A long, cylindrical, electrical heating element of diameter D = 12 mm, thermal conductivity k = 240 W/m ⋅ K, density ρ = 2,856 kg/m3, and specific heat cp = 908 J/kg ⋅ K is installed in a duct for which air moves in cross flow over the heater at a temperature and velocity of 30°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 1,238 W/m.

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