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Thermal diffusivity is a positive coefficient in the heat equation: [5] =. One way to view thermal diffusivity is as the ratio of the time derivative of temperature to its curvature , quantifying the rate at which temperature concavity is "smoothed out".
A direct practical application of the heat equation, in conjunction with Fourier theory, in spherical coordinates, is the prediction of thermal transfer profiles and the measurement of the thermal diffusivity in polymers (Unsworth and Duarte). This dual theoretical-experimental method is applicable to rubber, various other polymeric materials ...
The Fourier number can be derived by nondimensionalizing the time-dependent diffusion equation.As an example, consider a rod of length that is being heated from an initial temperature by imposing a heat source of temperature > at time = and position = (with along the axis of the rod).
Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, D. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation.
Thermal effusivity and thermal diffusivity are related quantities; respectively a product versus a ratio of a material's intensive heat transport and storage properties. The diffusivity appears explicitly in the heat equation, which is an energy conservation equation, and measures the speed at which thermal equilibrium can be reached by a body. [2]
The higher the thermal diffusivity of the sample, the faster the energy reaches the backside. A laser flash apparatus (LFA) to measure thermal diffusivity over a broad temperature range, is shown on the right hand side. In a one-dimensional, adiabatic case the thermal diffusivity is calculated from this temperature rise as follows:
For diffusion coefficients and thermal diffusion coefficients the picture is somewhat more complex. However, one of the major advantages of RET over classical Chapman–Enskog theory is that the dependence of diffusion coefficients on the thermodynamic factors, i.e. the derivatives of the chemical potentials with respect to composition, is ...
This is accomplished by solving heat equations in both regions, subject to given boundary and initial conditions. At the interface between the phases (in the classical problem) the temperature is set to the phase change temperature. To close the mathematical system a further equation, the Stefan condition, is required. This is an energy balance ...