A platinum hot-wire anemometer operated in the constant-temperature mode has been used to measure the velocity of a helium stream. The wire diameter is 20 ?m, its length is 5 mm, and it is operated at 90°C. The electronic circuit used to maintain the wire temperature has a maximum power output of 5 watts and is unable to accurately control the wire temperature if the voltage applied to the wire is less than 0.5 volt. Compare the operation of the wire in the helium stream at 20°C and 10 m/s with operation in air and water at the same temperature and velocity. The electrical resistance of the platinum at 90°C is 21.6 ?? - cm.

Question

GIVEN

• A constant temperature platinum hot-wire in a stream of helium

• Wire diameter = 20 ?m = 20 * 10–6 m

• Wire length (L) = 5 mm = 0.005 m

• Wire temperature (Tw) = 90°C

• Maximum electric power to wire (Pmax) = 5 W

• Minimum voltage (Vmin) = 0.5 V

• Helium temperature (T) = 20°C

• Helium velocity (U ) = 10 m/s

• Resistivity (re) = 21.6 ?? - cm.= 21.6 *10–8 ? - m FIND

• Compare the operation of the wire in helium to that in air and water

ASSUMPTIONS

• Radiation is negligible

PROPERTIES AND CONSTANTS

Answer 1

The Nusselt number is given by



The rate of convective heat transfer must equal the electrical power dissipated. Therefore, the power

capabilities of the unit are sufficient for these conditions in helium and air but not in water. The voltage for the case with air is too low for the device. Therefore, the device will perform adequately

only for the helium flow under these conditions.