A long, cylindrical, electrical heating element of diameter D 10 mm, thermal conductivity k = 240 W/mK, density rho = 2700 kg/m3, and specific heat Cp-900 J/kg-K is installed in a duct for which air moves in cross flow over the heater at a temperature and velocity of 27°C and 12 m/s, respectively. The electrical energy is being dissipated at a rate of 537 W/m Evaluate air properties at 450 K. Solve for the following:
a) Reynolds number
b) Nusselt number
c) steady state temp, in K
d) Biot number
e) How long does it take for the element to come within 10°C of the steady state temperature, in s?
f) Knowing the steady state temperature, what is the actual value of the film temperature that should be used to find the air properties, in K? (Hint: Do not redo the problem.)