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# Electronic device radiator

The semiconductor device attached to a sapphire substrate installed on a copper header. The thermal resistance of interest is the resistance from the semiconductor device to the ambient.

**Problem Type:**

Plane problem of transient heat transfer.

**Geometry:**

The R_{ca} block represents the known thermal resistance from the header to the ambient.

**Given:**

Thermal load of semiconductor device: 60 W/mm^{2};

Heat conductivity of sapphire: 28 J/K·m;

Heat conductivity of copper: 394 J/K·m;

Heat conductivity of R_{ca}: 1 J/K·m;

Mass density of sapphire: 3985 kg/m^{3};

Mass density of copper: 8950 kg/m^{3};

Specific heat of sapphire: 3985 J/Kg·K;

Specific heat of copper: 8950 J/Kg·K;

**Solution:**

The transient thermal resistance is calculated as the instantaneous temperature increase divided by the heat flux. A normalized curve can be obtained by dividing the instantaneous temperature by the final temperature.

The shape of the graph can be qualitatively explained by the presence of two very different thermal time constants in the system. The first time constant corresponds to sapphire substrate (it works up to 0.005 sec.). The second time constant corresponds to copper header. The second time constant will be better visible if the simulation time is extended above 2 sec., so two simulations are necessary to visualize the system behavior.

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