Heat transfer HW

§Solve all the example problems (11.1 to 11.8) from the text book from this Chapter- 11
§Solv

e 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

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 vap

or

– 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)

<

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)

<

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.

35

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’ .

36