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### Description

Known: Area, emissivity and temperature of a surface placed in a large, evacuated chamber of prescribed temperature.
Find: a) Rate of surface radiation emission.
b) Net rate of radiation exchange between surface and chamber walls.
Assumptions
Area of the enclosed surface is much less than that of the chamber walls.

Calculation Reference
Fundamentals of Heat and Mass Transfer by Frank P. Incropera

To determine the rate of surface radiation emission and the net rate of radiation exchange between the surface and the chamber walls, considering the area, emissivity, and temperature of the surface in a large, evacuated chamber, you can follow these steps:

a) Rate of surface radiation emission:

1. Calculate the Stefan-Boltzmann constant: The Stefan-Boltzmann constant (σ) is approximately 5.67 x 10^-8 W/(m^2·K^4).

2. Use the Stefan-Boltzmann Law to calculate the rate of surface radiation emission (Q_emit):

Q_emit = ε * σ * A * (T_surface^4)

Where ε is the emissivity of the surface, A is the area of the surface, T_surface is the temperature of the surface in Kelvin, and σ is the Stefan-Boltzmann constant.

b) Net rate of radiation exchange between surface and chamber walls:

1. Calculate the temperature of the chamber walls: Determine the prescribed temperature of the chamber walls in Kelvin (T_chamber).

2. Use the Stefan-Boltzmann Law to calculate the rate of radiation emission from the chamber walls (Q_walls):

Q_walls = σ * A_walls * (T_walls^4)

Where A_walls is the area of the chamber walls and T_walls is the temperature of the chamber walls in Kelvin.

3. Calculate the net rate of radiation exchange between the surface and the chamber walls (Q_net) as the difference between the rate of surface radiation emission and the rate of radiation emission from the chamber walls:

Q_net = Q_emit - Q_walls

Where Q_emit is the rate of surface radiation emission and Q_walls is the rate of radiation emission from the chamber walls.

By following these steps, you can determine the rate of surface radiation emission and the net rate of radiation exchange between the surface and the chamber walls. These calculations consider the area, emissivity, and temperature of the surface, as well as the temperature of the chamber walls. The assumption that the area of the enclosed surface is much less than that of the chamber walls allows for simplified analysis and neglects any significant radiation exchange between the chamber walls and the surface.

24 Jan 2007
18 Jul 2023
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