Along, cylindrical, electrical heating element of diameter d = 10 mm, thermal conductivity k = 240 w/m-k, density rho = 2700 kg/m^3, and specific heat c_p = 900 j/kgk is installed in a duct for which air moves in cross flow over the heater at a temperature and velocity of 27 degree c and 10 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 1000 w/m.

b. if the heater is activated from an initial temperature of 27 degree c, estimate the time required for the surface temperature to come within 10 degree c of the steady state value.