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Applicability of arrays of microjet heat transfer correlations to design compact heat exchangers
Accepted Manuscript Title: Applicability of arrays of microjets heat transfer correlations to design compact heat exchangers Author: Tomasz Muszynski, Rafal Andrzejczyk PII: DOI: Reference:
S1359-4311(16)30070-9 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.120 ATE 7680
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
12-11-2015 28-1-2016
Please cite this article as: Tomasz Muszynski, Rafal Andrzejczyk, Applicability of arrays of microjets heat transfer correlations to design compact heat exchangers, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.120. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Applicability of arrays of microjets heat transfer correlations to design compact heat exchangers Tomasz Muszynski1 , Rafal Andrzejczyk1 1: Gdansk University of Technology, Faculty of Mechanical Engineering, Department of Energy and Industrial Apparatus Narutowicza 11/12, 80-233 Gdansk, Poland E-mail: [email protected], [email protected] Highlights
A prototype heat exchanger was built and tested.
The obtained overall heat transfer coefficient reaches over 10000 W/m2K.
New experimental correlation was suggested.
Graphical Abstract
Abstract
The article presents experimental studies on a compact heat exchanger with heat transfer intensification by means of impinging microjets. The pursuit to provide high performance of heat exchangers is a response to the demand both in economics and in the universal tendency to miniaturization of industrial equipment. This paper presents the design and tests of a prototype, microjet heat exchanger. The modular design of the heat exchanger allows to change its geometrical dimensions, as well as changing the heat exchange membrane material. The study of heat transfer in water-water flow, allows to determine the heat transfer efficiency, the characteristics of heat transfer, and the heat transfer coefficient values. Data were collected for the pressure drops in heat exchanger not exceeding 15 kPa, i.e. such as in conventional heat
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exchangers. Hydraulic characteristics of a model heat exchanger were obtained. Experimental values of heat transfer for jet impingement were calculated by means of Wilson’s plot method. Obtained values of heat transfer coefficient were compared with literature correlations. Authors also proposed their own empirical correlation for jet impingement heat transfer coefficient. Keywords: microjets, heat exchangers, heat transfer intensification, Wilson’s plot method, theory of similarity,
1. INTRODUCTION
Achieving the technological control on the micoscale heat and energetic installations and making them high- efficient is the challenge of 21st century. This direction of development has been delineated by the general trend towards miniaturization and by the expected widespread. The main elements of such systems must be highly compact and highly efficient heat exchangers. Regarding to that fact one of the technical problems associated with the heat removal in refrigeration and air-conditioning is an installation of high-performance heat exchangers i.e. evaporator, condenser or regenerative heat exchanger. Striving to ensure high performance of these elements is today a source of universal trend both to the miniaturization of these devices for both industrial and domestic applications, while maintaining the highest possible size to thermal energy ratio. As is well known, in recuperators heat transfer coefficient have decisive influence their efficiency. Overall heat transfer coefficient depends mainly on the lower value of HTC from working media. It is therefore most significant to improve the heat transfer with special attention on the side of the medium with lower heat transfer coefficient. Overall methods to intensify the heat exchange in channels using passive techniques have been presented in the work of Gupta [1] and Webb [2]. Stone [3] worked on intensifiction of heat transfer in compact heat exchangers. Sun et al. [ 4] studied the effect of porous coatings on heat transfer intensification in the channel. The horizontal rectangular channels were tested with hydraulic diameters of 0.49 mm, 0.93 mm and 1.26 mm. Only the bottom channel wall had developed surface. Three types of microcoatings of the average grain diameter of 20 μm, 50 μm and 120 μm, and the working fluid FC-72 were used. There was a significant increase in heat transfer coefficient, when
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compared to a smooth surface. For the optimal variant of coverage, the wall overheating, necessary for the boiling initiation, decreased by 7.4 K and the temperature of the heating surface by 10.3 K. The influence of the channel size was analyzed and the conclusion was made that the size reduction leads to a reduction in the critical heat flux. Wang and Peterson [5] used small metallic porous nettings as one of the walls of four parallel microchannels with a depth of 510 μm and a length of 57.1 mm. As a working medium HFE7000 was used. The obtained data were compared with the case of smooth microchannel. Analyzing the boiling curves, the lower overheating was observed for the case of heating surface with intensification, at significantly lower heating surface temperature. The authors suggested that the use of porous netting affects the magnification of steam bubbles and increase of their numbers. There has been no change in the pressure drop during the flow in comparison with plain channels. Jones and Garimela [6] analyzed the effect of surface roughness on the heat transfer and pressure drop in the 10 parallel microchannels section of 500 μm x 500 μm and a length of 25.4 mm, using distilled water. They found a slight effect of surface roughness on the boiling initiation point and on the value of the heat transfer coefficient for saturated boiling heat at low heat fluxes. For higher heat fluxes (over 1500 kW /m2) and the bigger surface roughness, the 2035% higher heat transfer coefficients were obtained, in comparison to the smallest surface roughness. Only for the highest surface roughness (6.7 microns) an adverse effect on pressure drop was observed. In many studies the problems of small hydraulic resistance that is also taken into consideration. Numerous studies regarding both experimental and numerical studies of convective heat transfer during single phase flow and the boiling/condensation flow [7÷13] show that there is a great demand to improve existing technologies. Issues related to the development of the design of compact plate heat exchangers can be found in [14], and optimization analyzes were carried out by Wang [10]. Lot of interest regarding microjet cooling use especially in electronic systems [8] was observed so far. Fabbri and Dhir [15] studied single-phase heat transfer using microjet arrays with three different systems of round nozzles circumferential and radial spacing of 1 mm, 2 mm and 3 mm. The diameters of the jets were in the range of from 69 to 250 microns. The authors show that the heat transfer coefficient of 40 000 W / m2K can be achieved at a flow rate lower by about one order of magnitude than in a larger diameter nozzles (for orifice diameter D=0.173mm compared to D=1mm with jet velocity v≈6 m/s and 9 m/s respectively). Womac al. [16] studied the effect of geometry and working conditions of free and submerged array of jets of FC-77 and water. They tested 2 × 2 and 3 × 3 nozzle arrays with a
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diameter of 0.513 mm and 1.02 mm. The spacing between the nozzles was between 5d and 20d. The range of Nusselt numbers has not been clearly presented, but it was found that submerged nozzles typically achieve equal or better parameters than free jets. Michna et al. [17] used nozzles placed 200 microns over a cooled surface, the distance between the nozzles was 250 micrometers, and their diameters were 54 and 112 microns. Area ratio was 0.036 and 0.16. The jets hit the surface of the heater measuring 1 mm x 1 mm. The impact of the Reynolds number and area ratio on heat transfer were studied.
