Heat Flow
in the Soil
8
When the sun shines on the soil surface, some of the energy is absorbed,
heating the soil surface. This heat is lost from the surface through conduction to lower layers of the soil, through heating the atmosphere, and
through evaporation of water. Heat transport from the surface to the atmosphere was discussed in Ch. 7. This chapter considers heat transport
into the soil. Some of the results from an analysis of heat transport in soil
are presented in Ch. 2 to show typical temporal and spatial patterns of
soil temperature. Here we show how those equations are derived and how
they depend on soil properties.
8.1 Heat Flow and Storage in Soil
In analyzing heat flow in the soil or the atmosphere, it is usefbl to mentally
divide the medium into a large number of thin layers, and consider the heat
flow and storage in each layer. The amount of heat stored in a layer of air
is small compared to the amount of heat transferred through it. Within the
first few meters of the atmosphere the heat stored in the air is generally
ignored and heat transfer processes are assumed to be approximately
steady. The results of these assumptions are the equations developed in
Ch. 7.
In soil the storage term is much larger and cannot be ignored. The heat
flow from one layer to the next is still computed using the Fourier law
(Eq. (6.3)) but now the continuity equation must be solved simultaneously
to find the temperature variation with depth and time. The continuity
equation is:
where p, is the density of the soil, c, is the soil specific heat, p,c, is
the volumetric heat capacity, and G is the heat flux density in the soil
(from Eq. (6.3)). The left-hand side of Eq. (8.1) represents the rate of
heat storage in a layer of soil and the right-hand side represents the heat
flux divergence, or rate of change of heat flux density with depth.
in the Soil
8
When the sun shines on the soil surface, some of the energy is absorbed,
heating the soil surface. This heat is lost from the surface through conduction to lower layers of the soil, through heating the atmosphere, and
through evaporation of water. Heat transport from the surface to the atmosphere was discussed in Ch. 7. This chapter considers heat transport
into the soil. Some of the results from an analysis of heat transport in soil
are presented in Ch. 2 to show typical temporal and spatial patterns of
soil temperature. Here we show how those equations are derived and how
they depend on soil properties.
8.1 Heat Flow and Storage in Soil
In analyzing heat flow in the soil or the atmosphere, it is usefbl to mentally
divide the medium into a large number of thin layers, and consider the heat
flow and storage in each layer. The amount of heat stored in a layer of air
is small compared to the amount of heat transferred through it. Within the
first few meters of the atmosphere the heat stored in the air is generally
ignored and heat transfer processes are assumed to be approximately
steady. The results of these assumptions are the equations developed in
Ch. 7.
In soil the storage term is much larger and cannot be ignored. The heat
flow from one layer to the next is still computed using the Fourier law
(Eq. (6.3)) but now the continuity equation must be solved simultaneously
to find the temperature variation with depth and time. The continuity
equation is:
where p, is the density of the soil, c, is the soil specific heat, p,c, is
the volumetric heat capacity, and G is the heat flux density in the soil
(from Eq. (6.3)). The left-hand side of Eq. (8.1) represents the rate of
heat storage in a layer of soil and the right-hand side represents the heat
flux divergence, or rate of change of heat flux density with depth.