A long, cylindrical, electrical heating element of diameter D 10 mm, thermal conductivity k 240 W/mK, density 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 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 C, estimate the time required for the surface temperature to come within 10 C of its steady-state value.

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