Lmtd method of heat exchanger analysis

Fundamentals of Heat and Mass Transfer, Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera, David P. DeWitt, John Wiley & Sons, Inc.

•Chapter 1: Introduction

Conduction Heat Transfer •Chapter 2: Introduction to Conduction •Chapter 3: 1D, Steady-State Conduction •Chapter 4: 2D, Steady-State Conduction •Chapter 5: Transient Conduction

Convection Heat Transfer •Chapter 6: Introduction to Convection •Chapter 7: External Flow •Chapter 8: Internal Flow •Chapter 9: Free Convection •Chapter 10: Boiling and Condensation •Chapter 11: Heat Exchangers

Radiation Heat Transfer •Chapter 12: Radiation Processes and Properties •Chapter 13: Radiation Exchange Between Surfaces

1 Mass Transfer

•Chapter 14: Diffusion Mass Transfer

Chapter-11

(Heat Exchangers)

2

Chapter-11: Heat Exchangers

3

11.1 Heat Exchanger Types 11.2 The Overall Heat Transfer Coefficient

11.3 Heat Exchanger Analysis: Use of the Log Mean Temperature Difference

11.3.1 The Parallel-Flow Heat Exchanger 11.3.2 The Counterflow Heat Exchanger 11.3.3 Special Operating Conditions

11.4 Heat Exchanger Analysis: The Effectiveness–NTU Method

11.4.1 Definitions

11.4.2 Effectiveness–NTU Relations 11.5 Heat Exchanger Design and Performance Calculations 11.6 Additional Considerations

11.7 Summary

Heat Exchanger Types

Heat exchangers are ubiquitous in energy conversion and utilization. They involve heat exchange between two fluids separated by a solid and encompass a wide range of flow configurations.

• Concentric-Tube Heat Exchangers

Parallel Flow Counterf low

Ø Simplest configuration. Ø Superior performance associated with counter flow.

Cross-flow Heat Exchangers

Finned-Both Fluids Unmixed

Unfinned-One Fluid Mixed the Other Unmixed

Ø For cross-flow over the tubes, fluid motion, and hence mixing,

in the transverse direction (y) is prevented for the finned tubes, but occurs for the unfinned condition.

Ø Heat exchanger performance is influenced by mixing.

Shell-and-Tube Heat Exchangers

One Shell Pass and One Tube Pass

Ø Baffles are used to establish a cross-flow and to induce turbulent mixing of the shell-side fluid, both of which enhance convection.

Ø The number of tube and shell passes may be varied, e.g.:

One Shell Pass, Two Tube Passes

Two Shell Passes, Four Tube Passes

Compact Heat Exchangers

Ø Widely used to achieve large heat rates per unit volume, particularly when one or both fluids is a gas.

Ø Characterized by large heat transfer surface areas per unit volume, small flow passages, and laminar flow.

(a) Fin-tube (flat tubes, continuous plate fins) (b) Fin-tube (circular tubes, continuous plate fins) (c) Fin-tube (circular tubes, circular fins) (d) Plate-fin (single pass) (e) Plate-fin (multipass)

Overall Heat Transfer Coefficient (1/2)

• An essential requirement for heat exchanger design or performance calculations.

• Contributing factors include convection and conduction associated with the two fluids and the intermediate solid, as well as the potential use of fins on both sides and the effects of time- dependent surface fouling. • With subscripts c and h used to designate the cold and hot fluids, respectively, the most general expression for the overall coefficient is:

Overall Heat Transfer Coefficient (2/2)

Ø

→ Table 11.1

Ø

Assuming an adiabatic tip, the fin efficiency is

Ø

A Methodology for Heat Exchanger Design Calculations (Log Mean Temperature Difference (LMTD) Method)

• A form of Newton’s law of cooling may be applied to heat exchangers by using a log-mean value of the temperature difference between the two fluids:

ΔT = ΔT

1 − ΔT2

l m 1n (ΔT1 / ΔT2 )

Evaluation of depends on the heat exchanger type.

• Counter-Flow Heat Exchanger:

ΔT ≡ T − T 1 h ,1 c,1

= T

h ,i −

T

c ,o

ΔT ≡ T − T 2 h ,2 c,2

= T

h ,o −

T

c ,i

Parallel-Flow HeatΔT1≡Th,1− TExchangerc,1

= T

h ,i −

T

c ,i

Ø Note that Tc,o cannot exceed Th,o for a PF HX, but can do so for a CF HX.

Ø For equivalent values of UA and inlet temperatures,

• Shell-and-Tube and Cross-Flow Heat Exchangers:

Overall Energy Balance

• Application to the hot (h) and cold (c) fluids:

• Assume negligible heat transfer between the exchanger and its surroundings and negligible potential and kinetic energy changes for each fluid.

• Assuming no l/v phase change and constant specific heats,

Special Operating Conditions

Ø Case (a): Ch>>Cc or h is a condensing vapor – Negligible or no change in Th (Th,o=Th,i)

Ø Case (b): Cc>>Ch or c is an evaporating liquid

– Negligible or no change in Tc (Tc,o=Tc,i) Ø Case (c): Ch=Cc.

