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Chapter 3: Problem 105

Hot air is to be cooled as it is forced to flow through the tubes exposed to atmospheric air. Fins are to be added in order to enhance heat transfer. Would you recommend attaching the fins inside or outside the tubes? Why? When would you recommend attaching fins both inside and outside the tubes?

Short Answer

Expert verified
Answer: To enhance heat transfer during the cooling process, fins should be attached outside the tubes because this increases heat transfer to the atmospheric air, which is cooler than the hot air inside the tubes. Attaching fins both inside and outside the tubes would be recommended in situations where maximizing heat transfer efficiency is crucial, such as in systems with minimal temperature differences or high-performance industrial applications.

Step by step solution

01

Understand the heat transfer process

The cooling process of hot air being forced through tubes involves convective heat transfer, which occurs when heat is transferred between a solid surface and a fluid, such as air, due to their temperature difference.
02

Understand the role of fins

Fins are added to increase the efficiency of heat transfer. They do this by increasing the total surface area available for heat transfer, thus allowing more heat to be transferred between the solid surface and the surrounding fluid.
03

Analyze fin placement with regard to heat transfer

If we attach the fins inside the tubes, they would increase the internal surface area, thus, enhancing heat transfer between the hot air flowing inside the tubes and the tubes' internal walls. On the other hand, if we attach the fins outside the tubes, they would increase the external surface area, thus, enhancing heat transfer between the tubes' external walls and the atmospheric air.
04

Determine which placement would be more effective

In this case, the goal is to cool the hot air as it flows through the tubes. Attaching the fins outside the tubes would be more effective at increasing heat transfer to the atmospheric air, hence cooling the hot air. This is because the atmospheric air is cooler than the air inside the tubes, which will facilitate a more efficient heat transfer.
05

When would fins be attached both inside and outside the tubes?

Fins would be attached both inside and outside the tubes in situations where maximization of heat transfer efficiency is the primary concern. This could include scenarios where the temperature difference between the hot air inside the tubes and the atmospheric air is minimal or in systems that require very high heat transfer rates, such as high-performance industrial applications. So, the recommended option is to attach fins outside the tubes to enhance heat transfer with the atmospheric air. Attaching fins both inside and outside the tubes would be recommended in situations where maximizing heat transfer efficiency is crucial.

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Most popular questions from this chapter

In a combined heat and power (CHP) generation process, by-product heat is used for domestic or industrial heating purposes. Hot steam is carried from a CHP generation plant by a tube with diameter of \(127 \mathrm{~mm}\) centered at a square crosssection solid bar made of concrete with thermal conductivity of \(1.7 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). The surface temperature of the tube is constant at \(120^{\circ} \mathrm{C}\), while the square concrete bar is exposed to air with temperature of \(-5^{\circ} \mathrm{C}\) and convection heat transfer coefficient of \(20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). If the temperature difference between the outer surface of the square concrete bar and the ambient air is to be maintained at \(5^{\circ} \mathrm{C}\), determine the width of the square concrete bar and the rate of heat loss per meter length.

The \(700 \mathrm{~m}^{2}\) ceiling of a building has a thermal resistance of \(0.52 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\). The rate at which heat is lost through this ceiling on a cold winter day when the ambient temperature is \(-10^{\circ} \mathrm{C}\) and the interior is at \(20^{\circ} \mathrm{C}\) is (a) \(23.1 \mathrm{~kW} \quad\) (b) \(40.4 \mathrm{~kW}\) (c) \(55.6 \mathrm{~kW}\) (d) \(68.1 \mathrm{~kW}\) (e) \(88.6 \mathrm{~kW}\)

Consider a very long rectangular fin attached to a flat surface such that the temperature at the end of the fin is essentially that of the surrounding air, i.e. \(20^{\circ} \mathrm{C}\). Its width is \(5.0 \mathrm{~cm}\); thickness is \(1.0 \mathrm{~mm}\); thermal conductivity is \(200 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\); and base temperature is \(40^{\circ} \mathrm{C}\). The heat transfer coefficient is \(20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Estimate the fin temperature at a distance of \(5.0 \mathrm{~cm}\) from the base and the rate of heat loss from the entire fin.

An 8-m-internal-diameter spherical tank made of \(1.5\)-cm-thick stainless steel \((k=15 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) is used to store iced water at \(0^{\circ} \mathrm{C}\). The tank is located in a room whose temperature is \(25^{\circ} \mathrm{C}\). The walls of the room are also at \(25^{\circ} \mathrm{C}\). The outer surface of the tank is black (emissivity \(\varepsilon=1\) ), and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. The convection heat transfer coefficients at the inner and the outer surfaces of the tank are \(80 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(10 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), respectively. Determine \((a)\) the rate of heat transfer to the iced water in the tank and \((b)\) the amount of ice at \(0^{\circ} \mathrm{C}\) that melts during a 24 -h period. The heat of fusion of water at atmospheric pressure is \(h_{i f}=333.7 \mathrm{~kJ} / \mathrm{kg}\).

A 6-m-diameter spherical tank is filled with liquid oxygen \(\left(\rho=1141 \mathrm{~kg} / \mathrm{m}^{3}, c_{p}=1.71 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) at \(-184^{\circ} \mathrm{C}\). It is observed that the temperature of oxygen increases to \(-183^{\circ} \mathrm{C}\) in a 144-hour period. The average rate of heat transfer to the tank is (a) \(249 \mathrm{~W}\) (b) \(426 \mathrm{~W}\) (c) \(570 \mathrm{~W}\) (d) \(1640 \mathrm{~W}\) (e) \(2207 \mathrm{~W}\)
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