Chapter 4
Heat Exchangers
Types & Applications,
LMTD Derivation & problems
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shell-and-tube-
Definition heat-exchanger-
best-practices/
A heat exchanger is defined as an equipment which transfers the heat
from a hot fluid to a cold fluid
fluid.
Types of heat exchangers:
Criteria for classification of heat exchangers:
(i) Nature of heat exchange process
(ii) Relative direction of fluid motion
(iii) Design and constructional features
(iv) Physical state of fluids
I Nature of heat exchange process:
I.
a) Direct contact heat exchangers or Open heat exchangers
Examples: Cooling g towers, Direct contact feed heaters
b) Indirect contact heat exchangers.
Examples: IC engines, gas turbines, Air pre heaters, Economisers. 2
HEAT EXCHANGERS
II. Relative direction of fluid motion:
a. Parallel flow heat exchanger – Fluids move in same direction
b Counter flow heat exchanger – Fluids move in opposite direction
b.
c. Cross flow heat exchanger – Fluids make right angle to each other
III. Design and constructional features:
a. Concentric tubes
b. Shell and tube (most widely used)
c
c. Multiple shell and tube passes
d. Compact heat exchangers
IV. Physical state of fluids:
a. Condensers
b. Evaporators.
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HEAT EXCHANGERS
A li ti
Applications
• Automobiles (Radiators, Air preheater, Exhaust gas heat removal)
• Gas turbines
• Cooling towers
• Industrial Furnaces (Economizers)
Temperature variation in a heat exchanger
Parallel flow Counter flow
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HEAT EXCHANGERS
Introduction to LMTD
• Temperature difference between the hot and cold fluids in a heat
exchanger varies from point to point
• In addition various modes of heat transfer are involved
• Hence,
Hence based on the concept of appropriate mean temperature difference
difference,
also called logarithmic mean temperature difference, the total heat transfer rate
in the heat exchanger is expressed as
Q = UA (∆T)lm
where
U – Overall heat transfer co-efficient, W/m2K
A – Area, m2
((∆T))lm – Logarithmic
g mean temperature
p difference.
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HEAT EXCHANGERS
LMTD Derivation - Assumptions
In order to derive expression for LMTD for various types of heat
exchangers the following assumptions are made
exchangers,
1. Flow is steady
2. The overall heat transfer co-efficient is constant.
3. The specific heats of both fluids are constant.
4. The mass flow rate of both fluids are constant.
5. Axial conduction along the tube is negligible.
6 The chance in kinetic and potential energies of the fluids are negligible
6. negligible.
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HEAT EXCHANGERS
LMTD Derivation – Parallel flow
A single pass parallel flow heat exchangers is shown in fig
Let us consider an elemental area dA of the heat exchanger.
The heat flow rate is given by
dQ = U dA (T – t) Æ(1)
Let
mh – Mass flow rate of hot fluid We know that
mc – Mass flow rate of cold fluid
Cph – Specific heat of hot fluid dQ = -mhCph dT = mcCpc dt Æ ((2))
Cpc – Specific heat of cold fluid dQ = -mhCph dT
T1 – Entry temperature of hot fluid dT = -dQ / mhCph
T2 – Exit temperature of hot fluid dT = -dQ / Ch [since Ch = mh x Cph] Æ (3)
t1 – Entry temperature of cold fluid
t2 – Exit temperature of cold fluid
U – Overall heat transfer co-efficient From equation (2),
dQ = mcCpc dt
dt = dQ / mcCpc
dt = dQ / Cc [since Cc = mc x Cpc] Æ (4)
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HEAT EXCHANGERS
LMTD Derivation – Parallel flow
dT – dt = (–dQ / Ch) – (dQ / Cc)
= –dQ [(1 / Ch) + (1 / Cc)]
dθ = –dQ [(1 / Ch) + (1 / Cc)] [since dθ = dT – dt] Æ (5)
Substituting dQ value from Equation (1) in Equation (5),
dθ = – U dA (T – t) [(1 / Ch) + (1 / Cc)]
= – U dA θ [(1 / Ch) + (1 / Cc)] [since θ = T – t]
(dθ / θ) = – U dA [(1 / Ch) + (1 / Cc)]
Integrating
2
∫(dθ / θ) = – [(1 / Ch) + (1 / Cc)] ∫ U dA
1
2
[ln θ] = – U [(1 / Ch) + (1 / Cc)] A
1
[ln θ2 - ln θ1] = – U A [(1 / Ch) + (1 / Cc)]
ln (θ2 / θ1) = – U A [(1 / Ch) + (1 / Cc)] Æ (6)
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HEAT EXCHANGERS
LMTD Derivation – Parallel flow
We know that,
Q = mhCph(T1 – T2) = mcCpc(t2 – t1)
Q = Ch (T1 – T2) = Cc (t2 – t1) [since C = m x Cp] Æ (7)
Q = Ch (T1 – T2)
1/Ch = (T1 – T2) / Q Æ (8)
From equation
F ti (7),
(7)
Q = Cc (t2 – t1)
1/Cc = (t2 – t1) / Q Æ (9)
Substitute 1/Ch and 1/Cc values in equation (6) and rearranging,
rearranging
ln (θ2 / θ1) = – U A [((T1 – T2) / Q) + ((t2 – t1) / Q)]
ln (θ2 / θ1) = – (U A / Q) [T1 – T2+ t2 – t1]
Q = – U A [T1 – T2+ t2 – t1] / ln (θ2 / θ1)
= U A [T2 – T1+ t1 – t2] / ln (θ2 / θ1)
= U A [(T2 – t2) – (T1 – t1)] / ln (θ2 / θ1)
Q = U A [(T2 – t2) – (T1 – t1)] / ln ((T2 – t2) / (T1 – t1)) [since θ = T – t]
Q = U A [(T1 – t1) – (T2 – t2)] / ln ((T1 – t1) / (T2 – t2)) Æ (10) 9
HEAT EXCHANGERS
LMTD Derivation – Parallel flow
Q = U A [(T1 – t1) – (T2 – t2)] / ln ((T1 – t1) / (T2 – t2))
(or)
Q = UA (∆T)lm
where (∆T)lm – logarithmic mean temperature difference
(∆T) lm = [(T1 – t1) – (T2 – t2)] / ln ((T1 – t1) / (T2 – t2))
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HEAT EXCHANGERS
LMTD Derivation – Counter flow
Let
LMTD for Counter
flow heat exchanger mh – Mass flow rate of hot fluid
mc – Mass flow rate of cold fluid
Cph – Specific heat of hot fluid
Cpc – Specific
p heat of cold fluid
T1 – Entry temperature of hot fluid
T2 – Exit temperature of hot fluid
t1 – Entry temperature of cold fluid
t2 – Exit temperature of cold fluid
U – Overall heat transfer co-efficient
Q = UA (∆T)lm
where (∆T)lm – logarithmic mean temperature difference
(∆T) lm
l = [(T1 – t2) – (T2 – t1)] / ln ((T1 – t2) / (T2 – t1))
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