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 nonhomogenous 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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