Heat Exchange
1.) Aim of the experiment
To study the fundamentals of heat transfer processes on a continuous-operating „shell and
tube” type heat exchanger.
2.) Theoretical background
General criterilal equations for heat transfer processes by flowing fluids, depending on the
type of flow, can be written as the following.
In the range of turbulent and intermediate flow (Re >2,1ּ103):
Nu  A  Re a  Pr b
(1)
In the range of laminar flow (Re < 2,1ּ103), where heat transfer is highly affected by
convection:
c
D
 D

Nu  B    Re Pr     Pr  Gr 
 l
  l

d
(2)
Criterial numbers:
Nu 
D

Re 
D vρ
μ
Pr 
μ c
λ
β  D3  Δt '  ρ 2  g
Gr 
μ2
Nusselt number
(3)
Reynolds number
(4)
Prandtl number
(5)
Grasshof number
(6)
Notations used in equations (3-6):
α=
heat transfer coefficient [J/m2Ks],
D=
flow diameter [m],
λ=
linear thermal conductivity of the flowing fluid [J/m Ks],
ν=
linear velocity of the flowing fluid [m/sec],
ρ=
density of the flowing fluid [kg/m3],
μ=
viscosity of the flowing fluid [kg/m·s],
c=
specific heat of the flowing fluid [J/kgK],
β=
cubic thermal expansion coefficient of the flowing fluid [1/K],
g=
gravitational acceleration [m/s2],
Δt' =
temperature difference between heat transfering wall and the flowing fluid [K],
A, B, a, b, c, d =
constants of criterial equations,
D/l =
geometrical simplex, ratio of the diameter and the length of tube.
Thermal conductivity can be derived based on equations (1-6) as the following:
1
k calc

1 δw 1


α1 λ w α 2
(7)
where:
kcalc = calculated thermal conductivity [J/m2 Ks],
α1 = heat transfer coefficient of medium 1 [J/m2 Ks],
α2 = heat transfer coefficient of medium 2 [J/m2 Ks],
δw = thickness of heat transfering wall [m],
λ w = linear thermal conductivity of the heat transfering wall [J/m Ks],
Heat transfer rate can be calculated based on transfer rates and temperatures:
J 
 s 
Q  w    c  t
(8)
where
Q = derived heat transfer rate [J/ s],
W = volumetric flow rate of the medium [m3 /s],
ρ = density of the medium [kg/m3],
c = specific heat of the medium [J/kg K],
Δt = temperature change of the medium [K].
Based on the derived heat transfer rate and the instrument parameters, measured thermal
conductivity can be also calculated:
Q  k m  A Δt a
J 
s 
 
