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Chapter 8: Problem 143

Air enters a 7-cm-diameter and 4-m-long tube at \(65^{\circ} \mathrm{C}\) and leaves at \(15^{\circ} \mathrm{C}\). The tube is observed to be nearly isothermal at \(5^{\circ} \mathrm{C}\). If the average convection heat transfer coefficient is \(20 \mathrm{~W} / \mathrm{m}^{2} \cdot{ }^{\circ} \mathrm{C}\), the rate of heat transfer from the air is (a) \(491 \mathrm{~W}\) (b) \(616 \mathrm{~W}\) (c) \(810 \mathrm{~W}\) (d) \(907 \mathrm{~W}\) (e) \(975 \mathrm{~W}\)

Short Answer

Expert verified
Answer: The rate of heat transfer from the air in the tube is approximately 616 W.

Step by step solution

01

Find the surface area of the tube

To find the surface area (A) of the tube, we need its diameter (D) and length (L). We have D=7 cm and L=4 m. First, we need to convert the diameter to meters: D=0.07 m. The surface area of the tube is given by the formula A = πDL.
02

Calculate the temperature difference

Given that air enters at 65°C and leaves at 15°C, the average air temperature inside the tube is \(T_{avg} = (65+15)/2 = 40^{\circ}\mathrm{C}\). The temperature of the tube's surface is nearly isothermal at 5°C. So, the temperature difference between the air and the surface of the tube is \(\Delta T = T_{avg} - T_s = 40^{\circ}\mathrm{C} - 5^{\circ}\mathrm{C} = 35^{\circ}\mathrm{C}\).
03

Apply the heat transfer formula

The rate of heat transfer (Q) from the air in the tube can be found using the formula Q = hAΔT, where h is the average convection heat transfer coefficient, A is the surface area of the tube, and ΔT is the temperature difference. We have h = 20 W/m²°C, A from step 1, and ΔT from step 2.
04

Calculate the rate of heat transfer

Now, we will plug in the values from the previous steps into the formula Q = hAΔT and calculate the rate of heat transfer: Q = 20 W/m²°C × π × 0.07 m × 4 m × 35°C. After calculating, we get Q ≈ 616 W. Hence, the rate of heat transfer from the air is 616 W (Answer option 'b').

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Most popular questions from this chapter

In a manufacturing plant that produces cosmetic products, glycerin is being heated by flowing through a \(25-\mathrm{mm}\)-diameter and \(10-\mathrm{m}\)-long tube. With a mass flow rate of \(0.5 \mathrm{~kg} / \mathrm{s}\), the flow of glycerin enters the tube at \(25^{\circ} \mathrm{C}\). The tube surface is maintained at a constant surface temperature of \(140^{\circ} \mathrm{C}\). Determine the outlet mean temperature and the total rate of heat transfer for the tube. Evaluate the properties for glycerin at \(30^{\circ} \mathrm{C}\).

Consider turbulent forced convection in a circular tube. Will the heat flux be higher near the inlet of the tube or near the exit? Why?

Cooling water available at \(10^{\circ} \mathrm{C}\) is used to condense steam at \(30^{\circ} \mathrm{C}\) in the condenser of a power plant at a rate of \(0.15 \mathrm{~kg} / \mathrm{s}\) by circulating the cooling water through a bank of 5 -m-long \(1.2-\mathrm{cm}\)-internal-diameter thin copper tubes. Water enters the tubes at a mean velocity of \(4 \mathrm{~m} / \mathrm{s}\) and leaves at a temperature of \(24^{\circ} \mathrm{C}\). The tubes are nearly isothermal at \(30^{\circ} \mathrm{C}\). Determine the average heat transfer coefficient between the water, the tubes, and the number of tubes needed to achieve the indicated heat transfer rate in the condenser.

A tube with a bell-mouth inlet configuration is subjected to uniform wall heat flux of \(3 \mathrm{~kW} / \mathrm{m}^{2}\). The tube has an inside diameter of \(0.0158 \mathrm{~m}(0.622 \mathrm{in})\) and a flow rate of \(1.43 \times\) \(10^{-4} \mathrm{~m}^{3} / \mathrm{s}(2.27 \mathrm{gpm})\). The liquid flowing inside the tube is ethylene glycol-distilled water mixture with a mass fraction of \(2.27\). Determine the fully developed friction coefficient at a location along the tube where the Grashof number is \(\mathrm{Gr}=\) 16,600 . The physical properties of the ethylene glycol-distilled water mixture at the location of interest are \(\operatorname{Pr}=14.85, \nu=\) \(1.93 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\), and \(\mu_{b} / \mu_{s}=1.07\).

Someone claims that in fully developed turbulent flow in a tube, the shear stress is a maximum at the tube surface. Do you agree with this claim? Explain.
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