Three electric resistance heaters of length L 250 mm and

Chapter , Problem 1.51

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Three electric resistance heaters of length L 250 mm and diameter D 25 mm are submerged in a 10-gal tank of water, which is initially at 295 K. The water may be assumed to have a density and specific heat of 990 kg/m3 and c 4180 J/kg K. (a) If the heaters are activated, each dissipating q1 500 W, estimate the time required to bring the water to a temperature of 335 K. (b) If the natural convection coefficient is given by an expression of the form h 370 (Ts T) 1/3, where Ts and T are temperatures of the heater surface and water, respectively, what is the temperature of each heater shortly after activation and just before deactivation? Units of h and (Ts T) are W/m2 K and K, respectively. (c) If the heaters are inadvertently activated when the tank is empty, the natural convection coefficient associated with heat transfer to the ambient air at T 300 K may be approximated as h 0.70 (Ts T) 1/3. If the temperature of the tank walls is also 300 K and the emissivity of the heater surface is 0.85, what is the surface temperature of each heater under steady-state conditions? 1.