Chapter 1
Heat Transfer
steps just outlined. It can also be obtained directly by coordinate transformation using the following relations between the coordinates of a point in rectangular and cylindrical coordinate systems
Figure 3: A differential volume element in cylindrical coordinates.
After lengthy manipulations we obtain (
*
(
*
(
*
̇
Spherical Coordinates The general heat conduction equations in spherical coordinates can be obtained from an energy balance on a volume element in spherical coordinates, shown in Figure 4, by following the steps outlined above. It can also be obtained directly by coordinate transformation using the following relations between the coordinates of a point in rectangular and spherical coordinate systems
Again after lengthy manipulations, we obtain (
*
(
*
(
*
̇
Conduction through a cylindrical wall For a cylinder at steady state, with no internal heat generation, the equation becomes
O
b
B. ’
w
b
equation as
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