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Everyday Heat Transfer Problems: Sensitivities to Governing Variables

M. Kemal Atesmen
M. Kemal Atesmen
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ASME Press
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Maximum current in an open-air single electrical wire (not in a bundle), will be analyzed under steady-state and one-dimensional cylindrical coordinates, with constant property conditions. The wire is assumed to be a cylindrical conductor with a certain diameter and with certain material characteristics; i.e., resistivity. The wire conductor is insulated with concentric layers of insulation material that can stand up to a certain wire conductor temperature, Tc which will be the temperature rating of the wire. Heat generated in the wire conductor is I2R and the temperature within the wire conductor is assumed to be uniform—the conductor temperature does not vary radially from the center to the outer radius of the wire conductor.

Heat is transferred by conduction through the wire insulator and by convection from the surface of the wire insulator to the environment. Radiation heat transfer from the surface of the wire insulator is neglected. The conduction heat transfer from the conductor to the outer radius of the wire insulator can be written by the rate equation in cylindrical coordinates:  
Q=2ΠLkins(TcTinsulation outer radius)ln(rwrc)
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