Question

13.45 At the bottom of a large vacuum chamber whose walls are at 300 K, a black panel 0.1 m in diameter is maintained at 77 K. To reduce the heat gain to this panel, a radiation shield of the same diameter D and an emissivity of 0.05 is placed close to the panel. Calculate the net rate of heat gain to the panel. The illustration is of the bottom of a large vacuum chamber is of square shape whose walls are at 300 K, a black panel is maintained at 77 K. A radiation shield of the same diameter D is placed close to the panel.

Answer 1

To calculate the net rate of heat gain to the black panel, we can use the Stefan-Boltzmann Law and find the rates of heat transfer from the panel to the radiation shield and from the walls to the panel. Subtracting these rates will give the net rate of heat gain to the panel.

Step-by-step explanation:

To calculate the net rate of heat gain to the black panel, we can use the Stefan-Boltzmann Law, which relates the rate of heat transfer by radiation to the temperatures and emissivities of the objects involved.

1. 
   
3. First, we can find the total rate of heat transfer from the panel to the radiation shield using the formula: Qt = εσA(T1^4 - T2^4), where Qt is the rate of heat transfer, ε is the emissivity, σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2 K^4), A is the surface area, and T1 and T2 are the temperatures in Kelvin.
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6. Next, we can find the rate of heat transfer from the walls of the vacuum chamber to the panel using the same formula. The only difference is that T1 is now 300 K (temperature of the walls) and T2 is 77 K (temperature of the panel).
7. 
   
9. Finally, we can subtract the rate of heat transfer from the walls to the panel from the rate of heat transfer from the panel to the radiation shield to get the net rate of heat gain to the panel.

By plugging in the given values, we can calculate the net rate of heat gain to the panel.