Lesson 6.4: Heat Exchangers (LMTD, NTU)

Heat exchangers are devices that transfer heat between two fluids. GATE and PSU exams often test types, design methods, and heat transfer calculations.

🔹 1. Introduction

• Definition: A heat exchanger allows heat flow from a hot fluid to a cold fluid without mixing them.

• Applications: Power plants, chemical process industries, refrigeration, HVAC systems

• Key Concepts:

  1. Temperature difference drives heat transfer

  2. Overall heat transfer coefficient (U)

  3. Log Mean Temperature Difference (LMTD) method

  4. Number of Transfer Units (NTU) method

🔹 2. Types of Heat Exchangers

• Based on Flow Arrangement:

  1. Parallel Flow: Hot and cold fluids move in same direction

  2. Counter Flow: Fluids move in opposite directions (more efficient)

  3. Cross Flow: Fluids move perpendicular to each other

• Based on Construction:

  • Shell and Tube

  • Plate

  • Finned Tube

🔹 3. Log Mean Temperature Difference (LMTD) Method

• Definition: Average temperature difference between hot and cold fluids over length of exchanger

ΔTlm=ΔT1−ΔT2ln⁡(ΔT1/ΔT2)\Delta T_\text{lm} = \frac{\Delta T_1 – \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}ΔTlm​=ln(ΔT1​/ΔT2​)ΔT1​−ΔT2​​

Where ΔT₁ = inlet temp difference, ΔT₂ = outlet temp difference

• Heat Transfer Rate:

q=UAΔTlmq = U A \Delta T_\text{lm}q=UAΔTlm​

Where:
U = overall heat transfer coefficient, A = heat transfer area

• Example: Counterflow exchanger, Th,in = 150°C, Th,out = 100°C, Tc,in = 50°C, Tc,out = 90°C, U = 500 W/m²K → A = ?

🔹 4. NTU (Number of Transfer Units) Method

• Used when outlet temperatures are unknown

NTU=UACmin,C=m˙cp\text{NTU} = \frac{U A}{C_\text{min}}, \quad C = \dot{m} c_pNTU=Cmin​UA​,C=m˙cp​

• Effectiveness (ε):

ϵ=qactualqmax\epsilon = \frac{q_\text{actual}}{q_\text{max}} ϵ=qmax​qactual​​

• Relationship: q = ε Cmin (Th,in – Tc,in)

• Applications: Shell & tube design, compact heat exchangers, thermal systems with unknown outlet temperatures

🔹 5. Solved Examples (PYQ Style)

1. Compute heat transfer area using LMTD for parallel and counterflow exchangers

2. Determine NTU and effectiveness for given shell & tube exchanger

3. Compare heat transfer rate between parallel and counterflow arrangements

🔹 6. Practice Exercises

1. Calculate ΔTlm for given inlet and outlet temperatures

2. Compute A using U and ΔTlm

3. Determine NTU and effectiveness for given flow rates and heat capacities

4. Solve counterflow and crossflow exchanger problems

5. Analyze performance of shell & tube exchanger under different operating conditions

🔹 7. Summary

• Heat Exchanger Types: Parallel, counter, crossflow; shell & tube, plate, finned tube

• Design Methods: LMTD method (known outlet temperatures), NTU method (unknown outlet temperatures)

• Key Parameters: Overall heat transfer coefficient (U), ΔTlm, NTU, effectiveness

• Applications: Power plants, chemical industries, HVAC, refrigeration