Coupl3: Temperature distribution in an electric wire
Calculate the temperature distribution in a long current carrying wire.
Problem Type:
Axisymmetric problem of electro-thermal coupling.
Geometry:
Given:
Wire diameter d = 10 mm;
Resistance ρ = 3·10-4 Ohm/m;
Electric current I = 1000 A;
Thermal conductivity λ = 20 W/K·m;
Convection coefficient α = 800 W/K·m2;
Ambient temperature To = 20 °C.
Problem:
Calculate the temperature distribution in the wire.
Solution:
We arbitrary chose a 10 mm piece of wire to be represented by the model. For data input we need the wire diameter d=10 mm, and the resistivity of material: R=ρ·πd2/4 Ohm·m, and voltage drop for our 10 mm piece of the wire: ΔU=I·R·L = 3·10-3 V.
For the conduction problem we specify two different voltages at two sections of the wire, and a zero current condition at its surface. For heat transfer problem we specify zero flux conditions at the sections of the wire and a convection boundary condition at its surface.
Comparison of results
Center line temperature:
|
T (°C) |
Theory |
33.13 |
QuickField |
33.14 |
The Coupl3CF.pbm and Coupl3HT.pbm problems are corresponding DC conduction and heat transfer parts of this problem.
Reference
W. Rohsenow and H. Y. Choi, "Heat, Mass, and Momentum Transfer", Prentice-Hall, N.J., 1963.
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