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Temperature distribution in the conducting sheet

The voltage is applied to the sides of conducting sheet placed vertically. The flowing current heats the sheet due to resistive losses. The front and back surfaces of the sheet are cooled by the air (natural convection).

Problem Type:
Plane problem of electro-thermal coupling.

Geometry:

conducting sheet model

Given:
Sheet thickness d = 1 mm;
Material resistance ρ = 10-7 Ohm/m;
Voltage applied U = 0.02 V;
Material heat conductivity λ = 380 W/K·m;
Convection coefficient α = 10 W/K·m2;
Ambient air temperature T0 = 0°C.

Problem:
Calculate the current and temperature distribution in a conducting sheet.

Solution:
The resistive losses are calculated in the DC conduction problem. Then these losses are transferred to the linked heat transfer problem.
All faces are washed by the air and subjected to the same cooling conditions:
Q(T) = -α·T, where α - convection coefficient
The convection from front and back faces is modelled by temperature depended heat sink
Q(T) = - k·T.

conducting sheet convection

Results:

Current distribution in the conducting sheet
conducting sheet current distribution

Temperature distribution in the conducting sheet
conducting sheet temperature distribution

The Coupl5CF.pbm is the problem of calculating the current distribution in the sheet, and Coupl5HT.pbm analyzes temperature field.

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