Martin [18] analyzed different impinging gas jets configurations and grouped them according to the number of jets involved (single or arrays) and the geometric characteristics (round, or slot) for the different flow configurations (single jet, arrays, round nozzles, slots, etc.). Martin analyzed and rearranged the empirical fitting data equations with their ranges of validity. He found negligible effect of H/D. Li and Garimella [19] focused on the effect of Prandtl number on the local and average heat transfer coefficient in a turbulent, submerged and confined jet impingement configuration. Experiments were conducted on three different fluids water (Pr=7), FC-72 (Pr=25) and air (Pr=0.7) with varying Reynolds number (4000 to 23000), nozzle diameters (1.59 mm to 12.7 mm) and nozzle to plate distance (1 mm to 5 mm). Secondary peaks in the Nusselt Number along the radial direction away from the stagnation point were observed for all the cases. These secondary peaks were more pronounced for smaller nozzle- to- plate distances and high Reynolds Numbers and tended to diminish for higher to nozzle to plate distances. Fluids with lower Prandtl Numbers showed higher stagnation Nusselt Numbers at smaller nozzle diameters. Correlation for the average Nusselt Numbers include effects of the area weighted average of the impingement region and the walljet region. It is very important to add that similar conclusion has been founded in work by Wen and Jang [20].
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A recent review by Meola [21] proposed a new correlation for the average Nusselt number, for an array of round nozzle jets impinging on a surface, based on literature data. New correlation tries to include effects of jet forming orifice on obtained heat transfer. The flow along the plate from the geometric centre through the stagnation zone and the eventual formation of the wall jet are investigated by Lytle and Webb [22]. Authors studied air jet impingement for nozzle-plate spacing less than one nozzle diameter in the Reynolds number range 3600 < Re < 27600. Considerable heat transfer enhancement was observed due to acceleration of the impinging fluid as it escapes from the nozzle-plate gap, as well as significant increases in the turbulence level. These phenomena yield a stagnation point minimum and an inner and outer peak in the local heat transfer. Nusselt number results were correlated empirically and revealed functionally that stagnation point heat transfer coefficients increase significantly for decreasing nozzle-plate spacings. They proposed their own correlation for heat transfer coefficient in case of small nozzle-plate spacing. As a part of the article, a systematic experimental study on intensification of heat transfer in the model microjet heat exchanger consisting of a series of plates (where the surface of the middle plate is a heat transfer area). Plates were then connected with leading collectors. The result of it is a model heat exchanger, which allows the fundamental study of pressure and thermal fluid flow characteristics. Heat exchanger is based on modular elements used in authors previous work [23]. The paper presents labor that was carried out several stages. In the first part of this paper presents the construction of the test facility and the construction of the microjet test exchanger. Plates were then mounted with leading collectors. Experiments were carried out on single-phase convection heat transfer with distilled water as a working medium. Paper also presents the results of mathematic modeling of exchanger on the basis of available empirical correlations, and its comparison with the data obtained experimentally. The characteristics of heat exchanger are calculated with Wilson’s plot method. A direct comparison of the obtained thermal and hydraulic characteristics allow for verification of the literature models in the construction of the heat exchanger. 2. TEST FACILITY
Present study shows results of steady state heat transfer experiments, conducted for single phase cooling in order to obtain working fluids temperatures and heat fluxes. It consisted of the
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heat exchanger, fluid supplying system, the measuring devices, constant temperature bath and chiller. Cold working fluid was fed by a pulsation free gear pump from a supply tank. Desired fluid flow rate was obtained by means of power inverter and flow control valve. Detailed view of heat exchanger module is presented in next section. Temperature was measured at the inlets and outlets of heat exchanger by a T-type thermocouples. All thermocouples are pre-calibrated with a dry box temperature calibrator. They are connected to the National Instruments data acquisition set The signal from thermocouples was processed with the aid of the LabVIEW application. Heat is supplied by a constant temperature bath in hot water circuit. Total power input is determined by measuring volumetric flow rate and temperature rise. During tests heat exchanger was capable of dissipating up to 232W.The whole set was thermally insulated. The heat source is a laboratory grade ultra-thermostat with electric heater power of 2kW, with temperature stability of ±0.05°C. Ultra-thermostat can operate with different working fluids, i.e distilled water, water solutions of glycols and silicone oils. Thus it is possible to obtain a wide range of parameter change, and study the influence of fluid properties on present system. Cold water circulates in a second circuit with heat rejection controlled by an industrial grade chiller. Scheme of test facility is shown in Figure 1.
The pump is a magnetic gear pump company Verder VS120. The use of magnetic drive means that the device will be 100% tight so that, safe for the environment. It allows the pump to operate at a high pressure, at high temperatures, with chemically reactive media, such as glycols, saline, fluorinated agents, etc. The flow rate is measured using a Coriolis mass flow meter, the advantage of this type of measurement is a simultaneous measure of the mass and density of the pumped liquid. Heat is supplied to them through the water circulating in constant temperature bath. The total power of the heat exchanger is determined from the mass and energy balance. Measurements take place in steady state conditions, in order to exclude the heat capacity of the systems casing. The amount of heat transferred is determined during each measurement point. Pressure drop measurement is carried out at the cold water circuit using the piezoelectric smart differential pressure transmitter. Microprocessor control, enables temperature and hysteresis compensation, also it allows to provide an extended linear temporal stability. The measuring range of the transmitter is of 5 kPa to 500 kPa, and the measuring
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accuracy is 0.065%FS. Pressure at the inlet and outlet of the heat exchanger is also measured using conventional pressure transducers (measurement is thus duplicated.) At the inlet absolute pressure transducer with a measuring range of 0 to 4 bar and a precision of 0.25%FS is mounted. At the outlet gauge pressure transducer with the range 0-6 bar and accuracy of 0.5%FS is installed. This along with measured barometric pressure allows the exact determination of the parameters of the fluid in the measuring point and doubling the measured pressure drop. It is important to verify the operation of the system and capture any hardware failure. On the side of the hot fluid, the temperature at the inlet and outlet of the heat exchanger, is measured by means of thermocouples T in class 1 is also measured by means of the T-type thermocouples in 1st class, also a control gauge pressure transmitters in the range 0 to 25 bar and accuracy of 0.3%FS are installed at the inlet and outlet. As part of the thermal and flow measurement the following parameters are recorded: the hot fluid temperature at the inlet (Th’) and outlet (Th”) of the exchanger, the temperature of the cold fluid at the inlet (Tc’) and outlet (Tc”) of the exchanger, and volumetric flow rate of the two fluids. The pressure at the inlet (Ph’and Pc’) and the outlet of the heat exchanger (Ph”and Pc”). The applied power losses through conduction into the insulation and radiation to the surroundings are accurately calculated and accounted for in all tests according to the following procedure. Air side heat transfer coefficient was determined for case of natural convection, [24]. (1) The characteristic dimension d was taken as the casing insulation width. The thermodynamic properties of air were determined for ambient temperature. The influences of radiation heat transfer was omitted in calculations. The total thermal resistance was calculated as: (2) where the thermal conductivity of insulation is i=0.03 W/m-K. Finally the total loss was calculated as: (3) In all cases the total heat loses were smaller than 5% of transferred heat. In order to determine the reliability of the experimental results, an uncertainty analysis was conducted on all measured quantities as well as the quantities calculated from the measurement results. Uncertainties were estimated according to the standard procedures described by NIST
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[25]. Overall, the uncertainty in the calculated Nusselt number is lower than 30 %. Uncertainties of the other calculated variables, are shown in Table 1.
