Consider the electrical space heater, where the electric resistance heating coil is enclosed in a straight horizontal polished metallic cylinder that has an outer diameter of 1 cm and an emissivity of 0.9. If its surface temperature is at 110°C and the room air temperature is at 20°C, calculate the total heat loss per unit length of the cylinder due to both convection and radiation. For the purpose of this calculation, assume that the reflector is so designed that it “collects” all of the radiant heat from the back half of the horizontal heater and that it reflects 95% of the incident radiation.

Question

GIVEN

• An electric resistance heating coil enclosed in horizontal metallic cylinder.

• Emissivity (?) = 0.9

• Diameter of cylinder (D) = 1 cm= 0.01 m

• Surface temperature (Ts) = 110°C= 383 K

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

• Reflects 95% of incident radiation.

FIND

Total heat loss per unit length of cylinder due to convection and radiation.

ASSUMPTIONS

• Air is still

• Surface temperature is uniform and constant

PROPERTIES AND CONSTANTS

for dry air at the mean temperature of 65°C

Thermal expansion coefficient (?) = 0.00296 1/K

Thermal conductivity (k) = 0.02825 W/(m K)

Kinematic viscosity (?) = 19.92 × 10–6 m2/s

Prandtl number (Pr) = 0.71

Answer 1

The Grashof number is



we have



Thus total heat loss per unit length by both convection and radiation is given by