A bar heater of length L 300 mm and outer diameter of D 30

A bar heater of length L = 300 mm and outer diameter of D = 30 mm is used to heat a swimming pool. Under normal operating conditions, the heater dissipates 3 kW while submerged in the water flow that is at 20 C and provides a convection heat transfer coefficient of 5000 W/m2K.

a) Neglecting the heat transfer from the ends of the heater, determine its surface temperature Ts . Where qconv= hA(Ts-T).

b) If the water flow is inadvertently terminated while the heater continues to operate, the heater surface is exposed to air that is also at 20 C but for which h = 50 W/m2K. What is the corresponding surface temperature?

c) What are the consequences of such an event?

d) What assumptions are being made in this calculation?

e) In order to find out how uniform the temperature is in the pool, an engineer suggests performing a simulation. Discuss possible boundary conditions for the simulation

Solution

a) power dessipated = h*A*(Ts-Tamb)

3000W = 5000W/m^2.K*(Ts-20 degrees C) * Area in m^2

area = 0.02826 square meters

hence, solving the aove equation, we get,

Ts = 41.23 degrees celcius.

b) substituting h = 50 W/m2.K in place of 5000, we get

t = 2143 degrees celcius

c) by keepin the heater exposed in air, the temperature of the heater exceeds that of melting point of the equipment and this can cause meltdown of the electrode

d) assumption is made that the water is contimously in flow or heater is being moved in the pool. if thats not the case, the layers of water near the heater boundry shall not be at 20 degrees celcius and the temperature of the heater shall be higher.