An electric room heater has been designed in the shape of a vertical cylinder 2-m-tall and 30 cm in diameter. For safety, the heater surface cannot exceed 35°C. If the room air is 20°C, find the power rating of the heater in watts.

Question

GIVEN

• An electric heater in the shape of a vertical cylinder

• Heater height (H) = 2 m

• Heater diameter (D) = 30 cm = 0.3 m

• Room air temperature (T?) = 20°C = 293 K

FIND

• The power rating of the heater (q) in watts

ASSUMPTIONS

• Radiation is negligible

• Heat transfer from the top and bottom of the tank is negligible

SKETCH



PROPERTIES AND CONSTANTS

for dry air at the mean temperature of 27.5°C

Thermal expansion coefficient (?) = 0.00332 1/K

Thermal conductivity (k) = 0.0256 W/(m K)

Kinematic viscosity (?) = 16.4 × 10–6 m2/s

Prandtl number (Pr) = 0.71

Answer 1

When the heater surface temperature is 35°C, the Grashof number for the heater sides is



Therefore, the flow is turbulent.

The average heat transfer coefficient is given by



The power rating of the heater must equal the rate of heat transfer from the heater



COMMENTS

This heater would probably not suffice for most applications. Either the surface temperature needs to be raised, of the size of the heater needs to be increased.