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Chapter 13: Problem 32

What are the two methods used in radiation analysis? How do these two methods differ?

Short Answer

Expert verified
Answer: The two methods used in radiation analysis are deterministic methods and stochastic methods. Deterministic methods, such as point-kernel methods, involve direct calculations using mathematical equations and are suitable for simple geometries and problems involving a small number of particles. Stochastic methods, such as Monte Carlo methods, use random sampling to simulate radiation interactions and are better suited for complex geometries and materials with varying properties. While deterministic methods are typically faster and require less computational power, stochastic methods are more accurate for complex problems and can account for uncertainties in the input data.

Step by step solution

01

Identify the two methods used in radiation analysis

The two methods used in radiation analysis are deterministic methods and stochastic methods.
02

Define deterministic methods in radiation analysis

Deterministic methods, also known as point-kernel methods, involve the direct calculation of radiation intensity at specific locations using mathematical equations. These methods are useful when dealing with simple and well-defined geometries, and can provide quick solutions to radiation shielding problems. Some examples of deterministic methods are ray-tracing and the three-dimensional (3D) discrete ordinates method.
03

Define stochastic methods in radiation analysis

Stochastic methods, also known as Monte Carlo methods, involve random sampling to simulate the interaction of radiation with matter. These methods take into account the randomness of radiation processes and give more accurate results, especially in cases involving complex geometries or several materials with different properties. Monte Carlo simulations track particle histories and use random numbers to simulate particle interactions and spatial distributions.
04

Compare deterministic methods and stochastic methods

Deterministic methods are typically faster and require less computational power, making them suitable for simple geometries and problems involving a small number of particles. However, these methods can become inaccurate when dealing with complex problems or materials that have a wide range of physical properties. Stochastic methods, on the other hand, may require more computational power and time to achieve accurate results, but they can handle complex geometries and materials more effectively. Due to their probabilistic nature, these methods can also account for uncertainties in the input data and provide error estimates for the results. Monte Carlo methods specifically excel in situations where there are multiple radiation interactions and complex geometries.

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Most popular questions from this chapter

A thermocouple shielded by aluminum foil of emissivity \(0.15\) is used to measure the temperature of hot gases flowing in a duct whose walls are maintained at \(T_{w}=380 \mathrm{~K}\). The thermometer shows a temperature reading of \(T_{\text {th }}=530 \mathrm{~K}\). Assuming the emissivity of the thermocouple junction to be \(\varepsilon=0.7\) and the convection heat transfer coefficient to be \(h=120 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), determine the actual temperature of the gas. What would the thermometer reading be if no radiation shield was used?

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) \(415 \mathrm{~K}\)

\(3 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), and both natural convection and radiation heat transfer occur at the outer shield surface. To keep the ammonia inside the tube in its liquid state, determine the surrounding temperature that would maintain temperatures of the outer tube and the shield at the specified values. 13-68 PtD A hot liquid is being transported inside a long tube with a diameter of \(25 \mathrm{~mm}\). The hot liquid causes the tube surface temperature to be \(150^{\circ} \mathrm{C}\). To prevent thermal burn hazards, the tube is enclosed with a concentric outer cylindrical cover of \(5 \mathrm{~cm}\) in diameter allowing a vacuumed gap in between the two surfaces. The concentric outer cover has an emissivity of \(0.6\) and the outer surface is exposed to natural convection with a heat transfer coefficient of \(8 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and radiation heat transfer with the surrounding at a temperature of \(20^{\circ} \mathrm{C}\). Determine the necessary emissivity of the inside tube so that the outer cover temperature is below \(45^{\circ} \mathrm{C}\) to prevent thermal burns.

A car mechanic is working in a shop whose interior space is not heated. Comfort for the mechanic is provided by two radiant heaters that radiate heat at a total rate of \(4 \mathrm{~kJ} / \mathrm{s}\). About 5 percent of this heat strikes the mechanic directly. The shop and its surfaces can be assumed to be at the ambient temperature, and the emissivity and absorptivity of the mechanic can be taken to be \(0.95\) and the surface area to be \(1.8 \mathrm{~m}^{2}\). The mechanic is generating heat at a rate of \(350 \mathrm{~W}\), half of which is latent, and is wearing medium clothing with a thermal resistance of \(0.7 \mathrm{clo}\). Determine the lowest ambient temperature in which the mechanic can work comfortably.

How can you determine the view factor \(F_{12}\) when the view factor \(F_{21}\) and the surface areas are available?
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