Abstract
In this chapter we start the second part of the book, which is devoted to heat and mass transport, by studying the diffusive heat transport, called heat conduction. First, in Sect. 9.1, we introduce some general concepts of heat transport, including the heat transfer coefficient. Then, in Sect. 9.2, heat conduction problems are solved in Cartesian, cylindrical and spherical coordinate. An important application of these concepts is the composite solid, that we consider in the following Sect. 9.3. Finally, in Sect. 9.4, we apply to heat transport the quasi-steady-state approximation that was studied in Sect. 5.5.
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Notes
- 1.
This fact that today is taken for granted, is not so obvious and, in fact, during the second half of the nineteenth century, many important physicists kept looking for a fluid medium, called ether, whose vibrations should produce the light waves, just in the same way as the vibrations of the air produce the sound waves.
- 2.
In the following, sometimes we will denote the heat flux by JQ, stressing that we consider only the part of internal energy that can be associated with heat.
- 3.
As a curiosity, note that k ≈ 1 W/mK for bricks and k ≈ 0.1 W/mK for wood, which means that a house with wooden walls is 10 times better thermally insulated than a house with brick walls of the same thickness.
- 4.
Naturally, this is true only approximately, that is neglecting the temperature dependence of ρ, c and k.
- 5.
Named after Jean-Baptiste Biot (1774–1862), a French physicist, astronomer, and mathematician.
- 6.
Trivially, if the two processes were in parallel, we should add the inverses of the two characteristic times.
- 7.
For example, when we take a potato out of the oven, as it cools down, the inside temperature is much higher than that of its skin.
- 8.
It is equivalent to the quasi-static process in thermodynamics.
- 9.
The QSS approximation here concerns the steady state within the membrane, and so its characteristic distance is d.
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Mauri, R. (2023). Heat Conduction. In: Transport Phenomena in Multiphase Flows. Fluid Mechanics and Its Applications, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-031-28920-0_9
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DOI: https://doi.org/10.1007/978-3-031-28920-0_9
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