In the present paper appear to continue a study on heat transfer by convection in a fixed bed of particles. Were studied cylindrical particles made of alumina, with geometrical characteristics well defined by the ratio H/D =8/3,2 mm. The particles are situated inside the tube of a coaxial heat exchanger . Were established the criterial relationship for calculating the partial coefficient of heat transfer fluid - solid particles by convection.
Beds of particles are used in oil processing industry for making catalytic processes, combustion processes, processes of mass transfer and heat transfer processes. This paper is part of a comprehensive study on heat transfer in the fixed layer of particles [1-3]. Chosen for this study were cylindrical particles with well defined geometrical ratio H / De = 8 / 3, 2 mm, made of alumina. The study was conducted on a coaxial heat exchanger tube, made of steel. For the same type of particles have been studied and fluid-dynamic aspects [4].
2.Experimental part
Cylindrical particles used in the study were placed in the inner tube of heat exchanger to circulate warm water flow, and countercurrent flow of cold water circulated through the annular space of the heat exchanger. In table 1are presented the geometrical characteristics of cylindrical particles used.
Rates were measured for both streams (hot and cold) and their temperatures at both entry and exit of the heat exchanger. All physical properties of water (density, dynamic viscosity, specific heat, thermal conductivity) were calculated from the average temperature for this criterion as data processing.
Table 1. Geometric characteristics of the filling [5]
Characteristic cylindrical particle
Symbol
Value
Height, mm
H
8
Diameter, mm
d
3,2
Particle area ·106, m2
A = ap
96,51
Particle volume· 108, m3
vp
6,4
Particle surface area, m2/m3
1508
Equivalent volume diameter ·103, m
d0
4,96
Surface area of the filling, m2/m3
656
Sphericity
ψ
0,802
Fig 1. Experimental scheme
1 - heat exchanger, R1, R2 - rotameters, 2 - furnace, 3 - gas lamp, 4 - temperature recorder;
5 - thermocouple, 6 - electronic thermometers; SU - filling bed
3. Calculation algorithm
Algorithm for calculating the optimal correlation of experimental data is presented below.
1. Calculation of heat transfer coefficient partial annular space, through which cold water was made with criteria relationship (1), which was deducted for heat exchanger shown in specific working conditions [2 ]. Knowing the value of Nusselt number in criteria relationship (1), calculating the partial heat transfer coefficient on the outside, αe, for the annular space.
(1)
2.Outer wall temperature, tpe, calculation with equation (2):
(2)
3. Determination of the inner surface temperature for the hot fluid, tpi, is the expression of heat flux transferred by conduction through the cylindrical wall and the relationship of the calculation is :
(3)
4. Determination of heat transfer coefficient partially inside, αi, between the warm fluid that goes through the bed of particles and the wall is done with the relationship (4):
(4)
5. Determination, based on experimental data processing, form a relationship criteria:
(5)
4. Results and discussion
Measurements and experimental data led to results presented in Tables 2-3.
Table 2. Sizes calculated values for cold fluid - cylinder filling with H / D = 8/3,2 mm
No.
det.
mr·103,
kg/s
Δtr,
0C
Q rec.,
W
wcold·103,
m/s
Prcold
Recold
Nucold
αe,
W/m2·0C
tpe,
0C
1
12.59
26
1368
4.38
5.97
181
41
688
47
2
11.63
24
1166
4.05
6.13
163
38
642
44
3
12.48
9
470
4.33
7.47
147
38
623
27
4
9.15
10
383
3.18
7.37
109
30
501
26
5
6.10
12
306
2.12
7.18
74
23
379
30
6
6.37
23
612
2.22
6.21
88
25
415
45
7
9.40
37
1451
3.28
5.19
153
34
590
62
Table 3. Sizes calculated values for the warm fluid - cylinder filling with H / D = 8/3,2 mm
No.
det.
mc·103,
kg/s
Δtc,
0C
Qwaste,
W
wwarm·103,
m/s
Prwarm
dech,
m
Rewarm
tpi,
0C
αi,
W/m2·0C
Nuwarm
Nucalc.
1
22.2
16
1483
42.4
3.38
0.00345
486
48.2
3787
20.16
19.97
2
26.9
11
1235
51.3
3.61
0.00345
556
44.7
4004
21.49
22.29
3
19.9
7
582
37.7
5.46
0.00345
284
27.1
2928
16.40
16.42
4
20.7
5
433
39.2
5.60
0.00345
290
26.7
3025
16.99
16.79
5
11.1
9
415
20.9
5.07
0.00345
169
30.0
2004
11.14
11.35
6
8.2
26
893
15.7
3.43
0.00345
178
46.1
1852
9.87
10.36
7
15.5
29
1877
29.8
3.22
0.00345
347
64.0
3045
15.78
15.74
Applying a regression program, the results were set constant values C and exponents m and n in equation (5): C = 0.228, m = 0.658, n = 0.33. The criteria relationship obtained is:
(6)
The relationship for calculated partially heat transfer coefficient inside, αi, becomes:
(7)
If changes are plotted with the experimentally determined Nusselt number - calculated Nusselt number is observed placing items near the first bisectrix. The deviation of calculation lies within acceptable limits for criteria relationships of the heat transfer coefficients. This correlation is shown in Figure 2.
Figure 2. Corelations between Nusselt number
5.Conclusions
Algorithm was established for the determination of the partial heat transfer coefficients in the coaxial tube exchanger, in which solid particles are located inside the cylindrical shape with the ratio H/De = 8/ 3,2 mm. Relationship was derived criteria for Nu = f (Re, Pr) and relationship to partial coefficient of heat transfer fluid - fixed bed of particles, tubular heat exchanger. To set the value for standard deviation calculation for Nu, which ranged (- 4,73 % - + 1.18%), which established relations recommended for use in reactor design with a fixed layer of particles.
The values of the partial heat transfer coefficients are obtained by the hot fluid, ranging from 1852 -4004 W/m2 0C hot water at speeds of 1.57 • 10-2 -5.13 • 10-2 m/s.
6. Notations
αi, αe - the partial coefficients of heat transfer at the inside and outside of the central tube,
W/m2•° C;
dech - the equivalent diameter of the bed, m;
Qwaste - the heat flow waste for the warm water, W;
Ae - the area of the external surface of the inner tube, m2;
tc, tr - the average temperature of warm fluid and cold, ° C;
λsteel - the thermal conductivity of steel, λsteel = 40 W / m • ° C;
t pe, t pi - the temperature of the wall at the inlet and outlet of the exchanger, ° C;
d e, d I - the inner and outer of the small tube, mm;
H - the heat exchanger height, m.
