Pre-Analysis

Equations

The governing equation for heat transfer rate for a rectangular bar, as generalized by Fourier in 1807, is the following equation. In this equation, k is the proportionality factor as a function of material and temperature, A is the cross-sectional area and L is the length of the bar.

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The equation above can be written in terms of heat flux using the definition that heat flux is the amount of heat transfer per unit area. This one-dimensional form of Fourier’s law of heat conduction is found below.

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