# The basic equations required in the design of a heat exchanger by NpEdC855

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```									Shell and Tube Heat Exchangers
Goals:

By the end of today’s lecture, you should be able to:
 describe the common shell-and-tube HE designs
 draw temperature profiles for parallel and counter-current flow in a
shell-and-tube HE
 calculate the true mean temperature difference for a shell-and-tube
HE (use FG chart)
 make heat transfer calculations for shell-and-tube HEs
 describe how the inside and outside heat transfer coefficients are
determined for shell-and-tube HEs
 use the Donohue equation to estimate ho in a multiple pass heat
exchanger
 make heat transfer calculations for multiple pass shell-and-tube
heat exchangers
Outline:

I.     Review
II.    Shell-and-tube equipment
III.   Rate equation and DTTM
IV.    Example Problem - FG for multiple pass HE
V.     Heat transfer coefficients
VI.    Example Problem - Handout
I. Review
Last time, we reviewed heat transfer in double pipe
(concentric pipe) heat exchangers.

We considered cases of parallel and countercurrent flow
of the hot and cold fluids in the concentric pipe design.

The basic equations required in the design of a heat exchanger
are the enthalpy balances on both fluid streams and a rate equation
that defines the heat transfer rate.
Enthalpy balances for fluids without phase change:

qh  mhC ph DTh (hot stream)
                              and         qc  mc C pc DTc (cold stream)


If a phase change occurs (the hot stream is condensed), then the heat of
condensation (vaporization) must be accounted for:

qcond .  mh cond .


In most applications, the heat gained by the cold stream can be assumed to
equal the heat lost by the hot stream (i.e., qh = qc).
The rate of heat transfer for a concentric pipe heat exchanger with
parallel or countercurrent flow can be written as:

q  (Di L)U i DTTM        or    q  AiU i DTTM
where DTTM is the true mean temperature difference.

For concentric pipe heat exchangers, the true mean temperature
difference is equal to the log mean temperature difference (DTLM).
Recall, the overall heat transfer coefficient is
written as:

1      1       1      Dx      1 
                           
U o A o U i A i h i A i kA LM h o A o 
                     
II. Shell-and-Tube Equipment

Concentric Pipe vs. Shell & Tube Heat Exchangers:

The simple double pipe heat exchanger is inadequate for flow rates that cannot
readily be handled in a few tubes. Double pipe heat exchangers are not used for
required heat exchange areas in excess of 100-150 ft2. Several double pipe heat
exchangers can be used in parallel, but it proves more economical to have a single
shell serve for multiple tubes.
Typical Shell-and-Tube Heat Exchanger
Shell-and-tube heat exchangers are described based on the
number of passes the shell-side and tube-side fluids must undergo.

Exchangers are listed as 1-1, 1-2, 2-4, etc. in which the first number signifies
the number of passes for the shell-side fluid and the second number refers to the tube-side
fluid.

Single tube-side pass               Multiple tube-side passes

Single shell-side pass               Multiple shell-side passes
TEMA Designations
TEMA AES Exchanger
Baffles

How do baffles help? Where are they installed and which fluid is directly
affected?
Common practice is to cut away a segment having a height equal to one-
fourth the inside diameter of the shell. Such baffles are called 25 percent
baffles.
Baffle Arrangement
The RODbaffle heat exchanger design (Phillips Petroleum Co.)
Tube Bundles
Tube sizes
Tubes

Standard tube lengths are 8, 12,
16 and 20 ft.

Tubes are drawn to definite wall
thickness in terms of BWG and
true outside diameter (OD), and
they are available in all common
metals.
Tube Pitch

The spacing between the tubes
(center to center) is referred to
as the tube pitch (PT). Triangular
or square pitch arrangements are
used. Unless the shell side tends
to foul badly, triangular pitch is
Used. Dimensions of standard
tubes are given in the Handout
and in MSH Appendix 6.
Tube Pitch
III. Rate equation and DTTM

