Basic constitutive equations

Conduction through a circular wall

Heat flows through a circular wall with inner radius ri and outer radius ro as illustrated to the right: Circular wall, conduction
The rate of heat flow Q [W] over the area A [m2] and an infinitesimal thickness dr [m] of the wall may be written as:
FourierĀ“s law
where λ [W/m·K] is the wall thermal conductivity.

This equation is known as Fourier's law of conduction.
Integrating for a wall thickness (ro - ri) with boundary temperatures T1 and T2 gives:
FourierĀ“s law, integrated
The temperature profile is hence a logarithmic curve.
For thin walls the equation for a plane wall may be applied.



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