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Chapter 4: Problem 3

Give examples of radiative heat transfer processes dominated by surface- tosurface transfer and of processes for which the effects of absorption and emission in the space between surfaces (participating medium) are essential.

Short Answer

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Question: Identify and describe examples of two types of radiative heat transfer processes: one dominated by surface-to-surface transfer and another where absorption and emission in the space between surfaces play a significant role. Answer: An example of surface-to-surface radiative heat transfer is heat transfer between two parallel plates with a vacuum between them, such as in a vacuum thermos. In this case, heat transfer is solely due to the exchange of radiation between the surfaces of the plates. On the other hand, an example where absorption and emission between surfaces play a crucial role is the Earth's atmosphere. Here, the participating medium consists of various gases, water vapor, and aerosols. The atmosphere absorbs and emits solar radiation and longwave radiation originating from the Earth's surface, which is essential in understanding the greenhouse effect.

Step by step solution

01

Example of Surface-to-Surface Transfer

An example of surface-to-surface radiative heat transfer would be heat transfer between two parallel plates with a vacuum between them. In this case, the particles in the vacuum do not participate in the heat transfer process, and the heat transfer is solely due to the exchange of radiation between the surfaces of the plates. This type of heat transfer is typically seen in a vacuum thermos, where the space between the double walls is evacuated to minimize heat transfer by conduction and convection. The shiny inner surfaces of the thermos also minimize the heat transfer by reflecting the radiations.
02

Example of Participating Medium Transfer

An example of radiative heat transfer where absorption and emission in the space between surfaces play a significant role is in the Earth's atmosphere. In this case, the participating medium consists of various gases, water vapor, and aerosols. The incoming solar radiation is partly absorbed and partly scattered by the atmosphere. The atmosphere also absorbs and emits longwave radiation that originates from the Earth's surface. This participating medium heat transfer is essential in understanding the greenhouse effect, where certain gases (like carbon dioxide and water vapor) absorb outgoing longwave radiation, causing the Earth's atmosphere to warm up.

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Explain in what sense the set of equations Equation (4.11) provides a solution for the surface-to-surface radiative heat transfer problem. How would you solve the equations (a) in the case that the temperature of all surfaces is known and (b) in the case that for some surfaces the temperature and for other surfaces the heat flux are known?
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