Heat Transfer Tutorial

Conduction And Heat Transfer


Conduction heat transfer phenomena are found throughout virtually all of the physical world and the
industrial domain. The analytical description of this heat transfer mode is one of the best understood.
Some of the bases of understanding of conduction date back to early history. It was recognized that by
invoking certain relatively minor simplifications, mathematical solutions resulted directly. Some of these
were very easily formulated. What transpired over the years was a very vigorous development of
applications to a broad range of processes. Perhaps no single work better summarizes the wealth of these
studies than does the book by Carslaw and Jaeger (1959). They gave solutions to a broad range of
problems, from topics related to the cooling of the Earth to the current-carrying capacities of wires. The
general analyses given there have been applied to a range of modern-day problems, from laser heating
to temperature-control systems.
Today conduction heat transfer is still an active area of research and application. A great deal of
interest has developed in recent years in topics like contact resistance, where a temperature difference
develops between two solids that do not have perfect contact with each other. Additional issues of current
interest include non-Fourier conduction, where the processes occur so fast that the equation described
below does not apply. Also, the problems related to transport in miniaturized systems are garnering a
great deal of interest. Increased interest has also been directed to ways of handling composite materials,
where the ability to conduct heat is very directional.
Much of the work in conduction analysis is now accomplished by use of sophisticated computer
codes. These tools have given the heat transfer analyst the capability of solving problems in nonhomo-
genous media, with very complicated geometries, and with very involved boundary conditions. It is still
important to understand analytical ways of determining the performance of conducting systems. At the
minimum these can be used as calibrations for numerical codes.

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