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Chapter 3: Problem 107

What is the difference between the fin effectiveness and the fin efficiency?

Short Answer

Expert verified
Answer: The main difference between fin effectiveness and fin efficiency lies in their focus. Fin effectiveness measures the improvement in heat transfer achieved by adding a fin to an object compared to no fin, while fin efficiency evaluates how effectively the fin utilizes its surface area to transfer heat by comparing the actual heat transfer rate of a fin to the maximum possible heat transfer rate.

Step by step solution

01

Definition of fin effectiveness

Fin effectiveness is a dimensionless parameter that measures the improvement in heat transfer achieved by adding a fin to an object compared to the heat transfer without the fin. It is expressed as the ratio of the actual heat transfer rate with a fin (Q_fin) to the heat transfer rate without the fin (Q_base). Mathematically, fin effectiveness can be represented as follows: Fin effectiveness = \(\frac{Q_\text{fin}}{Q_\text{base}}\)
02

Definition of fin efficiency

Fin efficiency is a dimensionless parameter that represents the performance of a fin by comparing the fin's actual heat transfer rate (Q_fin) with the maximum possible heat transfer rate (Q_max) that could be achieved if the entire fin had the same temperature as its base. In other words, it is a measure of how effectively the fin utilizes its surface area to transfer heat. Mathematically, fin efficiency can be represented as follows: Fin efficiency = \(\frac{Q_\text{fin}}{Q_\text{max}}\)
03

Comparison of fin effectiveness and fin efficiency

Although both fin effectiveness and fin efficiency are dimensionless parameters used to evaluate the performance of a fin, their focus is different: - Fin effectiveness compares the heat transfer rate with a fin to that without a fin. It helps determine whether adding a fin to an object is useful in improving heat transfer. - Fin efficiency compares the actual heat transfer rate of a fin to the maximum possible heat transfer rate. It helps assess how well the fin is utilizing its surface area to transfer heat. In summary, fin effectiveness focuses on the improvement from using a fin, while fin efficiency evaluates how well the fin itself is performing given its available surface area for heat transfer.

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Most popular questions from this chapter

Hot water \(\left(c_{p}=4.179 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) flows through a 200-m-long PVC \((k=0.092 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) pipe whose inner diameter is \(2 \mathrm{~cm}\) and outer diameter is \(2.5 \mathrm{~cm}\) at a rate of \(1 \mathrm{~kg} / \mathrm{s}\), entering at \(40^{\circ} \mathrm{C}\). If the entire interior surface of this pipe is maintained at \(35^{\circ} \mathrm{C}\) and the entire exterior surface at \(20^{\circ} \mathrm{C}\), the outlet temperature of water is (a) \(39^{\circ} \mathrm{C}\) (b) \(38^{\circ} \mathrm{C}\) (c) \(37^{\circ} \mathrm{C}\) (d) \(36^{\circ} \mathrm{C}\) (e) \(35^{\circ} \mathrm{C}\)

Hot water at an average temperature of \(70^{\circ} \mathrm{C}\) is flowing through a \(15-\mathrm{m}\) section of a cast iron pipe \((k=52 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) whose inner and outer diameters are \(4 \mathrm{~cm}\) and \(4.6 \mathrm{~cm}\), respectively. The outer surface of the pipe, whose emissivity is \(0.7\), is exposed to the cold air at \(10^{\circ} \mathrm{C}\) in the basement, with a heat transfer coefficient of \(15 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The heat transfer coefficient at the inner surface of the pipe is \(120 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Taking the walls of the basement to be at \(10^{\circ} \mathrm{C}\) also, determine the rate of heat loss from the hot water. Also, determine the average velocity of the water in the pipe if the temperature of the water drops by \(3^{\circ} \mathrm{C}\) as it passes through the basement.

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.

Determine the winter \(R\)-value and the \(U\)-factor of a masonry cavity wall that is built around 4-in-thick concrete blocks made of lightweight aggregate. The outside is finished with 4 -in face brick with \(\frac{1}{2}\)-in cement mortar between the bricks and concrete blocks. The inside finish consists of \(\frac{1}{2}\)-in gypsum wallboard separated from the concrete block by \(\frac{3}{4}\)-in-thick (1-in by 3 -in nominal) vertical furring whose center- to-center distance is 16 in. Neither side of the \(\frac{3}{4}\)-in-thick air space between the concrete block and the gypsum board is coated with any reflective film. When determining the \(R\)-value of the air space, the temperature difference across it can be taken to be \(30^{\circ} \mathrm{F}\) with a mean air temperature of \(50^{\circ} \mathrm{F}\). The air space constitutes 80 percent of the heat transmission area, while the vertical furring and similar structures constitute 20 percent.

The plumbing system of a house involves a \(0.5-\mathrm{m}\) section of a plastic pipe \((k=0.16 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) of inner diameter \(2 \mathrm{~cm}\) and outer diameter \(2.4 \mathrm{~cm}\) exposed to the ambient air. During a cold and windy night, the ambient air temperature remains at about \(-5^{\circ} \mathrm{C}\) for a period of \(14 \mathrm{~h}\). The combined convection and radiation heat transfer coefficient on the outer surface of the pipe is estimated to be \(40 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), and the heat of fusion of water is \(333.7 \mathrm{~kJ} / \mathrm{kg}\). Assuming the pipe to contain stationary water initially at \(0^{\circ} \mathrm{C}\), determine if the water in that section of the pipe will completely freeze that night.
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