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Chapter 9: Problem 114

Consider a double-pane window whose air space width is \(20 \mathrm{~mm}\). Now a thin polyester film is used to divide the air space into two 10-mm-wide layers. How will the film affect \((a)\) convection and (b) radiation heat transfer through the window?

Short Answer

Expert verified
Answer: (a) Convection heat transfer is likely to be decreased, as the film divides the air space into smaller layers, limiting the air particle movement and current formation. (b) Radiation heat transfer might be slightly affected, as the film introduces additional radiation exchange surfaces. The overall impact on heat transfer depends on the properties of the film, such as emissivity, and the balance between the convective and radiative mechanisms.

Step by step solution

01

Understand Convection Heat Transfer

Convection heat transfer is the process of heat transfer through the movement of fluid particles (in this case, air) subjected to temperature differences. It occurs due to the energy transfer by the circulating air particles in the space between the two panes. In the double-pane window, the air space width is essential for the convection heat transfer process.
02

Analyze the Impact of the Film on Convection Heat Transfer

When a thin polyester film is introduced, the air space width is divided into two layers, each with a width of 10 mm. With the smaller air space width, the air particles have less freedom to move around, which generally limits the convection currents. As a result, the convection heat transfer will be decreased when the air space is divided by the film.
03

Understand Radiation Heat Transfer

Radiation heat transfer is the process of heat transfer that occurs due to the emission of electromagnetic energy, which travels as waves that carry energy from one surface to another without any medium (air or fluid). In the case of a double-pane window, the primary radiation heat exchange happens between two glass surfaces facing each other. The film will affect the radiation when it is placed between them.
04

Analyze the Impact of the Film on Radiation Heat Transfer

The polyester film is a thin, transparent material. Although it will block some of the radiation heat exchange, the majority of the radiation transfer might still occur. However, the film will also absorb and emit heat, depending on its emissivity and temperature. This introduces an additional layer for the radiation exchange process. So, although the radiation heat transfer may not be significantly reduced, it might be slightly affected due to the additional radiation exchange occurring at the film surfaces.
05

Conclusion

In conclusion, the addition of a thin polyester film in the double-pane window can affect both convection and radiation heat transfer. \((a)\) The convection heat transfer is likely to be decreased, as the film divides the air space into smaller layers, limiting the air particle movement and current formation. \((b)\) The radiation heat transfer might be slightly affected, as the film introduces additional radiation exchange surfaces. The overall impact on heat transfer depends on the properties of the film, such as emissivity, and the balance between the convective and radiative mechanisms.

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Most popular questions from this chapter

Consider a 2-m-high electric hot-water heater that has a diameter of \(40 \mathrm{~cm}\) and maintains the hot water at \(60^{\circ} \mathrm{C}\). The tank is located in a small room at \(20^{\circ} \mathrm{C}\) whose walls and ceiling are at about the same temperature. The tank is placed in a 44-cm-diameter sheet metal shell of negligible thickness, and the space between the tank and the shell is filled with foam insulation. The average temperature and emissivity of the outer surface of the shell are \(40^{\circ} \mathrm{C}\) and \(0.7\), respectively. The price of electricity is \(\$ 0.08 / \mathrm{kWh}\). Hot-water tank insulation kits large enough to wrap the entire tank are available on the market for about \(\$ 60\). If such an insulation is installed on this water tank by the home owner himself, how long will it take for this additional insulation to pay for itself? Disregard any heat loss from the top and bottom surfaces, and assume the insulation to reduce the heat losses by 80 percent.

Consider laminar natural convection from a vertical hot-plate. Will the heat flux be higher at the top or at the bottom of the plate? Why?

The two concentric spheres of diameters \(D_{i}=20 \mathrm{~cm}\) and \(D_{o}=30 \mathrm{~cm}\) are separated by air at \(1 \mathrm{~atm}\) pressure. The surface temperatures of the two spheres enclosing the air are \(T_{i}=320 \mathrm{~K}\) and \(T_{o}=280 \mathrm{~K}\), respectively. Determine the rate of heat transfer from the inner sphere to the outer sphere by natural convection.

A horizontal \(1.5\)-m-wide, \(4.5\)-m-long double-pane window consists of two sheets of glass separated by a \(3.5-\mathrm{cm}\) gap filled with water. If the glass surface temperatures at the bottom and the top are measured to be \(60^{\circ} \mathrm{C}\) and \(40^{\circ} \mathrm{C}\), respectively, the rate of heat transfer through the window is (a) \(27.6 \mathrm{~kW}\) (b) \(39.4 \mathrm{~kW}\) (c) \(59.6 \mathrm{~kW}\) (d) \(66.4 \mathrm{~kW} \quad(e) 75.5 \mathrm{~kW}\) (For water, use \(k=0.644 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \operatorname{Pr}=3.55, v=\) \(0.554 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}, \beta=0.451 \times 10^{-3} \mathrm{~K}^{-1}\). Also, the applicable correlation is \(\mathrm{Nu}=0.069 \mathrm{Ra}^{1 / 3} \operatorname{Pr}^{0.074}\) ).

A 150 -mm-diameter and 1-m-long rod is positioned horizontally and has water flowing across its outer surface at a velocity of \(0.2 \mathrm{~m} / \mathrm{s}\). The water temperature is uniform at \(40^{\circ} \mathrm{C}\) and the rod surface temperature is maintained at \(120^{\circ} \mathrm{C}\). Under these conditions are the natural convection effects important to the heat transfer process?
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