Relationship between Thermal Conductivity and Diffusivity

After reading this article you will learn about the relationship between thermal conductivity and diffusivity.

In thermal conductivity and diffusivity the movement of heat in the soil will be considered. Because it is found that much of the solar radiation is dissipated into the atmosphere. Part of it, however, moves slowly through the soil profile by conduction process.

Once the heat is gained by the soil, the soil temperature is governed by the thermal characteristics of the soil i.e. heat capacity, thermal conductivity and thermal diffusivity. The amount of heat required to produce a given change in the soil temperature depends upon the mass and the nature of the soil.

The change of heat dQ/dt flowing into or out of the soil depends on the temperature gradient dT/dz in the soil and the thermal conductivity K, for any given soil volume the change of heat flow is given by

dQ/dt= -K dT/dz

where, z is measured along the gradient.

K is the thermal conductivity of soils expressed in J/°C/cm/sec and it depends on the physical properties of the soil, namely porosity, air, moisture and soil minerals. The more compact the soil, and the wetter the soil, the greater its conductivity.

The effect of a heat flow on the rate of change of temperature at a given depth depends on the difference between the heat flow into and out of a small volume of soil at that depth, and is given by

dT/dt = K/ρc d²T/dz²

where ρ is the density of the soil and c is the specific heat.

K/ρc is called the thermal diffusivity of the soil and expressed in cm²/sec. The thermal diffusivity of soil may either increase or decrease with increasing moisture content since K, p and c all increase with it, but, in general, starting with a dry soil, it first increases and after reaching a peak, may decrease slightly.

The relationship between the thermal conductivity and thermal diffusivity of a sandy loam soil with moisture content is presented in Fig 6.1.

Thermal diffusivity of soil increased exponentially with the increasing bulk density; heat capacity and the degree of saturation with moisture. At a constant heat flow, the abundance of temperature variation decreased with soil depth. As density of soil increased, the gradient of temperature with depth decreased.