This Worked Problem considers a transient heat treatment on a slice of a railroad rail.
Heat treatment is a method used to alter the physical, and sometimes chemical, properties of a material. The most common application is metallurgical. Heat treatments are also used in the manufacture of many other materials, such as glass. Heat treatment involves the use of heating or chilling, normally to extreme temperatures, to achieve a desired result such as hardening or softening of a material. Heat treatment techniques include annealing, case hardening, precipitation strengthening, tempering and quenching...Also see, for example, R Reed-Hill, Principles of Physical Metallurgy, PWS Publishing, Boston, 1994.
... from Wikipedia accessed on 19 June 2008.
From the physical point of view, this Worked Problem illustrates many aspects of transient heat transfer: (i) heat conduction in the material; (ii) heat exchange with surrounding areas; (iii) the role played by Biot number in heat exchange; and (iv) the construction of a lumped capacitance model as a first approximation.