Rapid Reliable Solution
of the Parametrized Partial Differential Equations
of Continuum Mechanics and Transport


A Transient Heat Treatment Problem
Forward Problem

Authors: G Rozza & AT Patera
in collaboration with DBP Huynh & NC Nguyen


Engineering motivation

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...
... from Wikipedia accessed on 19 June 2008.
Also see, for example, R Reed-Hill, Principles of Physical Metallurgy, PWS Publishing, Boston, 1994.

Physical principles

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.

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