Example-cylindrical coordinates

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Presentation transcript:

Example-cylindrical coordinates Use the conduction equation to find an expression for the rate of heat transfer for the cylindrical analog of the situation depicted in the following figure.

Summary of the problem As shown in the sketch, the solid is in the form of a hollow cylinder and the outer and inner surfaces are maintained at temperatures T1 and T2, respectively. The ends of the cylinder are insulated so that heat can flow only in the radial direction.

Write down your assumptions No heat source Constant k

Consider a thin cylindrical shell element of thickness ∆r in a long cylinder as shown below

Energy balance equation

Simplifications

Simplifications

Compact form of the conduction equation in one direction for all coordinates

Examples

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