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5. Conduction

Conductive heat transfer occurs when energy exchange takes place by direct impact of molecules moving from a high temperature region to a low temperature region.

Conductive heat loading on a system may occur through lead wires, mounting screws, etc., which form a thermal path from the device being cooled to the heat sink or ambient environment.

The fundamental equation that describes conductive loading is:
Qcond =k A DT
Qcond = conductive heat load (W)
k = thermal conductivity of the material (W/m °C)
A = cross-sectional area of the material (m2)
L = length of the heat path (m)
DT = temperature difference across the heat path (°C) (usually ambient or heat sink temperature minus cold side temperature)

Table I
Thermal Conductivities of Various Wire Materials

Material Thermal Conductivity (W / m°C)
Aluminum 205
Copper 386
Gold 315
Platinum (90%) Iridium (10%) 31.1
Platinum 70.9
Manganin 22.2

Example calculation: A TEC is used as a black body reference. A temperature sensor is attached to the cold surface of the TEC. It has two platinum leads, which have a diameter of 25mm and are 12mm long. These leads are attached to pins on the heat sink. The cold plate is at -20°C while the heat sink is at 30°C.

The known parameters are:
k = 70.9 W/m°C, from Table I
DT = [30°C - (-20°C)] = 50°C
A(1 wire) = pd2 / 4 = p (25 mm)2 / 4
= 4.91 X 10 -10 m2
A(2 wires) = (2)(4.91 X 10 -10m2) = 9.82 X 10 -10 m2
L = 12 mm = 0.012 m

From the equation above:
Qcond = [(70.9 W/m°C) (9.82 X 10-10 m2)] (50°C) / (0.012 m)
= 0.0003 W

Since the conductive load is inversely proportional to the length of the wire, it can be reduced by using longer wires.