Experimental Analysis of the Pool Boiling Phenomenon
of Sugarcane Juice
Daniel Marcelo Aldana1,a, Paul Villar Yacila1,b, Raúl La Madrid Olivares1,c
1
Universidad de Piura, Av. Ramón Mugica 131, Urb. San Eduardo – Universidad de Piura, Perú
a
[email protected], [email protected], [email protected]
Keywords: Heat transfer, Correlation of Rohsenow, Pool boiling, Sugarcane juice, Jaggery.
Abstract. In Peru, jaggery making process has low energy efficiency and it is due to low heat
transfer coefficients for natural convection linked to the sugar cane movement generated by the heat
exchange between the sugarcane juice and the combustion gases. This low heat transfer coefficients
are caused by improper heat exchangers designs. In this work, is performed an experimental
analysis that consist in supplie heat to a pot containing sugarcane juice using a hot plate of constant
electrical power. This study consist in identify boiling regimes and estimate the heat transfer
coefficients linked to natural convection boiling, measuring: (i) the temperature at the bottom of the
pot (ii) the temperature at the bottom level of sugarcane juice (iii) the temperature at middle level of
sugarcane juice (iv) the temperature at free surface of sugarcane juice (v) rate of water evaporated.
The method of linear regression and the correlation of Rohsenow were used for obtaining the values
of the heat transfer coefficients ranging from 4088.6 W/m2°C to 12592.8 W/m2°C with power input
ranging from 700W to 1300W.
Introduction
The boiling phenomenon consists in the phase change form liquid state to vapor state which occurs
when the wall temperature of the heated surface is above than the saturation temperature of the
liquid [1]. This process is characterized by the rapid formation of vapor bubbles in the solid-liquid
interface which are separated from the surface when they reach a certain size and have a tendency
to rise to the top of the liquid [2].
In our study case, according to the classification suggested in the literature pool boiling is
analyzed, because quiescent liquid is heated in a pot [3]. The first attempts to study the boiling of
different liquids showed that the main parameters affecting the heat transfer coefficient in pool
boiling are: heat flux, saturation pressure, thermophysical properties of the working fluids and some
characteristics of the material contact surface (thermophysical properties, dimensions, surface
finishing, microstructure, etc) [4].
Besides knowing the process of boiling sugarcane juice and its dynamics, was also studied the
heat transfer rate associated with this process, mainly, to estimate heat transfer coefficients for each
case.
The production process to obtain jaggery begins when sugarcane pass through mills. The subproducts obtained are sugarcane juice and bagasse. The residual bagasse is burned in a combustion
chamber and the combustion products pass through a flue gas duct giving its thermal energy to the
open pan heat exchanger [5].The sugarcane juice contained in the pot is heated in order to evaporate
the water contained on it.
The equation of heat transfer is expressed by the Newton’s law of cooling [6]:
q
ho Tg
Tl
(1)
Where q (W/m2) is the heat flux exchanged between the hot combustion gases and the sugarcane
juice, ho (W/m2°C) is the global heat transfer coefficient, Tg (°C) is the temperature of hot gases
produced by the bagasse combustion, Tl is the sugarcane juice temperature.
The value of ho is calculated through the sum of the thermal resistances network acting on the
process. These resistances are in series and are: resistance to heat transfer by the flow of the
combustion gases ( 1 / hc ), the resistance offered by the wall thickness of the pan with its related
thermal conductivity ( e / k ), a factor representing the fouling layer (Rf) y and the resistance of the
heat exchange fluid to evaporate ( 1 / hl ). With this it can be calculated the overall heat transfer
coefficient as follows [7]:
1
1 e
1
(2)
Rf
ho hc k
hl
The term 1/hl of the equation 2 is the most relevant because the other three terms are negligible.
So, equation 2 can be simplified to:
(3)
ho hl
And equation 1 can be rewritten as:
q hl Ts Tl
(4)
Where Ts (°C) is the contact temperature between the pot bottom and the sugarcane juice.
