Along, cylindrical, electrical heating element of diameter d= 10 mm, thermal conductivity k= 240 w/m·k, 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 15 m/s, respectively.

(a) neglecting radiation, estimate the steady-state surface temperature when, per unit length of the heater, electrical energy is being dissipated at a rate of 1500 w/m.

(b) if the heater is activated from an initial temperature of 27°c, estimate the time required for the surface temperature to come within 10°c of its steady-state value. evaluate the properties of air at 450 k