Chapter 6, Problem 6.44P

A microscale detector monitors a steady flow $\left(T_{\infty }=27°\text{C,}V=10\text{m/s}\right)$ of air for the possible presence of small, hazardous particulate matter that may be suspended in the room. The sensor is heated to a slightly higher temperature to induce a chemical reaction associated with certain substances of interest that might impinge on the sensor's active surface. The active surface produces an electric current if such surface reactions occur; the electric current is then sent to an alarm. To maximize the sensor head's surface area and, in turn, the probability of capturing and detecting a particle, the sensor head is designed with a very complex shape. The value of the average heat transfer coefficient associated with the heated sensor must be known so that the required electrical power to the sensor can be determined.

Consider a sensor with a characteristic dimension of $L_s=80\text{μm}\text{.}$ A scale model of the sensor is placed in a recirculating (closed) wind tunnel using hydrogen as the working fluid. If the wind tunnel operates at a hydrogen absolute pressure of 0.5 atm and velocity of $V=0.5\text{m/s}\text{.}$ find the required hydrogen temperature and characteristic dimension of the scale model, $L_m.$