Nukiyama´s experiments
To predict the value of heat transfer coefficient of the liquid phase in this process is necessary to
know the boiling process.
In 1934, Nukiyama was the first researcher to identify the different regimes of boiling water
[9], using a platinum resistance wire placed horizontally as heat source submerged in saturated
water at atmospheric pressure. The heat flux Q (W) from the horizontal wire to the saturated
water was determined by measuring electrical current I (Amperes) in the wire and voltage V
(Volts). The temperature of the wire was determined by calculating the electrical resistance [10].
Boiling regimes identified in this experiment were defined in relation to the temperature
difference (), as shown in the following figure:
Fig. 1 shows that the heat transfer coefficient for nucleate boiling for saturated pure water will
increase from point A to point C, reaching a maximum value that matches the critical heat flow.
For pure water, the critical or maximum heat flow quantity exceeds 1 MW/m2 [11].
The nucleate boiling regime is the most appropriate in the case of jaggery making process
because in this regimen it can achieve the higher heat transfer rates. It should be noted that
although the boiling curve given in the Fig. 1 is for water, its general shape is the same for
different fluids [6], including sugarcane juice.
Procedure
The experiment involves placing 3 kg of sugarcane juice in a circular stainless steel pot of 0.5 cm
thick, 22 cm in diameter and a height of 25 cm, under constant heat inputs. Heat inputs to sugarcane
juice will be provided by hot plate of 2000W capacity. A variac is used to ensure that the electrical
power provided to the hot plate is constant, which is measured by watt meter.
Four sensors PT-100 were used, which were place (see Fig. 2) to measure: temperature at the
bottom of the pot (T1), temperature at the bottom level of sugarcane juice (T2), temperature at
middle level of sugarcane juice (T3) temperature at free surface of sugarcane juice (T4). These
sensors were connected to a data acquisition module that showed temperature values at real time
and the data was taken for each 5 minutes.
In order to measure the quantity of evaporated water (in kilograms) it was used a digital high
precision balance.
Fig. 3 shows a scheme of the system. It can be seen that the heating is carried out at atmospheric
pressure, which is an important consideration for the calculation of thermophysical properties of
sugarcane juice. The data was taken at four constants heat input rate: 700W, 900W, 1100W,
1300W.
HEAT INPUT 900 W
HEAT INPUT 700 W
Mass
evap.
(g)
Time
difference
(min)
T1
(°C)
T2
(°C)
T3
(°C)
T4
(°C)
Weight
(g)
3000
0
5
91.17
88.94
85.39
84.56
3118
0
2950
50
5
97.61
97.78
94.50
96.44
3100
18
92.88
2890
60
5
99.72
99.44
96.39
98.11
3032
68
94.14
2810
80
5
99.78
99.78
96.22
96.89
2950
82
95.50
94.36
2735
75
5
99.83
99.89
95.70
96.67
2871
79
95.67
95.45
2660
75
5
99.72
100.11
96.34
96.26
2787
84
99.56
95.72
95.99
2590
70
5
99.72
99.78
96.52
96.01
2698
89
101.06
99.39
96.30
96.10
2515
75
5
99.78
100.00
96.72
96.7
2593
105
100.00
99.28
97.13
96.26
2455
60
5
99.67
99.78
97.63
96.88
2501
92
5
100.61
99.61
97.44
96.71
2380
75
5
100.11 100.17
97.40
96.99
2409
92
5
100.56
99.61
97.54
96.64
2300
80
5
99.78
100.00
97.78
97.10
2325
84
5
100.89
99.67
97.60
97.68
2230
70
5
99.67
99.78
98.10
97.48
2232
93
5
101.28
99.78
97.45
97.66
2170
60
5
99.89
99.56
98.46
97.62
2146
86
5
102.00
99.83
95.38
97.92
2090
80
5
100.11
99.41
98.61
97.68
2055
91
5
100.28
99.31
98.74
97.94
1973
82
5
100.06
99.73
99.00
98.00
1882
91
5
100.06 100.13
98.77
98.12
1784
98
5
101.06 100.48
99.25
98.24
1649
135
5
101.06 100.30
99.48
98.47
1629
20
5
101.11 100.95
99.50
99.13
1540
89
5
101.56 101.18
99.82
99.51
1450
90
5
102.10 101.25 100.02
99.78
1357
93
Time
difference
(min)
T1
(°C)
T2
(°C)
T3
(°C)
T4
(°C)
Weight
(g)
5
99.17
96.50
92.89
92.78
5
99.50
98.11
92.32
92.11
5
100.11
99.44
92.86
5
100.83
99.94
95.31
5
100.17
99.56
5
100.33
99.44
5
100.61
5
5
Table 1 Data obtained from boiling the sugarcane juice at 700 W.
