Two coaxial parallel plate discs are situated relative to each other as shown in the sketch. The diameter of the upper plate is 20 cm, and that of the lower plate is 40 cm. The lower plate is maintained at a uniform temperature of 500 K and the upper temperature is maintained at 456 K. To maintain these relative temperatures, a heater has to be installed in the upper plate. Assuming an environmental temperature of the surroundings at 300 K, determine the power necessary of the heater in the upper plate to maintain the two constant plate temperatures under steady state conditions.

Question

GIVEN

• Two coaxial parallel plate discs at distance of L = 20 cm=0.2 m

• Upper plate diameter (D1) = 20 cm = 0.2 m

• Lower plate diameter (D2) = 40 cm = 0.4 m

• Upper plate temperature (T1) = 456 K

• Lower plate temperature (T2) = 500 K

• Surrounding temperature (Tsurr) = 300 K

FIND

(a) Power necessary of the heater in upper plate to maintain the constant plate temperatures under steady state conditions.

SKETCH



PROPERTIES AND CONSTANTS

The Stephan-Boltzmann constant (?) = 5.67 × 10–8 W/(m2 K4)

Answer 1

Net heat radiation leaving the upper plate is given by



for Two parallel discs of unequal radius a and b separated apart by

distance L



where a=0.1 m, b= 0.2 m, L= 0.2 m



Now we have



Thus, heat flow rate from top plate is



Thus, power necessary of the heater in upper plate to maintain the constant plate temperatures under steady state conditions is 17.05 W