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Main >> Applications >> Sample problems >> Temperature distribution in the conducting sheet

Temperature distribution in the conducting sheet

QuickField simulation example

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-parallel multiphysics problem of DC conduction coupled to Steady-State Heat Transfer.

Geometry
Temperature distribution in the conducting sheet The resistive losses are calculated in the DC conduction problem. Then these losses are transferred to the linked heat transfer problem. Conductor U GND 1 mm 70 mm 30 mm 20 mm R10 mm R10 mm 20 mm 40 mm

Given
Sheet thickness d = 1 mm;
Material conductivity σ = 1 MS/m;
Voltage applied U = 0.02 V;
Material heat conductivity λ = 50 W/K-m;
Convection coefficient α = 10 W/K-m²;
Ambient air temperature T0 = 0°C.

Task
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 [W/m²] = -α·T, where α - convection coefficient.
The convection from front and back faces is modelled by temperature depended heat sink
Q [W/m³] = - k·T, where k = 2 * α / d
conducting sheet convection

Results
Current density and temperature distribution in the conducting sheet
conducting sheet current distribution

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