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Chapter 1: Problem 47

Consider heat loss through the two walls of a house on a winter night. The walls are identical, except that one of them has a tightly fit glass window. Through which wall will the house lose more heat? Explain.

Short Answer

Expert verified
Answer: The house will lose more heat through the wall with the tightly fit glass window due to the higher emissivity value of the glass, which causes more heat to be radiated away from the wall.

Step by step solution

01

Identify the modes of heat transfer

In this problem, there are three modes of heat transfer to consider: conduction, convection, and radiation. Conduction occurs through solid materials, convection occurs through air or fluids, and radiation occurs through electromagnetic waves. We need to examine each of these modes of heat transfer in the context of the walls with and without the glass window.
02

Compare conduction heat transfer for the two walls

Conduction is the primary mode of heat transfer through the solid materials of the walls. The walls are said to be identical, meaning they have the same material and thickness. Since the glass window is tightly fit, it can be assumed to conduct heat similarly to the rest of the wall material. Therefore, the conduction heat transfer through the two walls is nearly the same.
03

Compare convection heat transfer for the two walls

Convection is the mode of heat transfer that occurs through air or fluids. In this case, convection occurs at the inner and outer surfaces of both walls. However, the presence of the glass window can impact the convective heat transfer on that wall, as the glass surface might have different convective properties compared to the rest of the wall material. Nevertheless, the difference between the two walls in terms of convection would be relatively small and may not be a significant factor to consider.
04

Compare radiation heat transfer for the two walls

Radiation is the mode of heat transfer that occurs through electromagnetic waves. All objects emit heat radiation, but the amount of heat emitted depends on the object's emissivity, which is a property that measures how efficiently an object emits and absorbs heat radiation. Glass has a different emissivity value compared to the wall material, making it more efficient in emitting and absorbing heat radiation. As a result, there will be a difference in the radiative heat transfer between the two walls.
05

Determine which wall will lose more heat

Since conduction and convection heat transfers are similar for both walls, the difference in heat loss between the two walls is mainly determined by the radiation heat transfer. Since the glass window has a higher emissivity value compared to the rest of the wall material, the wall with the glass window will have more heat radiated away from it. Therefore, the house will lose more heat through the wall with the tightly fit glass window.

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Most popular questions from this chapter

How does forced convection differ from natural convection?

Air at \(20^{\circ} \mathrm{C}\) with a convection heat transfer coefficient of \(20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) blows over a pond. The surface temperature of the pond is at \(40^{\circ} \mathrm{C}\). Determine the heat flux between the surface of the pond and the air.

Steady heat conduction occurs through a \(0.3\)-m-thick \(9 \mathrm{~m} \times 3 \mathrm{~m}\) composite wall at a rate of \(1.2 \mathrm{~kW}\). If the inner and outer surface temperatures of the wall are \(15^{\circ} \mathrm{C}\) and \(7^{\circ} \mathrm{C}\), the effective thermal conductivity of the wall is (a) \(0.61 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) (b) \(0.83 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) (c) \(1.7 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) (d) \(2.2 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) (e) \(5.1 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\)

An electric heater with the total surface area of \(0.25 \mathrm{~m}^{2}\) and emissivity \(0.75\) is in a room where the air has a temperature of \(20^{\circ} \mathrm{C}\) and the walls are at \(10^{\circ} \mathrm{C}\). When the heater consumes \(500 \mathrm{~W}\) of electric power, its surface has a steady temperature of \(120^{\circ} \mathrm{C}\). Determine the temperature of the heater surface when it consumes \(700 \mathrm{~W}\). Solve the problem (a) assuming negligible radiation and (b) taking radiation into consideration. Based on your results, comment on the assumption made in part ( \(a\) ).

Consider a \(3-\mathrm{m} \times 3-\mathrm{m} \times 3-\mathrm{m}\) cubical furnace whose top and side surfaces closely approximate black surfaces at a temperature of \(1200 \mathrm{~K}\). The base surface has an emissivity of \(\varepsilon=0.4\), and is maintained at \(800 \mathrm{~K}\). Determine the net rate of radiation heat transfer to the base surface from the top and side surfaces. Answer: \(340 \mathrm{~kW}\)
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