Mass
evap.
(g)
Table 2 Data obtained from boiling the sugarcane juice at 900 W.
HEAT INPUT 1100 W
Time
difference
(min)
HEAT INPUT 1300 W
Mass
evap.
(g)
Time
(min)
T1
(°C)
T2
(°C)
T3
(°C)
T4
(°C)
3000
0
5
93.44
92.06
83.39
84.11
3002
0
2984
16
5
100.56
99.89
96.63
95.50
2962
40
96.33
2900
84
5
100.89 100.00
97.67
96.17
2922
42
97.50
96.32
2810
90
5
100.84 100.00
97.98
97.41
2880
93
100.20 100.06
97.95
97.31
2727
83
5
101.64 101.38
99.15
98.89
2787
130
5
100.44 100.06
97.58
97.45
2629
98
5
100.61 100.39
98.20
97.52
2510
119
5
101.95 101.73
99.85
99.45
2657
119
5
102.18 101.76 100.38
99.51
2538
105
T1
(°C)
T2
(°C)
T3
(°C)
T4
(°C)
Weight
(g)
5
95.00
94.56
88.67
86.72
5
100.28
99.94
92.73
97.56
5
100.17 100.28
95.23
5
100.06 100.11
5
Weight Mass evap.
(g)
(g)
5
100.72 100.11
98.45
98.28
2364
146
5
101.00 100.47
98.73
98.62
2249
115
5
102.65 102.33 101.38 100.16
2433
102
5
101.06 100.84
99.03
99.41
2162
127
5
102.88 102.46 102.52 100.32
2331
116
5
101.28 100.88
99.73
98.96
2075
87
5
103.21 102.64 102.77 100.67
2215
89
5
102.41 101.05 100.00
99.40
1977
98
5
103.26 103.08 102.96 101.01
2126
95
5
102.65 101.20 100.31 100.05
1883
94
5
103.43 103.32 103.21 101.05
2031
116.3
5
102.86 101.37 100.15 100.21
1795
98
5
105.52 104.02 103.81 102.25
1915
113.5
5
103.12 101.61 100.77 100.76
1696
99
5
105.92 104.15 103.65 102.43
1802
110
5
103.59 101.87 101.28 100.49
1605
101
5
104.16 102.53 101.64 100.96
1520
95
5
106.47 104.61 104.18 103.16
1692
126
5
104.61 102.95 101.96 101.49
1432
108
5
107.40 105.00 104.29 102.71
1566
103.4
Table 3 Data obtained from boiling the sugarcane juice at 1100 W.
Table 4 Data obtained from boiling the sugarcane juice at 1300 W.
Figure 2 Arrangement PT-100
sensors.
Figure 1 Pool boiling curve for pure water
saturated at atmospheric pressure. [5]
Figure 3 Photography system.
