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# Effectiveness of heat exchanger
Unit 4, Lecture 31

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## Effectiveness of Heat Exchanger (NTU Method)

- Course: Heat and Mass Transfer (DI05019071)
- Unit 4: Heat Exchanger
- Lecture 31: Effectiveness - NTU Method

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Welcome. Today we introduce a powerful new tool for analyzing heat exchangers: The Effectiveness-NTU method.
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## Lecture Agenda

- 1. Limitations of the LMTD Method
- 2. The NTU Method Overview
- 3. Maximum Possible Heat Transfer (Q_max)
- 4. Heat Exchanger Effectiveness (Epsilon)
- 5. Number of Transfer Units (NTU)
- 6. Epsilon-NTU Relations

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We'll see why LMTD isn't always convenient, define effectiveness, and learn how to use the NTU charts.
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## Limitations of the LMTD Method

- LMTD is easy to use if all inlet and outlet temperatures are known (Design problems).
- If only the inlet temperatures are known, outlet temperatures must be guessed and iterated.
- Performance evaluation problems (finding Q for a given exchanger) are tedious with LMTD.
- Need a method that avoids iteration.

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If you don't know the outlet temperatures, you can't calculate LMTD without guessing and checking. This iterative process is time-consuming.
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## The Effectiveness-NTU Method

- Developed by Kays and London in 1955.
- Predicts the outlet temperatures and heat transfer rate without iteration.
- Based on a dimensionless parameter called heat exchanger effectiveness (epsilon).
- Highly preferred for performance evaluation of existing heat exchangers.

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The NTU method provides a direct, non-iterative mathematical path to find heat transfer when only inlet temperatures are known.
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## Determining C_min and C_max

- Recall heat capacity rates: C_h = m_h * c_ph and C_c = m_c * c_pc.
- Compare C_h and C_c.
- The smaller value is designated as C_min.
- The larger value is designated as C_max.
- The fluid with C_min will experience the largest temperature change.

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The first step in the NTU method is finding which fluid has the smaller heat capacity rate. This fluid dictates the theoretical limits of heat transfer.
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## Maximum Possible Heat Transfer (Q_max)

- What is the maximum heat transfer theoretically possible?
- It occurs in a very long counter-flow heat exchanger.
- The fluid with C_min would reach the inlet temperature of the other fluid.
- Q_max = C_min * (T_h,in - T_c,in)

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Maximum heat transfer happens if the fluid with the smaller capacity rate is heated or cooled to the absolute extreme—the inlet temperature of the other fluid.
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## Heat Exchanger Effectiveness

- Effectiveness (epsilon) = Actual heat transfer rate / Maximum possible heat transfer rate
- epsilon = Q / Q_max
- Since Q = C_c(T_c,out - T_c,in) = C_h(T_h,in - T_h,out)
- epsilon is a dimensionless number between 0 and 1.

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Effectiveness is basically an efficiency rating. It tells us what fraction of the theoretical maximum heat transfer we are actually achieving.
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## Number of Transfer Units (NTU)

- NTU is a dimensionless parameter widely used for heat exchanger analysis.
- NTU = (U * A) / C_min
- It is a measure of the heat transfer surface area (A).
- A larger NTU means a physically larger heat exchanger.

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NTU is proportional to the surface area. It tells us how 'big' the heat exchanger is relative to the fluid flow.
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## Capacity Ratio (c)

- Another dimensionless parameter is the capacity ratio, c.
- c = C_min / C_max
- c ranges from 0 to 1.
- For phase change (boiling or condensation), C_max approaches infinity, so c = 0.

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The capacity ratio gives us the relationship between the two flows. If a fluid is boiling, its capacity rate is infinite, making c equal to zero.
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## Effectiveness Relations: Parallel Flow

- Effectiveness can be expressed as a function of NTU and c: epsilon = f(NTU, c)
- For Parallel Flow:
- epsilon = [1 - exp(-NTU(1+c))] / (1+c)
- Charts are available to look up epsilon based on NTU and c.

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We can calculate effectiveness algebraically, or use standard charts where we look up NTU and c to find epsilon.
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## Effectiveness Relations: Counter Flow

- For Counter Flow (when c < 1):
- epsilon = [1 - exp(-NTU(1-c))] / [1 - c*exp(-NTU(1-c))]
- If c = 1 (C_min = C_max): epsilon = NTU / (1 + NTU)
- Counter flow charts show higher effectiveness for the same NTU.

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The formulas differ by arrangement, but you can see on the charts that counter flow always achieves a higher effectiveness for the same physical size.
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## Summary

- The NTU method eliminates iteration when outlet temperatures are unknown.
- Effectiveness (epsilon) compares actual heat transfer to theoretical maximum.
- NTU = UA / C_min is a dimensionless measure of size.
- Effectiveness charts map epsilon, NTU, and c.

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To summarize, the NTU method is our go-to tool for evaluating the performance of an existing heat exchanger.
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## Next Lecture Preview

- Topic: Advanced Heat Exchanger Concepts
- - Concept of heat pipe
- - Compact heat exchanger design
- - Specialized applications

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Next lecture, we will explore specialized heat exchangers like heat pipes and delve deeper into compact heat exchanger technology.
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