Heat Flow through a Pipe

An insulated pipe carrying steam is covered by insulation of width ; the inner and outer surface temperatures are and . The temperature as a function of the radius of the cross section for the steady state is shown. Fourier's law of heat conduction states that the heat flow normal and through an area is proportional to the area (in this case, the circular layers in the picture) and to the temperature gradient.

SNAPSHOTS

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DETAILS

Starting from the equation
,
where is the thermal conductivity, the solution is
,
where in the graphic.
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