3. HEAT EXCHANGER DESIGN The research object is a microjet heat exchanger, recuperator type. It’s essential core is a series of plates. Impinging jets are created by introducing plates with four nozzles of 400 and 600 microns in diameter. The nozzles were created by drilling 1mm thick plate. These plates are separated by spacers/gaskets made of PTFE. Microjet geometry can be varied by exchanging the nozzle plates and spacers of heat exchanger. Heat exchange between the working fluids is performed through 1 mm thick plate made of the aluminum alloy EN AW-1050A, with a heat exchange surface 4 cm2. Structural details and a description of the exchanger are shown in fig 2 and 3.
Figure 3 presents heat exchanger before screwing. Because the compression of spacers and membranes may cause some distortion in the collector (made with PMA) to prevent leakage between the channels of the collector seal with high temperature silicone compound was applied.
During experiment gathered data for two geometries with varying nozzle diameter were carried out, i.e. 4x0.4mm and 4x0.6mm. Figure 4 presents heat exchangers hydraulic characteristics for selected geometries for cold water flow. As expected, pressure drop of 4x0.6mm geometry is smaller, thus allow to pass larger flow rates of fluid.
4. Experimental data reduction
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As mentioned earlier experimental rig build in Gdansk university of Technology in Department of Energy and Industrial Apparatus, allows to gather data regarding convective heat transfer between two working fluids. Wilsons plot method [26] is a graphical way of calculating HTC of given working fluid , based on total heat transfer in heat exchanger for varying fluid flow rate.
Flow arrangement in tested heat exchanger, is presented on figure 5. Fluid microjets impinge the heat exchangers membrane from both sides. Thus heat exchange surface is in fact the wetted surface of membrane i.e. 4cm2. As shown in figure 5A flow arrangement is rather complicated, but if wall jet region is to be taken into account, it has evidently a co-current pattern (figure 5B). If we also assume constant heat flux on heat exchange surface, thus logarithmic mean temperature difference can be used as an acting temperature gradient between two fluids. It can be written as: T h ' T c ' T h " T c "
T
ln
Th ' Tc '
Th "Tc "
(4)
Than total amount of heat transferred can be written as: Q kA T
(5)
Knowing the fact that in tested heat exchanger flow pattern is identical thus heat transfer surface is identical for both fluids (fig 5). Thus it allows us to write the overall heat transfer coefficient k simply as : 1
k
1
c
1
1
h
(6)
Heat transfer correlations usually are presented in a dimensionless Nusselt number and are formed based on Dittus-Boelter [27] correlation: Nu C 0 Re
n
Pr
m
(7)
where C0, n, m are experimental correlation factors, and Nusselt, Reynolds and Prandtl numbers are described as: Nu
Re
Pr
D
,
VD S D c p
,
.
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After rearranging eq.(7) takes form: Vd C 0 S D
n
c p
m
D
(8)
For given flow geometry and assuming constant fluid properties in given temperature range, eq.(8) can be simplified to : C 1V
n
(9)
Where C1 is a constant and
V
is fluids volumetric flow rate. Description of heat transfer
coefficient of a cold fluid by eq.(9), with maintaining constant flow parameters on hot circuit side, can be written by rearranged eq.(6): 1 k
a n Vc
where
b
a 1
(10)
Cc
,
b
1 k
1
2
.
Therefore the heat transfer coefficient is a linear function of volumetric flow rate of cold fluid, where coefficient a is functions gradient and b is an ordinate as depicted on figure 6.
Based on experimental data and given data reduction procedure it is possible to calculate heat transfer coefficient on hot fluid side. The n parameter to which flow rate is raised, usually equals to 0.8, but best results are given for experimental fit of this coefficient. The value of b ordinate is calculated by extrapolation of experimental data to the vertical axis, which corresponds to infinite heat transfer coefficient of cold fluid. With neglible low thermal resistance of a membrane b is a HTC of hot fluid.
Experimental results
In tested heat exchanger, transferred heat can be calculated based on temperature raise of flowing medium both for hot and cold side as written in eq. (11) and (12). Q c m c c pc T c
(11)
Q h m h c ph T h
(12)
Based on calculated heat flux, total heat transfer coefficient is calculated from eq. (5). Due to minor loses heat flux values calculated by eq. (11) and (12) differ. Difference was typically less than 2%, after accommodating heat loses to ambient calculated with eq. (1-3). For further
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calculations heat absorbed by cold medium (11) was taken into account. The heat exchanger was capable of exchanging up to 800W of thermal energy at LMTD of 60 K. Figures 7 and 8 present experimental data series for calculating HTC with Wilsons plot method, for constant cold fluid velocity, and 14.5oC supply temperature. As can be expected higher velocities result in lower thermal resistance, corresponding to total heat transfer coefficient of k=14 kW/m2K for Re=2290 and k=8.5 kW/m2K for Re=1150. Figure 9 presents linear regression values for experimental series grouped in constant cold fluid velocities. The resulting heat transfer coefficient of cold fluid from experimental data was calculated by eq. (6). The heat transfer coefficient calculations by Wilson’s method were conducted for the plate thickness of 1 mm. The plate material (the aluminum alloy) has the thermal conductivity λ equal to 207 W/mK. Similarly,
figures 10 and 11 present experimental data series for calculating HTC with
Wilsons plot method, for constant hot fluid velocity. Because in general, inlet fluid parameters and the nozzle diameter is assumed as characteristic length and fluid properties in Reynolds number, thus despite constant flow rate Reynolds numbers can vary significantly with hot water supply temperature. Experimental data were collected for hot water was supply for three constant temperature levels i.e. 45, 62 and 82oC. As in in previous series, higher velocities result in lower thermal resistance, corresponding to total heat transfer coefficient of k=20 kW/m2K for v=4.5m/s and k=12.8 kW/m2K for v=2.2m/s. Figure 12 presents linear regression values for experimental series grouped in constant hot fluid velocities.