–

Exercise Problem 11.5: Determination of heat transfer per unit length for heat recovery device involving hot flue gases and water. (1/5)

Exercise Problem 11.5: Determination of heat transfer per unit length for heat recovery device involving hot flue gases and water. (2/5)

Exercise Problem 11.5: Determination of heat transfer per unit length for heat recovery device involving hot flue gases and water. (3/5)

Exercise Problem 11.5: Determination of heat transfer per unit length for heat recovery device involving hot flue gases and water. (4/5)

Exercise Problem 11.5: Determination of heat transfer per unit length for heat recovery device involving hot flue gases and water. (5/5)

Exercise Problem 11.54: Design of a two-pass, shell-and-tube heat exchanger to supply vapor for the turbine of an ocean thermal energy conversion system based on a standard (Rankine) power cycle. The power cycle is to generate 2 MWe at an efficiency of 3%. Ocean water enters the tubes of the exchanger at 300K, and its desired outlet temperature is 292K. The working fluid of the power cycle is evaporated in the tubes of the exchanger at its phase change temperature of 290K, and the overall heat transfer coefficient is known. (1/3)

SCHEMATIC:

Exercise Problem 11.54: Design of a two-pass, shell-and-tube heat exchanger to supply vapor for the turbine of an ocean thermal energy conversion system based on a standard (Rankine) power cycle. The power cycle is to generate 2 MWe at an efficiency of 3%. Ocean water enters the tubes of the exchanger at 300K, and its desired outlet temperature is 292K. The working fluid of the power cycle is evaporated in the tubes of the exchanger at its phase change temperature of 290K, and the overall heat transfer coefficient is known. (2/3)

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Exercise Problem 11.54: Design of a two-pass, shell-and-tube heat exchanger to supply vapor for the turbine of an ocean thermal energy conversion system based on a standard (Rankine) power cycle. The power cycle is to generate 2 MWe at an efficiency of 3%. Ocean water enters the tubes of the exchanger at 300K, and its desired outlet temperature is 292K. The working fluid of the power cycle is evaporated in the tubes of the exchanger at its phase change temperature of 290K, and the overall heat transfer coefficient is known. (3/3)

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General Considerations

• Computational Features/Limitations of the LMTD Method:

The LMTD method may be applied to design problems for which the fluid flow rates and inlet temperatures, as well as a desired outlet temperature, are prescribed. For a specified HX type, the required size (surface area), as well as the other outlet temperature, are readily determined.

Ø If the LMTD method is used in performance calculations for which both outlet temperatures must be determined from knowledge of the inlet temperatures, the solution procedure is iterative.

Ø For both design and performance calculations, the effectiveness-NTU method may be used without iteration.

Definitions (1/2)

• Heat exchanger effectiveness, : • Maximum possible heat rate: Ø Will the fluid characterized by Cmin or Cmax experience the largest possible temperature change in transit through the HX?

Ø Why is Cmin and not Cmax used in the definition of qmax?

Definitions (2/2)

• Number of Transfer Units, NTU

Ø A dimensionless parameter whose magnitude influences HX performance:

Heat Exchanger Relations (1/2)

q = ε Cmin (Th , i −Tc ,i ) • Performance Calculations: Ø

Cr Ø

Heat Exchanger Relations (2/2)

Design Calculations:

ε ↑ with ↓ Cr Ø Ø

• For all heat exchangers,

ε = 1 − exp (−NTU)

• For Cr

= 0, a single

or

relation applies to all HX types.

NTU = −1n (1 − ε )

Exercise Problem 11.35: Use of twin -tube (brazed) heat exchanger to heat air by extracting energy from a hot water supply. (1/5)

SCHEMATIC:

Exercise Problem 11.35: Use of twin -tube (brazed) heat exchanger to heat air by extracting energy from a hot water supply. (2/5)

Exercise Problem 11.35: Use of twin -tube (brazed) heat exchanger to heat air by extracting energy from a hot water supply. (3/5)

Exercise Problem 11.35: Use of twin -tube (brazed) heat exchanger to heat air by extracting energy from a hot water supply. (4/5)

Exercise Problem 11.35: Use of twin -tube (brazed) heat exchanger to heat air by extracting energy from a hot water supply. (5/5)

and from Eq. (1) the effectiveness is

Exercise Problem 11.39: Use of a cross-flow heat exchanger to cool blood in a cardio- pulmonary bypass procedure. (1/3)

Exercise Problem 11.39: Use of a cross-flow heat exchanger to cool blood in a cardio- pulmonary bypass procedure.(2/3)

Exercise Problem 11.39: Use of a cross-flow heat exchanger to cool blood in a cardio-pulmonary bypass procedure. (3/3)

Suggested Problems to Practice

•Example Problem: 11.1 (Page-716) to 11.8 (Page-742) •Exercise Problem: 11.1 (Page-748) to 11.94 (Page-765) •Derive equation 11.14 showing all the steps to find total heat transfer for parallel flow heat exchanger. Apply the same concept for counter- flow heat exchanger. •Derive equation 11.28a showing all the steps to find relation between heat exchanger effectiveness and NTU.

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Homework-5

§Solve all the example problems (11.1 to 11.8) from the text book from this Chapter- 11 §Solve all the exercise problems (11.5, 11.35, 11.39, and 11.54) mentioned in the slides from this Chapter-11 §Show all the steps (Given, Find, Assumptions, Solve, hand drawings etc.) to give impression that you understood the problem §Write all the necessary equations applied to those problems

§Due by Tuesday 7/31 by 8pm §You can submit the homework early, if you want §Write your solved problems, scan all the pages as one pdf §Please use the file name for attachment as: 'HW-5-Your First and Last name' .