combined mechanism: by conduction through its ...view middle of the document...

Note in the equation that heat is stored and conducted through both the water and soil matrix, but only water takes part in convection of heat here. The average linear groundwater velocity V over a cross-section of the medium may be determined by the hydraulic head distribution according to the Darcy’s law if the hydraulic conductivity of the medium is known. The effective thermal conductivity and the volumetric specific heat of the porous medium are weighted averages of those of the saturated water and solid matrix, and can usually be determined on basis of its porosity ε as k = εkw + (1 −ε)ksρc = ερwcw + (1 − ε)ρscs

Following the Eskilson’s model [8], a further approximation is accepted that the groundwater velocity is uniform in the whole domain concerned and parallel to the ground surface.

The term “advection” is often used to describe such a flow. Define the velocity u is in the direction of the x coordinate. Then, on the assumption of constant thermal properties Eq. (2) reduces to

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where U = uρwcw/(ρc), and the effective thermal diffusivity a = k/(ρc). And for the steady-state situations Eskilson studied, the heat transfer equation is further simplified to

U∂t∂x= a∇2t

The parameter used to account for the thermal coupling between grains and the insulating effect of pore spaces on conductivity is called solidity. Solidity, y, is defined as the ratio of the volume of solid to the bulk volume, or the ratio of bulk density to solid grain density, dg/dg; it is the complement of porosity,

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