5. Impinging jets heat transfer correlations Values of heat transfer coefficient are crucial in calculations of heat exchanger dimensions. In order to validate the applicability of experimental correlations to design and build microjet heat exchangers experimental results were compared to literature correlations for impinging jets heat transfer. The heat transfer with impinging jets depends on many factors, which are usually grouped into two main categories of fluid properties and geometric characteristics. The fluid properties include both thermal and dynamic characteristics, which can be conveniently expressed with the Prandtl, Pr, and the Reynolds, Re, numbers. The geometric parameters include the nozzle geometry, diameter D, nozzle-to-nozzle spacing, and nozzle to surface distance, H. Generally,
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the dimensionless quantities H/D, and d/D are considered. In general, the nozzle diameter is assumed as characteristic length in Nusselt and Reynolds numbers. Table 2 presents the correlations developed for microjet cooling based on a vast number of experimental data.
Direct comparison of experimentally obtained values of HTC in form of dimensionless Nusselt numbers is presented on figures 13 and 14 We need to observe that given literature correlations from table 2 are developed for average heat transfer rate on test surface. As can be clearly seen experimentally obtained values of heat transfer are lower than predictions. A very large discrepancies between prediction given in literature are visible. A best consistency is obtained for Lytle and Webb correlation [22], but still obtained results differ greatly from predictions. Unfortunately the difference between predictions and experimental data is higher for nozzle diameter of 0.4mm as can be seen on figure 14. Overall the increase of HTC with higher liquid jet velocities, gives a similar trend as their predictions. Difference may be attributed to different setup of outlet manifold in tested heat exchanger, thus different flow pattern than in specified test facilities. Which indicates that flow arrangement has significant influence on obtained results, and that given correlations are limited in validity to specific working fluids and ranges of operating parameters for the data upon which these models are based. Due to large differences between experimental and predicted data, depicted in table 3 and calculated as:
Nu
eq
Nu
Nu
exp
100 %
(13)
exp
Authors proposed own empirical correlation based on similarity theory [23] The experimentally collected heat transfer coefficient was approximated using the multiple regression method to yield the following relation:
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Nu 5 . 55 Re
0 . 65
Pr
0 .4
D d
2 .3
H d
1 .4
(14)
The developed correlation has a simple form, dependent only of Reynolds number (-) and diameter of the nozzle (expressed in m) ratio to equivalent wetted surface diameter (m). The Prandtl number is for the sake of capturing the change of specific properties of cooling fluid. Comparisons against authors own experimental data are presented in fig. 15. Experimental values of heat transfer coefficient were determined directly from Wilsons plot method, presented in the previous section.
6. Conclusions A prototype heat exchanger was built and tested. It incorporates very effective method of enhancing the heat transfer by means of impinging microjets. Modular configuration allows to carry out a series of tests with various working fluids, for both single phase and convective heat transfer and two phase boiling/condensation flow. The research allows the determination of the heat exchanger thermal performance, and to determine the usefulness of the intensification of heat exchange method in the refrigeration and air conditioning systems. Tested design has a great number of potential applications in a variety of machines and devices.
The Wilson plot method was successfully applied to determine the heat transfer coefficients in the laminar and transition flow regimes of a liquid-to-liquid heat exchanger. The heat exchanger is capable of exchanging 800W of thermal energy at LMTD of 60 K. The obtained overall heat transfer coefficient reaches over 10000 W/m2K.
Average Nu predictions of the Lytle and Webb [22] correlation were in best agreement with the experimentally determined average Nusselt numbers for Reynolds numbers in the range 700 < Re < 3000. Better correlation of the data was produced by Eq. (14). In the whole tested flow range, Nusselt numbers were not well correlated by any of the correlations from the literature and the experimentally determined Nusselt numbers were considerably lower than expected. In authors opinion the reason for this was due to narrow range of given literature correlations applicability. These discrepancies may be due to variations in the jet velocity along the flow path on both sides of the heat exchanger. New correlation was suggested, predicting the experimental results within 30%.
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The heat exchanger design will be further pursuit in the optimization with respect to the spacing and quantity of nozzles to reduce the pressure drop and increase heat transfer rates.
ACKNOWLEDGMENTS The work presented in the paper was partially funded by statuary activity of faculty of Mechanical Engineering of Gdansk University of Technology NOMENCLATURE A
surface of heat transfer [m2]
a
coefficient, function gradient []
Ar
area ratio []
b
ordinate []
C0
experimental factor, []
cp
specific heat, [J/kgK]
d/D
diameter [m]
g
gravitational acceleration [m/s2]
H
nozzle to impinged surface distance [m]
k
total heat transfer [W/m2K]
L
channel length [m]
LMTD logarithmic mean temperature difference [K] m
experimental factor, [] mass flow of fluid, [kg/s]
n
experimental factor []
Nu
Nusselt number []
P
pressure [Pa]
Pr
Prandtl number []
P
pressure drop [Pa]
Re
Reynolds number []
Ri
thermal resistance [mK/W]
T
temperature [K]
U
uncertainity [%]
v
velocity [m/s] volumetric flow rate [m3/s]
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q
heat flux [W/m2] heat flow [W]
Greek symbols heat transfer coefficient [W/m2K] thickness of membrane [m]
density [kg/m3]
l
liquid density [kg/m3]
λ
thermal conductivity [W/mK]
μ
dynamic viscosity [Pas]
kinematic viscosity [m2/s]
Superscripts air
air
c
cold
eq
equation
exp
experimental
h
hot
w
wall
LITERATURE [1] Gupta A., Uniyal M.: Review of heat transfer augmentation through different passive intensifier methods. IOSR Journal of Mechanical and Civil Engineering, vol. 1, pp. 14-21, 2012. [2] Webb R. L.: Principles of enhanced heat transfer. Wiley-Interscience, New York, 1994. [3] Stone. K.M.: Review of literature on heat transfer enhancement in compact heat exchangers. Air Conditioning and Refrigeration Center Technical Reports, 1996. [4] Sun Y., Zhang L., Xu H., Zhong X., Flow boiling enhancement of FC-72 from microporous surfaces, Experimental Thermal and Fluid Science, vol. 35 (2011), 1418-1426 [5] Wang H., Peterson R.B., Enhanced boiling heat transfer in parallel microchannels with diffusion brazed wire mesh, IEEE Transactions on Components and Packing Technology, vol. 33 (2010), 784-793 [6] Jones, B.J., McHale, J.P.&Garimella, S.V., The Influence of Surface Roughness on Nucleate Pool Boiling Heat Transfer, Journal of Heat Transfer, 131, 2009 [7] Dovic D., Palm B., Svaic S.: Generalized correlations for predicting heat transfer and pressure drop in plate heat exchanger channels of arbitrary geometry. International Journal of Heat and Mass Transfer, vol. 52, pp. 4553–4563, 2009.
