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Thermal diffusivity is a contrasting measure to thermal effusivity. [6] [7] In a substance with high thermal diffusivity, heat moves rapidly through it because the substance conducts heat quickly relative to its volumetric heat capacity or 'thermal bulk'. Thermal diffusivity is often measured with the flash method.
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 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:
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.
α is the thermal diffusivity, D is the mass diffusivity, λ is the thermal conductivity, ρ is the density, D im is the mixture-averaged diffusion coefficient, c p is the specific heat capacity at constant pressure. In the field of fluid mechanics, many sources define the Lewis number to be the inverse of the above definition. [3] [4]
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).
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]
where L is the characteristic length, u the local flow velocity, D the mass diffusion coefficient, Re the Reynolds number, Sc the Schmidt number, Pr the Prandtl number, and α the thermal diffusivity, = where k is the thermal conductivity, ρ the density, and c p the specific heat capacity.