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Chapter 13: Problem 166

Consider an enclosure consisting of \(N\) diffuse and gray surfaces. The emissivity and temperature of each surface as well as the view factors between the surfaces are specified. Write a program to determine the net rate of radiation heat transfer for each surface.

Short Answer

Expert verified
**Answer:** Q_net[i] = ϵ[i] * (Q_irad[i] - E[i])

Step by step solution

01

Gather Inputs

First, we need to collect information about the enclosure's surfaces: the number of surfaces (N), their temperatures (T[i]), emissivities (ϵ[i]), and view factors (F[i, j]). You will need to create variables and get the input values from the user for each surface.
02

Calculate Emissivity Power

Next, we need to calculate the emissive power of each surface. Emissive power is given by the equation: E[i] = ϵ[i] * σ * T[i]^4, where σ is the Stefan-Boltzmann constant (5.67 * 10^-8 W/m^2 K^4). Create an array of size N and populate it with the emissive power for each surface.
03

Calculate Incident Radiation

Now, we will calculate the incident radiation on each surface (Q_irad[i]), which is the sum of the emitted and reflected radiation from other surfaces. Use the following formula to compute Q_irad[i]: Q_irad[i] = Σ (ϵ[j] * F[j, i] * E[j]) + (1 - ϵ[j]) * F[j, i] * Q_irad[j], for each j ≠ i in the enclosure. You may need to loop through the N surfaces and calculate the incident radiation in each iteration.
04

Calculate Surface Emission

With the incident radiation and emissive power known, we can now calculate the surface emission for each surface. Surface emission (Q_emission[i]) is calculated as: Q_emission[i] = ϵ[i] * E[i]. Create an array of size N and fill it with the emission values for each surface.
05

Calculate Net Radiation Heat Transfer

Lastly, we will determine the net radiation heat transfer for each surface. Net radiation heat transfer (Q_net[i]) can be calculated as: Q_net[i] = ϵ[i] * (Q_irad[i] - E[i]). Create an array of size N and fill it with the net radiation heat transfer values for each surface.
06

Output Results

Output the net radiation heat transfer values (Q_net) for each surface in the enclosure. You can display the results in a table or print them as a list. Make sure you include appropriate units (W/m^2) and surface identifiers to ensure the results are clear and easy to interpret.

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Most popular questions from this chapter

Consider two infinitely long concentric cylinders with diameters 20 and \(25 \mathrm{~cm}\). The inner surface is maintained at \(700 \mathrm{~K}\) and has an emissivity of \(0.40\), while the outer surface is black. If the rate of radiation heat transfer from the inner surface to the outer surface is \(2400 \mathrm{~W}\) per unit area of the inner surface, the temperature of the outer surface is (a) \(605 \mathrm{~K}\) (b) \(538 \mathrm{~K}\) (c) \(517 \mathrm{~K}\) (d) \(451 \mathrm{~K}\) (e) \(415 \mathrm{~K}\)

Two very large parallel plates are maintained at uniform temperatures of \(T_{1}=600 \mathrm{~K}\) and \(T_{2}=400 \mathrm{~K}\) and have emissivities \(\varepsilon_{1}=0.5\) and \(\varepsilon_{2}=0.9\), respectively. Determine the net rate of radiation heat transfer between the two surfaces per unit area of the plates.

The base surface of a cubical furnace with a side length of \(3 \mathrm{~m}\) has an emissivity of \(0.80\) and is maintained at \(500 \mathrm{~K}\). If the top and side surfaces also have an emissivity of \(0.80\) and are maintained at \(900 \mathrm{~K}\), the net rate of radiation heat transfer from the top and side surfaces to the bottom surface is (a) \(194 \mathrm{~kW}\) (b) \(233 \mathrm{~kW}\) (c) \(288 \mathrm{~kW}\) (d) \(312 \mathrm{~kW}\) (e) \(242 \mathrm{~kW}\)

How does radiation transfer through a participating medium differ from that through a nonparticipating medium?

Define spectral transmissivity of a medium of thickness \(L\) in terms of \((a)\) spectral intensities and \((b)\) the spectral absorption coefficient.
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