The rate equation for a shell-and-tube heat exchanger is the same as
for a concentric pipe exchanger:

q  AiU i DTTM
However, Ui and DTTM are evaluated somewhat differently for shell-and-tube
exchangers. We will first discuss how to evaluate DTTM and then a little later
in the notes we will discuss how to evaluate Ui for shell-and-tube exchangers.
In a shell-and-tube exchanger, the flow can be single or multipass. As a result,
the temperature profiles for the two fluids in a shell-and-tube heat exchanger
are more complex, as shown below.

q  AiU i DTTM
Computation of DTTM:

For the concentric pipe heat exchanger, we showed the following (parallel and
countercurrent flow):

DTTM =                   DTlm

When a fluid flows perpendicular to a heated or cooled tube bank, and if both of
the fluid temperatures are varying, then the temperature conditions do not
correspond to either parallel or countercurrent. Instead, this is called crossflow.
For crossflow and multipass heat exchange designs, we must introduce a
correction for the log mean temperature difference (LMTD):

DTTM =           FG * DTLM

Tha  Thb
Z
Tcb  Tca

Tcb  Tca
H 
Tha  Tca
The factor Z is the ratio of the fall in temperature of the hot fluid to the rise
in temperature of the cold fluid.

The factor H is the heating effectiveness, or the ratio of the actual temperature
rise of the cold fluid to the maximum possible temperature rise obtainable (if the
warm-end approach were zero, based on countercurrent flow).

From the given values of H and Z, the factor FG can be read from the text book
figures:
Therefore, as with the concentric pipe heat exchanger, the true mean temperature
difference for the 1-1 exchanger is equal to the log mean temperature difference
(DTLM).

For multiple pass shell-and-tube designs, the flow is complex and the DTLM is less
than that for a pure countercurrent design.

We must account for the smaller temperature driving force using a correction factor,
FG, which is less than 1 and typically greater than 0.8.

The rate of heat transfer in multiple pass heat exchangers is written as:

q  UAFG DTLM
where DTLM is the log mean temperature difference for pure countercurrent flow
Textbook Figures 15.6 a, b

1-2 exchangers

2-4 exchangers
Ten Minute Problem -- FG for multiple pass HE

For a 2-4 heat exchanger with the cold fluid inside the tubes and the following
temperatures:

Tca = 85°F Tha = 200°F
Tcb = 125°F           Thb = 100°F

(a)        What is the true mean temperature difference?

(b)        What exchanger area is required to cool 50,000 lbm/hr of product
(shell-side fluid) if the overall heat transfer coefficient is 100 Btu/hr-ft2-°F
and Cp for the product is 0.45 Btu/lbm-°F?
V. Heat transfer coefficients

In a shell-and-tube exchanger, the shell-side and tube-side heat transfer
coefficients are of comparable importance and both must be large if a satisfactory
overall coefficient is to be attained.
Tube-side coefficient:

The heat transfer coefficient for inside the tubes (hi) can be calculated using
the Sieder-Tate equation for turbulent flow in a constant diameter pipe:

0.8                   0.14
hD         DG  C p  0.333   
 0.023            
 k             k   w 
Shell-side coefficient:

The heat transfer coefficient for the shell side cannot be calculated
using the correlations discussed so far since the direction of flow is
partly perpendicular to the tubes and partly parallel.

An approximate equation for predicting shell-side coefficients is the
Donohue equation:
The Donohue equation is based on the weighted average of the mass velocity of
the shell-side fluid flowing parallel to the tubes (Gb) and the mass velocity of the
shell-side fluid flowing across the tubes (Gc):

D o G e  C p     
0.6        0.33    0.14
h o D o 
          0.2
 k                                        where
    k   w 

Ge = (GbGc)1/2
 D 
Ds      D o
2            2
Gb  m / Sb ,
          Sb  f b      Nb                      Gc  m / S c
         Sc  PDs   o 
1
4        4                                              p 

fb = fraction of the shell cross-section
occupied by the baffle window.

Nb = number of tubes in baffle window
m is the mass flow rate of the shell-side fluid

Do = outside diameter of tubes
Ds = inside diameter of the shell
P = baffle spacing
p = tube pitch
Gb

Gb                       Gc
Exchanger Fouling

Electron microscope image showing fibers, dust, and other deposited material on a
residential air conditioner coil and a fouled water line in a water heater.
Exchanger Fouling
VI.   Text Example Problem 15.3

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