Sugarcane juice was heated before it reaches the honey state, reaching concentrations no greater
than 38 °Bx. Tables 1 to 4 shows the data obtained:
Analytical
Given the complexity presented by the dynamics of the process to be studied analytically,
Rohsenow proposed the following correlation [12]:
Csf Prl n
1
3
l h fg
1
g
l
v
6
c pl Ts
qnucleate
Tsat
h fg
(5)
The rate of mass evaporated ( mev ) is:
Qboiling
Aqnucleate
h fg
h fg
Taken into consideration the Eq. (6), Eq. (5) can be rearranged as follows:
mev
1
Csf Prl n
lA
mev
3
1
g
l
v
6
c pl Ts
Tsat
h fg
(6)
(7)
Using the following:
1
R
lA
mev
3
g
1
l
v
6
c pl Ts
Tsat
h fg
Where:
R Csf Prl n
Using the theory of logarithms to the above relation:
ln R n ln Prl ln Csf
(8)
For the Prandtl number ( Prl ), the following expression is used:
l c pl
(9)
Prl
Kl
This equation has the form of a straight line. The linear regression method to obtain the values of
the constants n y Csf. The form of the equation for a straight line is as follows:
y mx c
(10)
Linear regression method allows obtaining the constants of Rohsenow equation using the
following relations:
m
N
xy
x2
N
c
So:
n
Csf
x
y
x2
y
N
x2
(11)
2
x
x
x
xy
(12)
2
m
ec
Also, the average heat transfer coefficient by convection can be obtained as follows:
qnucleate
h
Ts Tsat
(13)
Results and discussions
With the experimental test, it was possible to appreciate the dynamics of this process, allowing
identify regimes of natural convection and nucleate boiling.
The data in tables 1 to 4 were used to calculate the values of the heat transfer coefficients and
constants for Rohsenow pool boiling correlation, corresponding to each heat input, as shown Tab. 5.
The expressions for finding the thermophysical properties present in this correlation are listed in
Appendix-I [13-15].
To obtain the results shown in Tab. 5, it was considered that the surface temperature of the pot
(Ts) is the temperature corresponding to the T1 and the temperature at which the thermophysical
properties of sugarcane juice were found is the average of T2, T3 y T4.
Heat input
(W)
Csf
n
h
(W/m2°C)
700
900
1100
1300
0.0090
0.0039
0.0393
0.0027
-0.0475
-0.0300
-0.0164
-0.0100
4088.6
10556.8
10901.2
12592.8
Table 5 Values of constants for Rohsenow pool boiling correlation and heat transfer coefficients associated with the nucleate
boiling of sugarcane juice for each heat input.
Heat transfer
coefficient
(W/m2°C)
The heat transfer coefficient due to natural convection movement on nucleate boiling of
sugarcane juice range from 4088.6 to 12592.8 W/m2°C for heat inputs ranging from 700 to 1300W.
Fig. 4 shows the variation of heat transfer coefficient as a function of the heat input.
14000
12000
10000
8000
6000
4000
2000
0
700
900
1100
1300
Heat input(W)
Figure 2 Variation of heat transfer coefficient as a function of the heat input.
Conclusions
The value of the heat transfer coefficient increase proportionally with thermal power to
sugarcane juice. In the same way with the increment of the thermal power, the difference
temperature increases (Ts – Tsat) and that causes the acceleration in the rate of formation of vapor
bubbles at the bottom of the pot. This factor also influences the mentioned heat transfer coefficient.
While more nucleation places are generated, more vapor bubbles nucleate emerged increasing
the heat (qnucleate) and the heat transfer coefficient.
In the experimental test was observed that
transmitted to the juice.
The vertical movement of the vapor bubbles
boiling.
Apendix I
1043 4.854 Bx 1.07T
l
1.718 10 5 4.620 10 8 T
l
Kl 0.3815 0.0051 Bx 0.001866T
c pl
4187 (1 0.006 Bx)
T
T
0.001016 sat s
2
h fg 2499e
Acknowlegdements
the bubble size depends on the thermal power
is the driving force for heat transfer by nucleate
[kg/m3]
[kg/ms]
[W/m°C]
[J/kg°C]
[kJ/kg]
This paper have been supported by the Fondo para la
Tecnología (FINCyT), Perú, under the contract 174-FINCyT-IA-2013.
Innovación,
Ciencia
y
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