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[8] Galeazzo F.C.C., Tadini C.C., Gut J.A.W.: The effect of flow arrangement on the pressure drop of plate heat exchangers. Chemical Engineering Science, vol. 63, pp. 5386-5393, 2008. [9] Kanaris A.G., Mouza A.A., Paras S.V.: Optimal design of a plate heat exchanger with undulated surfaces. International Journal of Thermal Sciences, vol. 48, pp. 1184–1195, 2009. [10] Wang L., Sunden B.: Optimal design of plate heat exchangers with and without pressure drop specifications. Applied Thermal Engineering, vol. 23, pp. 295–311, 2003. [11] Wang E.N., Zhang L., Goodson K.E., Kenny T.W., Micromachined jets for liquid impingement cooling of VLSI chips, J. Microelectromech. Syst. 2004. [12] Wolf D.H., Incropera F.P., and Viskanta R., Local jet impingement boiling heat transfer, Int. J. Heat Mass Transfer,1996 [13] Garimella S.V., Rice R.A., Confined and submerged liquid jet impingement heattransfer, J. Heat Transfer,1995 [14] Muszyński T., Andrzejczyk R.: Zastosowanie korelacji opisujących wymianę ciepła w obszarze pęczków mikrostrug do projektowania kompaktowych wymienników ciepła: cz.1. Budowa modelowego wymiennika ciepła i jego charakterystyka// Pomiary Automatyka Kontrola. -Vol. 60., nr. 11 (2014), s.1021-1024 [15] Fabbri, M; Dhir, V. K. Optimized heat transfer for high power electronic cooling using arrays of microjets. Journal of heat transfer, 2005, 127.7: 760-769. Womac, D. J., Incropera, F. P., and Ramadhyani, S., 1994, “Correlating Equations for [16] Impingement Cooling of Small Heat Sources With Multiple Circular Liquid Jets,” ASME J. Heat Transfer, 1162, pp. 482–486. [17] Gregory J. Michna, Eric A. Browne, Yoav Peles, Michael K. Jensen, Single-Phase Microscale Jet Stagnation Point Heat Transfer, Journal of Heat Transfer, NOVEMBER 2009, Vol. 131, [18] Martin, H. Heat and Mass Transfer between Impinging Gas Jets and Solid Surfaces (1977) Advances in Heat Transfer, 13 (C), pp. 1-60. [19] Li C-Y, Garimella S. V. Prandtl-number effects and generalized correlations for confined and submerged jet impingement International Journal of Heat and Mass Transfer, Volume 44, Issue 18, September 2001, Pages 3471-3480 [20] Wen MY, Jang KJ (2003) An impingement cooling on a flat surface by using circular jet with longitudinal swirling strips. Int J Heat Mass Transf 46:4657–4667 [21] Meola C. A New Correlation of Nusselt Number for Impinging Jets Heat Transfer Engineering, 30(3):221–228, 2009 [22] D. Lytle, B.W. Webb, Air jet impingement heat transfer at low nozzle–plate spacings, Int. J. Heat Mass Transfer 37 (1994) 1687–1697. [23] T. Muszynski, R. Andrzejczyk, Heat transfer characteristics of hybrid microjet microchannel cooling module, Applied Thermal Engineering, Volume 93, pp 1360-1366, 2016 [24] Florschuetz, L. W., Truman, C. R., and Metzger, D. E., 1981, “Streamwise Flow and Heat Transfer Distributions for Jet Array Impingement With Cross- flow,” ASME J. Heat Transfer, 1032, pp. 111–134
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[25] B.N. Taylor, C.E. Kuyatt Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results National Institute of Standards and Technology Technical Note 1297 (1994) [26] John W. Rose, Heat-transfer coefficients, Wilson plots and accuracy of thermal measurements, Experimental Thermal and Fluid Science 28 (2004) 77–86, [27] Dittus, F.W., Boelter, L.M.K., 1930. Publications on Engineering, vol. 2. University of California, Berkeley, s. 443.
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Fig.1. Schematic of a test facility: 1- heat exchanger, 2 - Corriolis mass flow meter, 3 pulsation free gear pump, 4 - filter, 5 - inspection glass, 6 - fluid tank , 7 - heater, 8 - chiller
Fig. 2. View on microjet heat exchanger
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Fig. 3. Schematic of microjet HX
160 4x0.6mm 4x0.4mm
p [kPa]
120
80
40
0 0
500
1000
1500
Re [-]
2000
2500
Fig. 4. Hydraulic Characteristics of tested heat exchanger
Page 19 of 25
Fig. 5. A) Possible flow pattern in tested heat exchanger, B) Flow pattern and temperature distribution of impinging jet
Fig. 6. Graphical scheme for calculating heat transfer coefficient by Wilsons plot method
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
5.0x10-5 0.0 0
104
2x104
wh [(m /s) ] n
3
3x104
4x104
n
Fig. 7. Graphical scheme for calculating heat transfer coefficient by Wilsons plot method, for case of cold fluid jet velocity of v=4.5m/s corresponding to Re=2290
Page 20 of 25
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
5.0x10-5 0.0 0
104
2x104
whn[(m3/s)n]
3x104
4x104
Fig. 8. Graphical scheme for calculating heat transfer coefficient by Wilsons plot method, for case of cold fluid jet velocity of v=1.6m/s corresponding to Re=1150
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
Linear fit Re=840 Linear fit Re=1150 Linear fit Re=1660 Linear fit Re=1910 Linear fit Re=2110 Linear fit Re=2290
5.0x10-5 0.0 0
104
2x104
whn[(m3/s)n]
3x104
4x104
Fig. 9 Linear regression of experimental data for calculating heat transfer coefficient by Wilsons plot method, for varying hot and constant cold fluid jet velocity
Page 21 of 25
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
5.0x10-5 0.0 0
104
2x104
wc [(m /s) ] n
3
3x104
4x104
n
Fig. 10. Graphical scheme for calculating heat transfer coefficient by Wilsons plot method, for case of cold fluid jet velocity of v=2.2m/s corresponding to Re=2200-3800
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
5.0x10-5 0.0 0
104
2x104
wc [(m /s) ] n
3
3x104
4x104
n
Fig. 11. Graphical scheme for calculating heat transfer coefficient by Wilsons plot method, for case of cold fluid jet velocity of v=4.5m/s corresponding to Re=4400-7600
Page 22 of 25
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
Linear fit v=4.5m/s Linear fit v=4.2m/s Linear fit v=3.8m/s Linear fit v=3.2m/s Linear fit v=2.2m/s Linear fit v=1.6m/s
5.0x10-5 0.0 0
104
2x104
wc [(m /s) ] n
3
3x104
4x104
n
Fig. 12 Linear regression of experimental data for calculating heat transfer coefficient by Wilsons plot method, for varying cold and constant hot fluid jet velocity
400
Exp. Meola 2009 Wen i Jang 2003 Li i Garimella 2001 Lytle i Web 1994 Womac 1993 Martin 1977
Nu [-]
300
200
100
0 0
500
1000
1500
Re [-]
2000
2500
Fig. 13 Comparison between predicted and experimental average Nusselt numbers for 4x0.4mm geometry.
