Thermal conduction takes place by the transfer of kinetic energy of molecules or atoms of a warmer body to those of a colder body. The transfer of kinetic energy takes place through movement of the valence electrons (also called conduction electrons) in an atom, a process analogous to electrical conduction. This type of conduction can take place in both solids and uids.
Inside the Earth, however, conduction of heat takes place mainly through poorly conducting solid rocks constituting the crust and the mantle, which are comprised of minerals having a very few conduction electrons. Another type of conduction, called lattice or phonon conduction, caused by lattice vibrations in the rocks, is primarily responsible for heat transfer in such cases. Detailed treatment of heat conduction is provided in several textbooks (e.g., Carslaw and Jaeger, 1959; Jacob, 1964); applications of heat conduction to problems in geothermics have been dealt by Kappelmeyer and Haenel (1974), Lachenbruch and Sass (1977), Haenel et al. (1988) and others. In this section we shall discuss some basic concepts, which are useful in understanding the heat ow and temperature distribution inside the Earth.
Fourier’s Equation of Heat Conduction
When a temperature gradient exists within a body, heat energy will ow from the region of high temperature to the region of low temperature. This phenomenon is known as conductive heat transfer, and is described by Fourier’s equation, ~q ¼ k ~rT
ð3:6Þ
where ~q is the ow of heat per unit area per unit time (called as heat ow), k the thermal conductivity of the body (assumed isotropic) and ~ rT is the temperature gradient. The negative sign appears because heat ows in the direction of decreasingtemperature.
Inside the Earth, however, conduction of heat takes place mainly through poorly conducting solid rocks constituting the crust and the mantle, which are comprised of minerals having a very few conduction electrons. Another type of conduction, called lattice or phonon conduction, caused by lattice vibrations in the rocks, is primarily responsible for heat transfer in such cases. Detailed treatment of heat conduction is provided in several textbooks (e.g., Carslaw and Jaeger, 1959; Jacob, 1964); applications of heat conduction to problems in geothermics have been dealt by Kappelmeyer and Haenel (1974), Lachenbruch and Sass (1977), Haenel et al. (1988) and others. In this section we shall discuss some basic concepts, which are useful in understanding the heat ow and temperature distribution inside the Earth.
Fourier’s Equation of Heat Conduction
When a temperature gradient exists within a body, heat energy will ow from the region of high temperature to the region of low temperature. This phenomenon is known as conductive heat transfer, and is described by Fourier’s equation, ~q ¼ k ~rT
ð3:6Þ
where ~q is the ow of heat per unit area per unit time (called as heat ow), k the thermal conductivity of the body (assumed isotropic) and ~ rT is the temperature gradient. The negative sign appears because heat ows in the direction of decreasingtemperature.
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