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2015 | OriginalPaper | Chapter

9. Heat Conduction

Author : Roberto Mauri

Published in: Transport Phenomena in Multiphase Flows

Publisher: Springer International Publishing

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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 considered 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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previous chapter Laminar Boundary Layer

next chapter Conduction with Heat Sources

This fact that today is taken for granted, is not so obvious and, in fact, during the second half of the 19th 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.

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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.

Naturally, this is true only approximately, that is neglecting the temperature dependence of ρ, c and k.

Named after Jean-Baptiste Biot (1774–1862), a French physicist, astronomer, and mathematician.

Trivially, if the two processes were in parallel, we should add the inverses of the two characteristic times.

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.

It is equivalent to the quasi-static process in thermodynamics.

The QSS approximation here concerns the steady state within the membrane, and so its characteristic distance is d.

Title: Heat Conduction
Author: Roberto Mauri
Publisher: Springer International Publishing
Book: Transport Phenomena in Multiphase Flows
Print ISBN: 978-3-319-15792-4

Electronic ISBN: 978-3-319-15793-1

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-319-15793-1_9

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