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mohammed El-Kady
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- TL;DR Summary
- derivation of the law
I need to know the derivation of Cattaneo–Vernotte law. "if it has a proof"
The Cattaneo-Vernotte Law is a mathematical model that describes the transfer of heat in a material. It takes into account the time delay between the temperature gradient and the heat flux, which is not accounted for in the traditional Fourier's Law.
The Cattaneo-Vernotte Law was proposed by Italian physicist Carlo Cattaneo in 1838 and later refined by French engineer Maurice Vernotte in 1958.
The Cattaneo-Vernotte Law takes into account the time delay between the temperature gradient and the heat flux, while Fourier's Law assumes an instantaneous response. This makes the Cattaneo-Vernotte Law more accurate for materials with high thermal conductivity or in situations where there is a rapid change in temperature.
The proof for the Cattaneo-Vernotte Law involves using the Boltzmann transport equation and applying the relaxation time approximation. This results in a modified form of Fourier's Law with an additional term that accounts for the time delay between the temperature gradient and heat flux.
The Cattaneo-Vernotte Law has numerous applications in various fields such as materials science, engineering, and geophysics. It is particularly useful in situations where there is a rapid change in temperature, such as in microelectronics and high-speed machining processes. It also has applications in understanding heat transfer in geological processes and in modeling thermal behavior in materials with high thermal conductivity.