Page 23 of 25
80
Meola 2009 Wen & Jang 2003 Li & Garimella 2001
Lytle & Web 1994 Womac 1993 Martin 1977
Nu [-]
60
40
20
0 0
500
1000
1500
Re [-]
2000
2500
Fig. 14 Comparison between predicted and experimental average Nusselt numbers for 4x0.6mm geometry.
25
+30% 4x0.6mm 4x0.4mm
Nueq [-]
20
15
-30%
10
5
0 0
5
10
15
Nuexp [-]
20
25
Fig. 15 Comparison between experimental and predited values of nusselt number based on eq. (14)
Page 24 of 25
Table 1. Measurement uncertainties. Variable
Uncertainty (%)
Accuracy
0.5%
±0.5 g/s
ΔT
2.1%
±1.44 K
vjet
1.41%
±0.02 m/s
1.0%
±4 kW/m2
α
2.5%
±0.05 kW/m2K
Re
2.5%
±18
Table 2. Literature correlations for impinging jets heat transfer Source
Correlation
Exp. range
Martin [18]
Nu 2 Re
Womac [16]
Re D 1 200
0 , 55
0 ,5 D
Nu 0 , 509 Re
L*
0 ,5
Pr
D
0 ,5
1 1 ,1 D D R R 1 0 ,1 H 6 D D R
A r , w 0 , 0363 Re
0,4
2 L / 2 1 .9 D L / 2 1 .9 D
0 ,8 L*
D L*
1
Pr
Re
2000 0 , 42
A r , w Pr
D
400000
2 ,5 R / D 7 ,5 2 H / D 12
water 0,4
Re
d
50000
1, 65 d 6 , 55 mm
3 , 5 H / D 10
water, FC77
2
Li & Garimella [19] Wen & Jang [20] Lytle & Web [22]
Nu 0 ,160 Re
0 , 695
Nu 0 , 442 Re
Nu 0 , 726 Re
Pr
D
0 , 696 D
0 , 53 D
Pr
0 , 68 D
0 , 56
CF
1/3
h D
Meola [21]
Nu 0 , 3 Re
0,4
h D h D
0 , 11
0 , 20
d D
0 , 11
d /2 D
Re D 23000
1, 59 D 12 , 5 mm 1 H /D 5 0 , 41
500 Re
D
,air, water, FC77
27000
3 H / D 16
,
air 3600
0 , 191
D H
4000
Re
D
27600
0 . 1 H / D 10
,
air 250 Re
0 ,3 0 , 15
Ar
Pr
0 , 42
D
98000
0 . 39 D 50 mm
,
air, water
Table 3 – Relative error between predicted and experimental average Nusselt numbers Correlation Martin [18] Womac [16] Lytle& Web [19] Li & Garimella [20] Wen & Jang [22] Meola [21]
Min
Max
357% 770% 94% 456%
998% 2200% 348% 1178%
645% 221%
1612% 641%
Page 25 of 25
S1359-4311(16)30070-9 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.120 ATE 7680
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
12-11-2015 28-1-2016
Please cite this article as: Tomasz Muszynski, Rafal Andrzejczyk, Applicability of arrays of microjets heat transfer correlations to design compact heat exchangers, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.120. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Applicability of arrays of microjets heat transfer correlations to design compact heat exchangers Tomasz Muszynski1 , Rafal Andrzejczyk1 1: Gdansk University of Technology, Faculty of Mechanical Engineering, Department of Energy and Industrial Apparatus Narutowicza 11/12, 80-233 Gdansk, Poland E-mail: [email protected], [email protected] Highlights
A prototype heat exchanger was built and tested.
The obtained overall heat transfer coefficient reaches over 10000 W/m2K.
New experimental correlation was suggested.
