Calculate the temperature distribution in a long current carrying wire.
Problem Type:
An axisymmetric problem of electrothermal coupling.
Geometry:
Given:
Wire diameter d = 10 mm;
Resistance ρ = 3·10^{4} Ω/m;
Electric current i = 1000 A;
Thermal conductivity λ = 20 W/K·m;
Convection coefficient α = 800 W/K·m^{2};
Ambient temperature T_{0} = 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 · πd^{2}/ 4 = 2.356·10^{8} Ohm·m,
and voltage drop for our 10 mm piece of the wire:
ΔU = i · R · L = 3·10^{3} V.
For the DC 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 
Reference:
W. Rohsenow and H. Y. Choi, "Heat, Mass, and Momentum Transfer", PrenticeHall,
N.J., 1963.
See the Coupl3CF.pbm and Coupl3HT.pbm problems in the Examples folder for the corresponding DC conduction and steadystate heat transfer parts of this problem.