(9)
where
km = measured thermal conductivity [J/m2 Ks],
Δta = average temperature difference between the media [K]
A = Heat transfering surface area [m2].
Average temperature difference between the two ends of the heat exchanger:
Δt  Δt i
Δt a  o
Δt
ln o
Δt i
where
t 0 = temperature difference between the media at either end of the heat exhanger
ti = temperature difference between the media at the other end of the heat exhanger
(10)
Equation (10) can be used in the case of concurrent as well as counter-current flow.
Δt o
 2 – in most cases – mathematical average can be used instead for
Δt i
logarithmic average of temperatures:
In the case of
Δt a 
Δt o  Δt i
2
(11)
kcalc calculated by equations (1-7) and km calculated by equations (8-11) should be equal
(within experimental error), so their comparison can be used to check the accuracy of the
measurement.
In the experiment both media are water, hot water is indexed with 1, cold water with 2. Let’s
look through the equations above applied to our system.
Δt = temperature change of the media
In the case of hot water: Δtl= tlk-tlv,
In the case of cold water: Δt2= t2v-t2k, so
Q1 = wl·ρ·c·Δtl, and Q2 = w2 ρ·c·Δt2
In the case of concurrent:
Δt0 = tlv – t2v and Δti = tlk– t2k;
In the case of counter-current:
Δt0 = tlv – t2k and Δti = tlk– t2v;
(k index is for initial, v is for final temperatures)
t1k
t1k
w1
ti
t2v
ti
w1
w2
t1v
t0
t2v
t1v
w2
t0
t2k
t2k
w2 t2v
w2 t2v
w1 w1
t1v t1k
w1
t1k
w2
t2k
w1
t1v
w2
t2k
Counter-current heat exchanger
Concurrent heat exchanger
Diagrams upward indicate temperature changes.
3.) Measurement experiment
Using the current (concurrent or counter-current), flow rate and temperature settings given by
the supervisor, determine the temperatures at steady state. Calculate heat trasfer rate, thermal
conductivities (measured and calculated) and heat transfer coefficients for each setting.
3.1. Handling of the instrument
K1
V1
T
V3 R1
220 V
C
V4 R2
V5
V6
V7
V9
220 V
T4
V8
V10
T1
T2
T3
Legends
Jelmagyarázat
Cold water
Hideg ág
Hot water
Meleg ág
Cooling water
Hűtővíz
Regulation
Szabályozás
T
C
Valve
V
Szelep, csap
R
Rotaméter
K
Kontakthőmérő
T
Hőmérő
Flow meter
Contact thermometer
Thermometer
Concurrent
V5
V6
V7
V8
V9
V10
Open/Closed
C
O
O
O
O
C
Counter-current
V5
V6
V7
V8
V9
V10
Open/Closed
O
O
C
C
O
O
Figure 1. Scheme of the heat exchanger
T
C
K2
V2
Study the construction of the instrument, material and energy flows, handling of the
thermostate. Set the current with the valves, the temperature of the hot water on the
thermostate and the flow rates given by the supervisor. Record the 4 temperatures (T1 – T4) in
every 2 minutes until steady state (no change to the temperatures measured before).
Calculate the following parameters.
4. Calculation
Determine the calculated thermal conductivity (kcalc) and the measured one (km) at steady
state. During the calculation use index 1 for hot and 2 for cold water. Recommended order of
the calculation is Re, Pr, (Gr), Nu, α, kcalc.
Balance of the absorbed and the retained heat indicates the accuracy of the measurement. At
steady state absorbed, transferred and retained heat are equal, and km can be determined after
the calculation of w then Q.
Calculations must be done in SI units!
Figure 2 shows the most important parameters of the heat exchanger:
f
d
D
l
Figure 2. Parameters of the heat exchanger
d = inner tube inner diameter = 8 mm
δ = wall thickness of inner tube = 1 mm
D = shell inner diameter = 30 mm
l = length of heat exhanger tubes = 2 m
Based the data above heat transfering surface area and the linear velocities of the flowing
fluids can be calculated. The D geometrical size - used in equations (1-6) – is the diameter of
the tube in the case of the inner tube, and the so-called equivalent diameter generally
describing the flow diameter in the case of the outer flow, as the following:
De  4
Where
q
k
q = real flow cross-section [m2],
k = circumference touched by the flowing fluid in the cross-section of the flow [m].
Values of the material-based coefficients for calculations:
λwater = 0,62802 J/mKs,
λcopper = 3,94•102 J/mKs,
3
3
ρwater = 10 kg/m ,
λiron = 7,12•10l J/mKs,
3
cwater = 10 •4,19 J/kgK,
βwater = 2,07•10-4 K-1.
ηwater = use the nomogramme below!,
Values of criterial constants for equations (1) and (2):
A = 0,023
B = 1,86
a = 0,8
c = 0,33
b = 0,4
d = 0,28
When calculate Gr number, accept that values of Δt' and Δta are equal, because the wall
temperature cannot be measured.
When calculate heat transfer rate (Q), calculation must be done for both direction of water
flow (equation 8), and transferred heat should be accepted as the average heat transfer rate
(Qa), which is the average of absorbed (Q1) and retained (Q2) heat (equation 9) (these values
should not be differ too much).
Record the calculated values according to the following table (with units!):
w1v1Re1Pr1α1Nu1w2v2Re2Pr2Gr2α2Nu2kszt1kt1vt2kt2vΔt0ΔtiΔtaΔt1Q1Δt2Q2Qatlkm
Viscosity of water as a function of the temperature
Temperature
Viscosity
Temperature
(°C)
(10-3 Ns/m2)
(°C)
0
1,792
40
1
1,731
41
2
1,673
42
3
1,619
43
4
1,567
44
5
1,519
45
6
1,473
46
7
1,428
47
8
1,380
48
9
1,346
49
10
1,308
50
11
1,271
51
12
1,236
52
13
1,203
53
14
1,171
54
15
1,140
55
16
1,111
56
17
1,083
57
18
1,056
58
19
1,030
59
20
1,005
60
20,2
1,000
61
21
0,9810
62
22
0,9579
63
23
0,9358
64
24
0,9142
65
25
0,8937
66
26
0,8737
67
27
0,8545
68
28
0,8300
69
29
0,8180
70
30
0,8007
71
31
0,7840
72
32
0,7679
73
33
0,7523
74
34
0,7371
75
35
0,7225
76
36
0,7085
77
37
0,6947
78
38
0,6814
79
39
0,6685
80
Viscosity
(10-3 Ns/m2)
0,6560
0,6439
0,6321
0,6207
0,6097
0,5988
0,5883
0,5782
0,5683
0,5588
0,5494
0,5404
0,5315
0,5229
0,5146
0,5084
0,4985
0,4907
0,4832
0,4759
0,4688
0,4618
0,4559
0,4483
0,4418
0,4355
0,4293
0,4233
0,4174
0,4117
0,4061
0,4006
0,3952
0,3900
0,3849
0,3799
0,3759
0,3702
0,3655
0,3610
0,3605