Graphical Abstract
Abstract
The article presents experimental studies on a compact heat exchanger with heat transfer intensification by means of impinging microjets. The pursuit to provide high performance of heat exchangers is a response to the demand both in economics and in the universal tendency to miniaturization of industrial equipment. This paper presents the design and tests of a prototype, microjet heat exchanger. The modular design of the heat exchanger allows to change its geometrical dimensions, as well as changing the heat exchange membrane material. The study of heat transfer in water-water flow, allows to determine the heat transfer efficiency, the characteristics of heat transfer, and the heat transfer coefficient values. Data were collected for the pressure drops in heat exchanger not exceeding 15 kPa, i.e. such as in conventional heat
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exchangers. Hydraulic characteristics of a model heat exchanger were obtained. Experimental values of heat transfer for jet impingement were calculated by means of Wilson’s plot method. Obtained values of heat transfer coefficient were compared with literature correlations. Authors also proposed their own empirical correlation for jet impingement heat transfer coefficient. Keywords: microjets, heat exchangers, heat transfer intensification, Wilson’s plot method, theory of similarity,
1. INTRODUCTION
Achieving the technological control on the micoscale heat and energetic installations and making them high- efficient is the challenge of 21st century. This direction of development has been delineated by the general trend towards miniaturization and by the expected widespread. The main elements of such systems must be highly compact and highly efficient heat exchangers. Regarding to that fact one of the technical problems associated with the heat removal in refrigeration and air-conditioning is an installation of high-performance heat exchangers i.e. evaporator, condenser or regenerative heat exchanger. Striving to ensure high performance of these elements is today a source of universal trend both to the miniaturization of these devices for both industrial and domestic applications, while maintaining the highest possible size to thermal energy ratio. As is well known, in recuperators heat transfer coefficient have decisive influence their efficiency. Overall heat transfer coefficient depends mainly on the lower value of HTC from working media. It is therefore most significant to improve the heat transfer with special attention on the side of the medium with lower heat transfer coefficient. Overall methods to intensify the heat exchange in channels using passive techniques have been presented in the work of Gupta [1] and Webb [2]. Stone [3] worked on intensifiction of heat transfer in compact heat exchangers. Sun et al. [ 4] studied the effect of porous coatings on heat transfer intensification in the channel. The horizontal rectangular channels were tested with hydraulic diameters of 0.49 mm, 0.93 mm and 1.26 mm. Only the bottom channel wall had developed surface. Three types of microcoatings of the average grain diameter of 20 μm, 50 μm and 120 μm, and the working fluid FC-72 were used. There was a significant increase in heat transfer coefficient, when
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compared to a smooth surface. For the optimal variant of coverage, the wall overheating, necessary for the boiling initiation, decreased by 7.4 K and the temperature of the heating surface by 10.3 K. The influence of the channel size was analyzed and the conclusion was made that the size reduction leads to a reduction in the critical heat flux. Wang and Peterson [5] used small metallic porous nettings as one of the walls of four parallel microchannels with a depth of 510 μm and a length of 57.1 mm. As a working medium HFE7000 was used. The obtained data were compared with the case of smooth microchannel. Analyzing the boiling curves, the lower overheating was observed for the case of heating surface with intensification, at significantly lower heating surface temperature. The authors suggested that the use of porous netting affects the magnification of steam bubbles and increase of their numbers. There has been no change in the pressure drop during the flow in comparison with plain channels. Jones and Garimela [6] analyzed the effect of surface roughness on the heat transfer and pressure drop in the 10 parallel microchannels section of 500 μm x 500 μm and a length of 25.4 mm, using distilled water. They found a slight effect of surface roughness on the boiling initiation point and on the value of the heat transfer coefficient for saturated boiling heat at low heat fluxes. For higher heat fluxes (over 1500 kW /m2) and the bigger surface roughness, the 2035% higher heat transfer coefficients were obtained, in comparison to the smallest surface roughness. Only for the highest surface roughness (6.7 microns) an adverse effect on pressure drop was observed. In many studies the problems of small hydraulic resistance that is also taken into consideration. Numerous studies regarding both experimental and numerical studies of convective heat transfer during single phase flow and the boiling/condensation flow [7÷13] show that there is a great demand to improve existing technologies. Issues related to the development of the design of compact plate heat exchangers can be found in [14], and optimization analyzes were carried out by Wang [10]. Lot of interest regarding microjet cooling use especially in electronic systems [8] was observed so far. Fabbri and Dhir [15] studied single-phase heat transfer using microjet arrays with three different systems of round nozzles circumferential and radial spacing of 1 mm, 2 mm and 3 mm. The diameters of the jets were in the range of from 69 to 250 microns. The authors show that the heat transfer coefficient of 40 000 W / m2K can be achieved at a flow rate lower by about one order of magnitude than in a larger diameter nozzles (for orifice diameter D=0.173mm compared to D=1mm with jet velocity v≈6 m/s and 9 m/s respectively). Womac al. [16] studied the effect of geometry and working conditions of free and submerged array of jets of FC-77 and water. They tested 2 × 2 and 3 × 3 nozzle arrays with a
Page 3 of 25
diameter of 0.513 mm and 1.02 mm. The spacing between the nozzles was between 5d and 20d. The range of Nusselt numbers has not been clearly presented, but it was found that submerged nozzles typically achieve equal or better parameters than free jets. Michna et al. [17] used nozzles placed 200 microns over a cooled surface, the distance between the nozzles was 250 micrometers, and their diameters were 54 and 112 microns. Area ratio was 0.036 and 0.16. The jets hit the surface of the heater measuring 1 mm x 1 mm. The impact of the Reynolds number and area ratio on heat transfer were studied.
Martin [18] analyzed different impinging gas jets configurations and grouped them according to the number of jets involved (single or arrays) and the geometric characteristics (round, or slot) for the different flow configurations (single jet, arrays, round nozzles, slots, etc.). Martin analyzed and rearranged the empirical fitting data equations with their ranges of validity. He found negligible effect of H/D. Li and Garimella [19] focused on the effect of Prandtl number on the local and average heat transfer coefficient in a turbulent, submerged and confined jet impingement configuration. Experiments were conducted on three different fluids water (Pr=7), FC-72 (Pr=25) and air (Pr=0.7) with varying Reynolds number (4000 to 23000), nozzle diameters (1.59 mm to 12.7 mm) and nozzle to plate distance (1 mm to 5 mm). Secondary peaks in the Nusselt Number along the radial direction away from the stagnation point were observed for all the cases. These secondary peaks were more pronounced for smaller nozzle- to- plate distances and high Reynolds Numbers and tended to diminish for higher to nozzle to plate distances. Fluids with lower Prandtl Numbers showed higher stagnation Nusselt Numbers at smaller nozzle diameters. Correlation for the average Nusselt Numbers include effects of the area weighted average of the impingement region and the walljet region. It is very important to add that similar conclusion has been founded in work by Wen and Jang [20].
