A hot-wire anemometer is a common instrument used to measure the velocity of a flowing gas. A typical probe tip is shown below.

Electrical current is passed through a very thin wire of platinum or tungsten. The electrical resistance of the wire generates heat as the current passes through it, making the wire hot. This €œhot wire€ is placed normal to the flowing gas stream and the heat generated by the wire is dissipated to the gas stream flowing around the wire by convective heat transfer. The current passing through the wire and temperature of the wire are measured, and, from this information, the velocity of the gas flowing over the wire is estimated.
In the current set of measurements, the hot-wire anemometer is mounted inside a tube containing flowing N₂ gas at 20°C. During one test, the power load on the wire was 13 mW, and the temperature of the wire was 200°C. The diameter of the platinum wire is 4 μm, and its length is 1.2 mm.
a. What is the Prandtl number for the N₂ gas flowing around the hot wire?
b. What is the measured Nusselt number (Nu) for the N₂ gas flowing around the hot wire?
c. What is the estimated velocity of the flowing N₂ gas inside the tube at the point where the hot-wire anemometer probe tip is located?

Thermophysical properties of N₂ gas

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Viscosity, µ (kg/m-sec) Tempe- Density, Heat Thermal Conductivity, k (W/m · K) Capacity, Cp (J/kg · K) p (kg/m³) rature (°C) 0.9754 2.0000 × 10-5 0.8533 2.19950 × 10-5 0.029691 350 1042.1 400 0.033186 1049.9 platinum hot wire (4 µm thickness)