# Coupl3: Temperature distribution in an electric wire

Calculate the temperature distribution in a long current carrying wire.

Problem Type:
An axisymmetric problem of electro-thermal 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·m2;
Ambient temperature T0 = 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 = 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", Prentice-Hall, N.J., 1963.

See the Coupl3CF.pbm and Coupl3HT.pbm problems in the Examples folder for the corresponding DC conduction and steady-state heat transfer parts of this problem.