Question

A cylindrical electric heater is located at the centre of a room. The heater has an outer diameter of 0.05 m, length of 0.6 m and emmisivity of 0.97. The surface temperature of this heater is maintained at 105 °C. The internal dimension of the room is 5m x 10m x 3m. The inner surface of this room's wall and air inside this room is maintained at 20 °C using an air conditioning system. The heat transfer coefficient between the heater and surrounding air is 35 W/m2K. Determine the heating power that should be produced by the electric heater to maintain its surface temperature.

Answer 1

Ans

Surface area of the cylindrical heater,

A= adL = 7 * 0.05 * 0.6 = 0.09425m?

Heat transfer coefficient between the heater and surrounding, h = 35 W/m² K

Emissivity of the heater, $\varepsilon = 0.97$

Surface temperature of the heater wall, T_s = 105 ^oC

Surrounding temperature, T_a = 20 ^oC

Room wall temperature, T_w = 20 ^oC

Stefan - Boltzmann constant, $\sigma = 5.67 * 10^{-8} Wm^{-2} K^{−4}$ $\sigma = 5.67 * 10^{-8} Wm^{-2} K^{-4}$

Solution:

Heating power that should be produced = heat lost by the convection + heat lost by the radiation

  

Q=hAT, – T.) + €0 AT - T

  

(ans)