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Abstract

The Gradient in Steady State Heat Conduction

Interactive exercises on temperature and heat flow and discussion of laboratory observations lead to the statement of the fundamental law of heat conduction

q = - k grad T
Equation 1

which relates the temperature distribution T = T x y z and heat flux vector, q , at a point in space. The scalar proportionality factor, k , is called the thermal conductivity. Several examples of steady state, one dimensional Cartesian and cylindrical heat flow, for constant and non-constant k , provide practice in integration, solving simple ordinary differential equations and the physical understanding of real problems.