Question

Two 60 cm parallel disks are separated by 40 cm and are aligned directly on top of each other. Both disks are black surfaces with temperatures of 450 K. The backs of the disks are insulated and the surroundings may be treated as a black body at 300 K. Determine the net radiation heat transfer from the disks to the environment.

Answer 1

Answer:

775.48 W

Explanation:

given,

diameter of disk = 0.6 cm

length of the disk = 0.4 m

T₁ = 450 K         T₂ = 450 K      T₃ = 300 K

$\dfrac{d}{r_1}=\dfrac{0.4}{0.3}$ = 1.33

now,

the value of view factor (F₁₂)corresponding to 1.33

F₁₂ = 0.265

F₁₃ = 1 - 0.265 = 0.735

now,

net rate of radiation heat transfer from the disk to the environment:

$=\dot{Q_{1-3}+Q_{2-3}} = 2 \dot{Q_{1-3}}$

       = 2 F₁₃ A₁ σ (T₁⁴ - T₃⁴)

       = 2 x 0.735 x π x (0.3)² x (5.67 x 10⁻⁸ W/m²) (450⁴ - 300⁴)

       = 775.48 W

Net radiation heat transfer from the disks to the environment = 775.48 W