In a television weather report a wind chill factor is frequently stated. The actual factor is based

Question:

In a television weather report a "wind chill factor" is frequently stated. The actual factor is based on empirical data. You are asked to come up with an expression for wind chill based on the information presented in Chapters 6 and 7. In obtaining this relation you may assume that (1) a man can be approximated as a vertical cylinder 30 cm in diameter and 1.8 m tall, (2) wind chill expresses the equivalent air temperature the cylinder would experience in free convection when losing heat by forced convection to air at the ambient temperature and velocity uˆž, (3) forced convection heat loss from the cylinder can be obtained from Equation (6-17) with the appropriate values of C and n, and (4) free convection from the vertical cylinder can be obtained from the simplified expressions of Table 7-2. Based on these assumptions, devise relationship(s) to predict the wind chill for ambient temperatures between ˆ’12 and + 10oC and wind velocities between 5 and 40 mi/h (1 mi/h = 0.447 m/s). Other assumptions must be made in addition to the ones stated. Be sure to clearly note your assumptions in arriving at the relation(s) for wind chill. If convenient, check other sources of information to verify your results. If you are currently experiencing winter weather, compare your results with a television weather report.
Equation (6-17)