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Chapter 3: Problem 2

Consider heat conduction through a plane wall. Does the energy content of the wall change during steady heat conduction? How about during transient conduction? Explain.

Short Answer

Expert verified
Answer: The energy content of a plane wall does not change during steady heat conduction due to the constant temperature distribution. However, during transient conduction, the energy content of the wall changes as the temperature distribution is changing over time.

Step by step solution

01

Review steady heat conduction definition

Steady heat conduction is a condition where the temperature distribution in a material remains constant over time. In other words, the flow of heat within the material doesn't change with time.
02

Review transient heat conduction definition

Transient heat conduction, also known as unsteady heat conduction, is a condition where the temperature distribution inside a material is constantly changing over time. In this case, heat is still being exchanged within the material, but the rates and directions of flow may be varying.
03

Determine energy content changes during steady heat conduction

During steady heat conduction, the temperature distribution within the plane wall remains constant. This means that there is no change in internal energy within the system because the heat energy flowing into the wall equals the heat energy flowing out. Therefore, the energy content of the wall does not change during steady heat conduction.
04

Determine energy content changes during transient conduction

During transient conduction, the temperature distribution in the plane wall changes over time. This means that the system's internal energy is changing because the heat transfer is not constant. Consequently, the energy content of the wall changes during transient conduction.
05

Conclusion

In conclusion, during steady heat conduction, the energy content of the wall does not change due to the constant temperature distribution. However, during transient conduction, the energy content of the wall changes because the temperature distribution is changing over time.

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Most popular questions from this chapter

Hot water is flowing at an average velocity of \(1.5 \mathrm{~m} / \mathrm{s}\) through a cast iron pipe \((k=52 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) whose inner and outer diameters are \(3 \mathrm{~cm}\) and \(3.5 \mathrm{~cm}\), respectively. The pipe passes through a \(15-\mathrm{m}\)-long section of a basement whose temperature is \(15^{\circ} \mathrm{C}\). If the temperature of the water drops from \(70^{\circ} \mathrm{C}\) to \(67^{\circ} \mathrm{C}\) as it passes through the basement and the heat transfer coefficient on the inner surface of the pipe is \(400 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), determine the combined convection and radiation heat transfer coefficient at the outer surface of the pipe.

Hot water at an average temperature of \(53^{\circ} \mathrm{C}\) and an average velocity of \(0.4 \mathrm{~m} / \mathrm{s}\) is flowing through a \(5-\mathrm{m}\) section of a thin-walled hot-water pipe that has an outer diameter of $2.5 \mathrm{~cm}\(. The pipe passes through the center of a \)14-\mathrm{cm}$-thick wall filled with fiberglass insulation $(k=0.035 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\(. If the surfaces of the wall are at \)18^{\circ} \mathrm{C}\(, determine \)(a)$ the rate of heat transfer from the pipe to the air in the rooms and \((b)\) the temperature drop of the hot water as it flows through this 5 -m-long section of the wall.

A 0.2-cm-thick, 10-cm-high, and 15 -cm-long circuit board houses electronic components on one side that dissipate a total of \(15 \mathrm{~W}\) of heat uniformly. The board is impregnated with conducting metal fillings and has an effective thermal conductivity of $12 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$. All the heat generated in the components is conducted across the circuit board and is dissipated from the back side of the board to a medium at \(37^{\circ} \mathrm{C}\), with a heat transfer coefficient of $45 \mathrm{~W} / \mathrm{m}^{2}, \mathrm{~K}$. (a) Determine the surface temperatures on the two sides of the circuit board. (b) Now a \(0.1\)-cm-thick, \(10-\mathrm{cm}\)-high, and 15 -cm-long aluminum plate $(k=237 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\( with \)200.2-\mathrm{cm}$-thick, 2 -cm-long, and 15 -cm-wide aluminum fins of rectangular profile are attached to the back side of the circuit board with a \(0.03-\mathrm{cm}\) thick epoxy adhesive $(k=1.8 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$. Determine the new temperatures on the two sides of the circuit board.

Explain how the fins enhance heat transfer from a surface. Also, explain how the addition of fins may actually decrease heat transfer from a surface.

The overall heat transfer coefficient (the \(U\)-value) of a wall under winter design conditions is \(U=1.40 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Determine the \(U\)-value of the wall under summer design conditions.
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