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Chapter 11: Problem 83

Consider a heat exchanger in which both fluids have the same specific heats but different mass flow rates. Which fluid will experience a larger temperature change: the one with the lower or higher mass flow rate?

Short Answer

Expert verified
Answer: The fluid with a lower mass flow rate will experience a larger temperature change.

Step by step solution

01

Review heat transfer relations for a heat exchanger

The heat transfer between two fluids in a heat exchanger can be described using the following equation: Q = m1 * c1 * (T1_out - T1_in) = m2 * c2 * (T2_out - T2_in), where Q is the heat transfer, m1 and m2 are the mass flow rates of each fluid, c1 and c2 are the specific heats of each fluid, and T1_out, T1_in, T2_out, T2_in are the inlet and outlet temperatures of each fluid. Since both fluids have the same specific heats, we can simplify the equation as: Q = m1 * c * (T1_out - T1_in) = m2 * c * (T2_out - T2_in).
02

Determine the temperature change for each fluid

Now we will determine which fluid will experience a larger temperature change depending on their mass flow rates. To do so, we'll examine how the temperature difference in each fluid relates to their mass flow rates. Divide both sides of the equation by their respective mass flow rates and specific heats: (T1_out - T1_in) / m1 = (T2_out - T2_in) / m2. Let ΔT1 = T1_out - T1_in and ΔT2 = T2_out - T2_in be the temperature changes of each fluid. Then we have: ΔT1 / m1 = ΔT2 / m2.
03

Analyze the relationship between mass flow rates and temperature changes

Since we are given that the fluids have different mass flow rates (m1 ≠ m2), we now study the relationship between the mass flow rates and the corresponding temperature changes. From the equation we derived in Step 2, suppose m1 > m2, then from ΔT1 / m1 = ΔT2 / m2, it follows that ΔT1 < ΔT2. This means that if Fluid 1 has a higher mass flow rate, it will experience a smaller temperature change compared to Fluid 2. On the other hand, if m1 < m2, then from the same equation, we would have ΔT1 > ΔT2. This means that if Fluid 1 has a lower mass flow rate, it will experience a larger temperature change compared to Fluid 2.
04

Conclusion

The fluid with a lower mass flow rate will experience a larger temperature change in the heat exchanger, while the fluid with a higher mass flow rate will experience a smaller temperature change.

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Most popular questions from this chapter

A shell-and-tube heat exchanger is to be designed to cool down the petroleum- based organic vapor available at a flow rate of \(5 \mathrm{~kg} / \mathrm{s}\) and at a saturation temperature of \(75^{\circ} \mathrm{C}\). The cold water \(\left(c_{p}=4187 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) used for its condensation is supplied at a rate of \(25 \mathrm{~kg} / \mathrm{s}\) and a temperature of \(15^{\circ} \mathrm{C}\). The cold water flows through copper tubes with an outside diameter of \(20 \mathrm{~mm}\), a thickness of \(2 \mathrm{~mm}\), and a length of \(5 \mathrm{~m}\). The overall heat transfer coefficient is assumed to be \(550 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and the latent heat of vaporization of the organic vapor may be taken to be \(580 \mathrm{~kJ} / \mathrm{kg}\). Assuming negligible thermal resistance due to pipe wall thickness, determine the number of tubes required.

A cross-flow heat exchanger with both fluids unmixed has an overall heat transfer coefficient of \(200 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), and a heat transfer surface area of \(400 \mathrm{~m}^{2}\). The hot fluid has a heat capacity of \(40,000 \mathrm{~W} / \mathrm{K}\), while the cold fluid has a heat capacity of \(80,000 \mathrm{~W} / \mathrm{K}\). If the inlet temperatures of both hot and cold fluids are \(80^{\circ} \mathrm{C}\) and \(20^{\circ} \mathrm{C}\), respectively, determine (a) the exit temperature of the hot fluid and \((b)\) the rate of heat transfer in the heat exchanger.

Consider the flow of saturated steam at \(270.1 \mathrm{kPa}\) that flows through the shell side of a shell-and-tube heat exchanger while the water flows through 4 tubes of diameter \(1.25 \mathrm{~cm}\) at a rate of \(0.25 \mathrm{~kg} / \mathrm{s}\) through each tube. The water enters the tubes of heat exchanger at \(20^{\circ} \mathrm{C}\) and exits at \(60^{\circ} \mathrm{C}\). Due to the heat exchange with the cold fluid, steam is condensed on the tubes external surface. The convection heat transfer coefficient on the steam side is \(1500 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), while the fouling resistance for the steam and water may be taken as \(0.00015\) and \(0.0001 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\), respectively. Using the NTU method, determine \((a)\) effectiveness of the heat exchanger, \((b)\) length of the tube, and \((c)\) rate of steam condensation.

A 2-shell passes and 4-tube passes heat exchanger is used for heating a hydrocarbon stream \(\left(c_{p}=2.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) steadily from \(20^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\). A water stream enters the shellside at \(80^{\circ} \mathrm{C}\) and leaves at \(40^{\circ} \mathrm{C}\). There are 160 thin-walled tubes, each with a diameter of \(2.0 \mathrm{~cm}\) and length of \(1.5 \mathrm{~m}\). The tube-side and shell-side heat transfer coefficients are \(1.6\) and \(2.5 \mathrm{~kW} / \mathrm{m}^{2} \cdot \mathrm{K}\), respectively. (a) Calculate the rate of heat transfer and the mass rates of water and hydrocarbon streams. (b) With usage, the outlet hydrocarbon-stream temperature was found to decrease by \(5^{\circ} \mathrm{C}\) due to the deposition of solids on the tube surface. Estimate the magnitude of fouling factor.

A shell-and-tube heat exchanger is used for heating \(10 \mathrm{~kg} / \mathrm{s}\) of oil \(\left(c_{p}=2.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) from \(25^{\circ} \mathrm{C}\) to \(46^{\circ} \mathrm{C}\). The heat exchanger has 1 -shell pass and 6-tube passes. Water enters the shell side at \(80^{\circ} \mathrm{C}\) and leaves at \(60^{\circ} \mathrm{C}\). The overall heat transfer coefficient is estimated to be \(1000 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Calculate the rate of heat transfer and the heat transfer area.
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