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Conduction in the Cylindrical Geometry

1 Conduction in the Cylindrical Geometry R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University Chemical engineers encounter Conduction in the Cylindrical Geometry when they analyze heat loss through pipe walls, heat transfer in double-pipe or shell-and-tube heat exchangers, heat transfer from nuclear fuel rods, and other similar situations. Unlike Conduction in the rectangular Geometry that we have considered so far, the key difference is that the area for heat flow changes from one radial location to another in the Cylindrical Geometry . This affects the temperature profile in steady Conduction . As an example, recall that the steady temperature profile for one-dimensional Conduction in a rectangular slab is a straight line, provided the thermal conductivity is a constant. In the Cylindrical Geometry , we find the steady temperature profile to be logarithmic in the radial coordinate in an analogous situation.

2 . We use a shell balance approach. Consider a cylindrical shell of inner radius . r and outer radius rr+∆ located within the pipe wall as shown in the sketch.The shell extends the entire length L of the pipe. Let Qr( ) be the radial heat flow rate at the radial location r within the pipe wall. Then, in the end view shown above, the heat flow rate into the cylindrical shell is Qr( ), while

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