Consider the electrical heater of Problem 7.49. If the blower were to malfunction, terminating airflow while the heater continued to operate at 1000 W/m, what tem- perature would the heater assume? How long would it take to come within 10 C of this temperature? Allow for radiation exchange between the heater ( 0.8) and the duct walls, which are also at 27 C.
7.49) Along,cylindrical,electricalheatingelementofdiameter D 10 mm, thermal conductivity k 240 W/m K, den- sity 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 sur- face 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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