Three electric resistance heaters of length L = 250 mm and diameter D = 25 mm are submerged in a 10 gallon tank of water, which is initially at 295 K. The water may be assumed to have a density and specific heat of p = 990 kg/m3 and c = 4180J/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 T, 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 hand (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 Tx = 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 B = 0.85, what is the surface temperature of each heater under steady-state conditions?