Two parallel plates of infinite extent perpendicular to the page are situated relative to each other as shown in the figure. The upper plate is at 300°C and the lower plate is at 100°C. Determine the net rate of radiation heat transfer from the upper and lower plate assuming the environment is at a temperature below 100°C. Assume that both the lower surface of the upper plate and the upper surface of the lower plate are black.

Question

GIVEN

• Two parallel plates of infinite extent perpendicular to the page.

• Upper plate temperature (T2) = 3000C

• Lower plate temperature (T1)= 1000C

• Length of the plates L1 = L2 = 2 m

• Distance between the plates (R) = 1 m

FIND

(a) Net rate of radiation heat transfer from upper and lower plate.

ASSUMPTIONS

• Lower surface of upper plate and upper surface of lower plate are black.

SKETCH



PROPERTIES AND CONSTANTS

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

Answer 1

Two imaginary plates 3 and 4 are extended along the plate 1 so that the center of both upper and lower plates align.

By symmetry F21 = F23

Thus, F21= 0.5*(F2(1,4,3)- F24 )

Now, for plates of infinite extent perpendicular to the plane and of given dimensions y=6 m D=1

m y/D= 6 width of plates (x)= ?, x/D=?

Shape factor for directly opposed plane F2(1,3,4)= 0.88

For plates 2 and 4, the shape factor F24 is calculated as y=2 m D=1 m y/D= 2 width of plates (x)= ?, x/D=?

Shape factor for directly opposed plane F24= 0.65 Thus, the shape factor F21 is calculated as

F21= 0.5*(0.88- 0.65 ) = 0.115 Thus, net radiative heat transfer between upper and lower plates is Q/A2 = 4 4