Heat - The Solid Earth - page 269

Radiation involves direct transfer of heat by electromagnetic radiation (e.g., from
the Sun or an electric bar heater). Within the Earth, heat moves predominantly by
conduction through the lithosphere (both oceanic and continental) and the solid
inner core. Although convection cannot take place in rigid solids, over geological
times the Earth's mantle appears to behave as a very-high-viscosity liquid, which
means that slow convection is possible in the mantle (see Sections 6.1, 7.4 and
8.2); in fact, heat is generally thought to be transferred by convection through
most of the mantle as well as through the liquid outer core. Although hot lava
radiates heat, as do crystals at deep, hot levels in the mantle, radiation is a minor
factor in the transfer of heat within the Earth. Advection is a special form of
convection. When a hot region is uplifted by tectonic events or by erosion and
isostatic rebound, heat (called advected heat) is physically lifted up with the rocks.
It is not possible to measure temperatures deep in the Earth. Temperatures and
temperature gradients can be measured only close to the Earth's surface, usually
in boreholes or mines or in oceanic sediments. The deeper thermal structure
must be deduced by extrapolation, by inference from seismic observations, from
knowledge of the behaviour of materials at high temperatures and pressures, from
metamorphic rocks and from models of the distribution of heat production and
of the Earth's thermal evolution.

7.2 Conductive heat flow
7.2.1 The heat-conduction equation
Heat, as everyone knows, flows from a hot body to a cold body, not the other
way around. The rate at which heat is conducted through a solid is proportional
to the temperature gradient (the difference in temperature per unit length). Heat
is conducted faster when there is a large temperature gradient than when there
is a small temperature gradient (all other things remaining constant). Imagine an
infinitely long and wide solid plate, d in thickness, with its upper surface kept
at temperature T 1 and its lower surface at temperature T 2 ( T 2 > T 1 ). The rate of

flow of heat per unit area up through the plate is proportional to
T 2 − T 1
d

(7.1)

The rate of flow of heat per unit area down through the plate, Q ,istherefore

Q =− k T 2 − T 1
d

(7.2)

where k , the constant of proportionality, is called the thermal conductivity . The
thermal conductivity is a physical property of the material of which the plate
is made and is a measure of its physical ability to conduct heat. The rate of
flow of heat per unit area Q is measured in units of watts per square metre
(W m − 2 ), and thermal conductivity k is in watts per metre per degree centigrade