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Mechanism of Heat Transfer in Rocks

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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 solid matrix and liquid in its pores as well as by convection of the moving liquid. By applying the law of conservation of energy to a control volume, an equation for heat transfer in the saturated porous medium can be expressed as:

ρc∂t∂τ+ ρwcwV·∇t =∇ · (k∇t) (2) where k denotes the effective thermal conductivity of the porous medium; ρc is the volumetric specific heat of the porous medium, including both the solid matrix and water in its pores, ρwcw the volumetric specific heat of water.

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

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