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Temperature distribution in an electric wire
Coupl3: Temperature distribution in an electric wire
Calculate the temperature distribution in a long current carrying wire.
Problem Type:
Axisymmetric problem of electrothermal coupling.
Geometry:
Given:
Wire diameter d = 0.75";
Resistance ρ = 9.35·10^{8} Ohm/m;
Electric current I = 1000 A;
Thermal conductivity λ = 13 Btu·ft/(h·ft^{2}·°F) = 22.5 W/(K·m);
Convection coefficient α = 5 Btu/(h·ft^{2}°F) = 28.4 W/(K·m^{2});
Ambient temperature T_{o} = 70°F = 21.1°C.
Problem:
Calculate the temperature distribution in the wire.
Solution:
We arbitrary chose a 1foot (12") piece of wire to be represented by the model.
Material electric conductivity is σ = 1/ρ = 1/9.35e8 = 10.7·10^{6} S·m.
For the conduction problem we specify normal current density at one end j = I /(πd^{2}/4) [A/m^{2}] and zero voltage at another end of the wire, and a zero current condition at its surface.
For heat transfer problem we specify zero thermal flux conditions at the sections of the wire and a convection boundary condition at its surface.
Results:
Temperature distribution in an electric wire:

Center line temperature 
Surface temperature 
Theory 
419.9 F (215.5 °C) 
417.9 F (214.4 °C) 
QuickField 
215.5 °C 
214.3 °C 
* Reference: W. Rohsenow and H. Y. Choi, "Heat, Mass, and Momentum Transfer", PrenticeHall, N.J., 1963.
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