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Chapter 9: Problem 82

Consider a double-pane window consisting of two glass sheets separated by a \(1-\mathrm{cm}\)-wide air space. Someone suggests inserting a thin vinyl sheet in the middle of the two glasses to form two \(0.5\)-cm-wide compartments in the window in order to reduce natural convection heat transfer through the window. From a heat transfer point of view, would you be in favor of this idea to reduce heat losses through the window?

Short Answer

Expert verified
Answer: Yes, inserting a thin vinyl sheet in the middle of the air gap would reduce the heat loss through the window. By dividing the air space into two compartments of 0.5 cm each, it weakens the natural convection currents, leading to a reduction in heat transfer. This makes the window more efficient in terms of energy savings and thermal efficiency.

Step by step solution

01

Understand convection heat transfer

The heat transfer via convection in an air space depends on the temperature difference between the two glass sheets and the thickness of air space. The temperature difference causes natural convection currents, which transfers heat from the warmer side to the cooler side. One of the factors that affect the rate of heat transfer is the thickness (height) of the air gap.
02

Comparing the two cases

We can represent the two cases as follows: - Case A: The original scenario, where there is a 1 cm thick air space between the two glass sheets. - Case B: The modified scenario, where a thin vinyl sheet is inserted in the middle of the space, splitting it into two 0.5 cm compartments. When dividing the air space into two compartments, the height of each compartment is reduced by half, which weakens the natural convection currents. As a result, the heat transfer rate in each of the two compartments (Case B) will be lower than the heat transfer rate in the original air space (Case A).
03

Analyzing the heat transfer reduction

By introducing the vinyl sheet which would inevitably reduce the natural convection in both compartments of 0.5 cm air gap, we would get an overall reduction in heat transfer. By decreasing heating loss due to convection in those compartments, the window becomes more efficient in terms of heat transfer and energy saving.
04

Conclusion

From a heat transfer perspective, it would be beneficial to insert a thin vinyl sheet in the middle to reduce heat losses through the window. We can conclude that, based on the reduction of the convection currents from Case A to Case B, the idea is a valid and potentially useful way to improve thermal efficiency in double-pane windows.

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Most popular questions from this chapter

Show that the volume expansion coefficient of an ideal gas is \(\beta=1 / T\), where \(T\) is the absolute temperature.

Why are the windows considered in three regions when analyzing heat transfer through them? Name those regions and explain how the overall \(U\)-value of the window is determined when the heat transfer coefficients for all three regions are known.

Consider an industrial furnace that resembles a 13 -ft-long horizontal cylindrical enclosure \(8 \mathrm{ft}\) in diameter whose end surfaces are well insulated. The furnace burns natural gas at a rate of 48 therms/h. The combustion efficiency of the furnace is 82 percent (i.e., 18 percent of the chemical energy of the fuel is lost through the flue gases as a result of incomplete combustion and the flue gases leaving the furnace at high temperature). If the heat loss from the outer surfaces of the furnace by natural convection and radiation is not to exceed 1 percent of the heat generated inside, determine the highest allowable surface temperature of the furnace. Assume the air and wall surface temperature of the room to be \(75^{\circ} \mathrm{F}\), and take the emissivity of the outer surface of the furnace to be \(0.85\). If the cost of natural gas is \(\$ 1.15 /\) therm and the furnace operates \(2800 \mathrm{~h}\) per year, determine the annual cost of this heat loss to the plant. Evaluate properties of air at a film temperature of \(107.5^{\circ} \mathrm{F}\) and \(1 \mathrm{~atm}\) pressure. Is this a good assumption?

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 \(\mathrm{Nu}=0.069 \mathrm{Ra}^{1 / 3} \operatorname{Pr}^{0.074}\) ).

Consider a \(1.2\)-m-high and 2-m-wide double-pane window consisting of two 3-mm-thick layers of glass \((k=\) \(0.78 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) separated by a \(3-\mathrm{cm}\)-wide air space. Determine the steady rate of heat transfer through this window and the temperature of its inner surface for a day during which the room is maintained at \(20^{\circ} \mathrm{C}\) while the temperature of the outdoors is \(0^{\circ} \mathrm{C}\). Take the heat transfer coefficients on the inner and outer surfaces of the window to be \(h_{1}=10 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(h_{2}=25 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and disregard any heat transfer by radiation. Evaluate air properties at a film temperature of \(10^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) pressure. Is this a good assumption?
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