# 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**

**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 `T`_{0} = 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`

**Results**

Current density and temperature distribution in the conducting sheet

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

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