Chapter 3: Problem 45
Explain how the thermal contact resistance can be minimized.
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Chapter 3: Problem 45
Explain how the thermal contact resistance can be minimized.
These are the key concepts you need to understand to accurately answer the question.
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Two identical aluminum plates with thickness of \(30 \mathrm{~cm}\) are pressed against each other at an average pressure of \(1 \mathrm{~atm}\). The interface, sandwiched between the two plates, is filled with glycerin. On the left outer surface, it is subjected to a uniform heat flux of \(7800 \mathrm{~W} / \mathrm{m}^{2}\) at a constant temperature of \(50^{\circ} \mathrm{C}\). On the right outer surface, the temperature is maintained constant at \(30^{\circ} \mathrm{C}\). Determine the thermal contact conductance of the glycerin at the interface, if the thermal conductivity of the aluminum plates is \(237 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Discuss whether the value of the thermal contact conductance is reasonable or not.
A 50 -m-long section of a steam pipe whose outer (€) diameter is \(10 \mathrm{~cm}\) passes through an open space at \(15^{\circ} \mathrm{C}\). The average temperature of the outer surface of the pipe is measured to be \(150^{\circ} \mathrm{C}\). If the combined heat transfer coefficient on the outer surface of the pipe is \(20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), determine (a) the rate of heat loss from the steam pipe; \((b)\) the annual cost of this energy lost if steam is generated in a natural gas furnace that has an efficiency of 75 percent and the price of natural gas is $$\$ 0.52 /$$ therm ( 1 therm \(=105,500 \mathrm{~kJ})\); and \((c)\) the thickness of fiberglass insulation \((k=0.035 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) needed in order to save 90 percent of the heat lost. Assume the pipe temperature to remain constant at \(150^{\circ} \mathrm{C}\).
What is the reason for the widespread use of fins on surfaces?
Two 5-cm-diameter, 15-cm-long aluminum bars \((k=\) \(176 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) with ground surfaces are pressed against each other with a pressure of \(20 \mathrm{~atm}\). The bars are enclosed in an insulation sleeve and, thus, heat transfer from the lateral surfaces is negligible. If the top and bottom surfaces of the twobar system are maintained at temperatures of \(150^{\circ} \mathrm{C}\) and \(20^{\circ} \mathrm{C}\), respectively, determine \((a)\) the rate of heat transfer along the cylinders under steady conditions and (b) the temperature drop at the interface. Answers: (a) \(142.4 \mathrm{~W}\), (b) \(6.4^{\circ} \mathrm{C}\)
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. Answers: \(19.6 \mathrm{~W}, 0.024^{\circ} \mathrm{C}\)
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