Fluid velocities can be measured using hot-film sensors, and a common design is one for which the sensing element forms a thin film about the circumference of a quartz rod. The film is typically comprised of a thin (-100 nm) layer of platinum, whose electrical resistance is proportional to its temperature. Hence, when submerged in a fluid stream, an electric current may be passed through the film to maintain its temperature above that of the fluid. The temperature of the film is controlled by monitoring its electric resistance, and with concurrent measurement of the electric current, the power dissipated in the film may be determined.

Proper operation is assured only if the heat generated in the film is transferred to the fluid, rather than conducted from the film into the quartz rod. Thermally, the film should therefore be strongly coupled to the fluid and weakly coupled to the quartz rod. This condition is satisfied if the Biot number is very large, Bi = hD/2k >> 1, where h is the convection coefficient between the fluid and the film and k is the thermal conductivity of the rod.

(a) For the following fluids and velocities, calculate and plot the convection coefficient as a function of velocity: (i) water, 0.5 < V < 5 m/s; (ii) air, 1 < V < 20 m/s.

(b) Comment on the suitability of using this hot-film sensor for the foregoing conditions.

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Quartz rod, D= 1.5 mm k = 1.4 W/m-K Fluid VT= 20°C Power leads, thick films, no power dissipation Hot-film sensor, T, = 50°C w = 0.3 mm