Thermal diffusivity

The thermal conductivity or thermal diffusivity, and occasionally " thermal diffusivity " ( from English- thermal diffusivity ), is a material property that is used to describe the temporal change in the spatial distribution of temperature by thermal conduction as a result of a temperature gradient. It is related to the thermal conductivity, which is used to describe the energy transport.

Definition and unit

Is the thermal diffusivity defined as:

With   - Thermal conductivity   - Density   - Specific heat capacity

The thermal diffusivity has the SI unit. In the U.S. space, the indication is common in.

Is a temperature-dependent material properties, in particular since the thermal conductivity, but also the density and the specific heat capacity are dependent on temperature.

Heat conduction equation

The spatial and temporal distribution of temperature T ( x, t) in a body can be on the Fourier differential equation to calculate ( by JBJ Fourier ). She goes into the first considerations already on Newton back and presses a simple mathematical facts from: The change of the heat content of a spatial region flows as heat flow through the envelope. Or, expressed somewhat less mathematically: What is lost inside a body of heat flows as heat flow through the surface of the body and vice versa in the environment.

But constant heat capacity per volume For isotropic body with inhomogeneous thermal conductivity:

In mathematical symbols mean:

For homogeneous, isotropic media (ie, heat-transporting materials, everywhere show the same composition, and the show in any spatial direction characteristic altered characteristics ), the heat conduction equation simplifies to assuming independent of the temperature of thermal diffusivity:

In the mathematical symbolism means:

The differential equation is called " heat equation " and generally describes transport processes (such as diffusion processes - by which is meant, or in the case of the heat equation just a material transport due to a concentration difference a " wandering" of the temperature distribution in a body due to a temperature gradient ). Mathematically, the thermal diffusivity is therefore the " transport coefficient of heat conduction ". Strictly speaking, the two specified versions of the heat equation are only valid so long to bring or remove from it any extraneous heat effects in the considered body. If this is the case, a so-called source term should be added. The analytical solution to this equation is not possible in many cases. Today, we calculated technically relevant Wärmeleitaufgaben with the help of finite element programs. As a result, we obtain the temporal and spatial temperature distribution (temperature field). Thus one can, for example, close to the spatial expansion behavior of the components, which in its turn influenced the local stress state. Thus, the temperature field calculation is an important foundation for all engineering design tasks in which the thermal component stress can not be neglected.