Steady-State Temperature Profile of Two-Layer Pipe

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This Demonstration shows the steady-state temperature profile of a two-layer pipe with constant interior and exterior surface temperatures. You can vary the radii of the two material layers, their respective conductivities, and the two surface temperatures. You can see the resulting temperature profile as a function of pipe radius, with a slope discontinuity at the interface of the two materials. By minimizing the conductivity of one of the materials, an insulating layer can be simulated.

Contributed by: Fredericka Brown and Sara McCaslin (March 2011)
Open content licensed under CC BY-NC-SA



This solution uses the concept of thermal resistance circuits. Thermal resistance for a cylindrical shape as a function of radius is given by , where is the maximum cylinder radius and is the thermal conductivity. Heat transfer per unit length using thermal resistance is given by , which is then used to solve for the temperature as a function of radial distance .


Thermal Resistance Circuits

D. Pitts and L. E. Sissom, Schaum's Outline of Heat Transfer, New York: McGraw-Hill, 1998.

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