An electrically heated plate, 10 cm square, is placed in a horizontal position 5 cm below a second plate of the same size as shown schematically below.

The heating surface is gray (emissivity = 0.8) while the receiver has a black surface. The lower plate is heated uniformly over its surface with a power input of 300 W. Assuming that heat losses from the backs of the radiating surface and the receiver are negligible and that the surroundings are at a temperature of 27°C, calculate the following

(a) The temperature of the receiver

(b) The temperature of the heated plate.

(c) The net radiation heat transfer between the two surfaces.

(d) The net radiation loss to the surroundings.

(e) Estimate the effect of natural convection between the two surfaces on the rate of heat transfer.

GIVEN

A square heated plate below a second plate of equal size as shown above

Plate size = 10 cm x 10 cm = 0.1 m x 0.1 m

Distance between plates (L) = 5cm = 0.05 m

Heated surface (A1) is gray with an emissivity (ε 1) = 0.8

Receiver (A2) is black (ε2 = 1.0)

Heater power input (qG) = 300 W

ASSUMPTIONS

Steady state

Heat losses from the back of each plate are negligible

Temperature of surroundings (T3) = 27°C = 300 K

The surroundings behave as a blackbodyenclosure

Recelver 2 Heated Plate 1 5 cm -10 cm- * 10 cm