Page 4 of 25
A recent review by Meola [21] proposed a new correlation for the average Nusselt number, for an array of round nozzle jets impinging on a surface, based on literature data. New correlation tries to include effects of jet forming orifice on obtained heat transfer. The flow along the plate from the geometric centre through the stagnation zone and the eventual formation of the wall jet are investigated by Lytle and Webb [22]. Authors studied air jet impingement for nozzle-plate spacing less than one nozzle diameter in the Reynolds number range 3600 < Re < 27600. Considerable heat transfer enhancement was observed due to acceleration of the impinging fluid as it escapes from the nozzle-plate gap, as well as significant increases in the turbulence level. These phenomena yield a stagnation point minimum and an inner and outer peak in the local heat transfer. Nusselt number results were correlated empirically and revealed functionally that stagnation point heat transfer coefficients increase significantly for decreasing nozzle-plate spacings. They proposed their own correlation for heat transfer coefficient in case of small nozzle-plate spacing. As a part of the article, a systematic experimental study on intensification of heat transfer in the model microjet heat exchanger consisting of a series of plates (where the surface of the middle plate is a heat transfer area). Plates were then connected with leading collectors. The result of it is a model heat exchanger, which allows the fundamental study of pressure and thermal fluid flow characteristics. Heat exchanger is based on modular elements used in authors previous work [23]. The paper presents labor that was carried out several stages. In the first part of this paper presents the construction of the test facility and the construction of the microjet test exchanger. Plates were then mounted with leading collectors. Experiments were carried out on single-phase convection heat transfer with distilled water as a working medium. Paper also presents the results of mathematic modeling of exchanger on the basis of available empirical correlations, and its comparison with the data obtained experimentally. The characteristics of heat exchanger are calculated with Wilson’s plot method. A direct comparison of the obtained thermal and hydraulic characteristics allow for verification of the literature models in the construction of the heat exchanger. 2. TEST FACILITY
Present study shows results of steady state heat transfer experiments, conducted for single phase cooling in order to obtain working fluids temperatures and heat fluxes. It consisted of the
Page 5 of 25
heat exchanger, fluid supplying system, the measuring devices, constant temperature bath and chiller. Cold working fluid was fed by a pulsation free gear pump from a supply tank. Desired fluid flow rate was obtained by means of power inverter and flow control valve. Detailed view of heat exchanger module is presented in next section. Temperature was measured at the inlets and outlets of heat exchanger by a T-type thermocouples. All thermocouples are pre-calibrated with a dry box temperature calibrator. They are connected to the National Instruments data acquisition set The signal from thermocouples was processed with the aid of the LabVIEW application. Heat is supplied by a constant temperature bath in hot water circuit. Total power input is determined by measuring volumetric flow rate and temperature rise. During tests heat exchanger was capable of dissipating up to 232W.The whole set was thermally insulated. The heat source is a laboratory grade ultra-thermostat with electric heater power of 2kW, with temperature stability of ±0.05°C. Ultra-thermostat can operate with different working fluids, i.e distilled water, water solutions of glycols and silicone oils. Thus it is possible to obtain a wide range of parameter change, and study the influence of fluid properties on present system. Cold water circulates in a second circuit with heat rejection controlled by an industrial grade chiller. Scheme of test facility is shown in Figure 1.
The pump is a magnetic gear pump company Verder VS120. The use of magnetic drive means that the device will be 100% tight so that, safe for the environment. It allows the pump to operate at a high pressure, at high temperatures, with chemically reactive media, such as glycols, saline, fluorinated agents, etc. The flow rate is measured using a Coriolis mass flow meter, the advantage of this type of measurement is a simultaneous measure of the mass and density of the pumped liquid. Heat is supplied to them through the water circulating in constant temperature bath. The total power of the heat exchanger is determined from the mass and energy balance. Measurements take place in steady state conditions, in order to exclude the heat capacity of the systems casing. The amount of heat transferred is determined during each measurement point. Pressure drop measurement is carried out at the cold water circuit using the piezoelectric smart differential pressure transmitter. Microprocessor control, enables temperature and hysteresis compensation, also it allows to provide an extended linear temporal stability. The measuring range of the transmitter is of 5 kPa to 500 kPa, and the measuring
Page 6 of 25
accuracy is 0.065%FS. Pressure at the inlet and outlet of the heat exchanger is also measured using conventional pressure transducers (measurement is thus duplicated.) At the inlet absolute pressure transducer with a measuring range of 0 to 4 bar and a precision of 0.25%FS is mounted. At the outlet gauge pressure transducer with the range 0-6 bar and accuracy of 0.5%FS is installed. This along with measured barometric pressure allows the exact determination of the parameters of the fluid in the measuring point and doubling the measured pressure drop. It is important to verify the operation of the system and capture any hardware failure. On the side of the hot fluid, the temperature at the inlet and outlet of the heat exchanger, is measured by means of thermocouples T in class 1 is also measured by means of the T-type thermocouples in 1st class, also a control gauge pressure transmitters in the range 0 to 25 bar and accuracy of 0.3%FS are installed at the inlet and outlet. As part of the thermal and flow measurement the following parameters are recorded: the hot fluid temperature at the inlet (Th’) and outlet (Th”) of the exchanger, the temperature of the cold fluid at the inlet (Tc’) and outlet (Tc”) of the exchanger, and volumetric flow rate of the two fluids. The pressure at the inlet (Ph’and Pc’) and the outlet of the heat exchanger (Ph”and Pc”). The applied power losses through conduction into the insulation and radiation to the surroundings are accurately calculated and accounted for in all tests according to the following procedure. Air side heat transfer coefficient was determined for case of natural convection, [24]. (1) The characteristic dimension d was taken as the casing insulation width. The thermodynamic properties of air were determined for ambient temperature. The influences of radiation heat transfer was omitted in calculations. The total thermal resistance was calculated as: (2) where the thermal conductivity of insulation is i=0.03 W/m-K. Finally the total loss was calculated as: (3) In all cases the total heat loses were smaller than 5% of transferred heat. In order to determine the reliability of the experimental results, an uncertainty analysis was conducted on all measured quantities as well as the quantities calculated from the measurement results. Uncertainties were estimated according to the standard procedures described by NIST
Page 7 of 25
[25]. Overall, the uncertainty in the calculated Nusselt number is lower than 30 %. Uncertainties of the other calculated variables, are shown in Table 1.
3. HEAT EXCHANGER DESIGN The research object is a microjet heat exchanger, recuperator type. It’s essential core is a series of plates. Impinging jets are created by introducing plates with four nozzles of 400 and 600 microns in diameter. The nozzles were created by drilling 1mm thick plate. These plates are separated by spacers/gaskets made of PTFE. Microjet geometry can be varied by exchanging the nozzle plates and spacers of heat exchanger. Heat exchange between the working fluids is performed through 1 mm thick plate made of the aluminum alloy EN AW-1050A, with a heat exchange surface 4 cm2. Structural details and a description of the exchanger are shown in fig 2 and 3.
Figure 3 presents heat exchanger before screwing. Because the compression of spacers and membranes may cause some distortion in the collector (made with PMA) to prevent leakage between the channels of the collector seal with high temperature silicone compound was applied.
During experiment gathered data for two geometries with varying nozzle diameter were carried out, i.e. 4x0.4mm and 4x0.6mm. Figure 4 presents heat exchangers hydraulic characteristics for selected geometries for cold water flow. As expected, pressure drop of 4x0.6mm geometry is smaller, thus allow to pass larger flow rates of fluid.
4. Experimental data reduction
Page 8 of 25
As mentioned earlier experimental rig build in Gdansk university of Technology in Department of Energy and Industrial Apparatus, allows to gather data regarding convective heat transfer between two working fluids. Wilsons plot method [26] is a graphical way of calculating HTC of given working fluid , based on total heat transfer in heat exchanger for varying fluid flow rate.
Flow arrangement in tested heat exchanger, is presented on figure 5. Fluid microjets impinge the heat exchangers membrane from both sides. Thus heat exchange surface is in fact the wetted surface of membrane i.e. 4cm2. As shown in figure 5A flow arrangement is rather complicated, but if wall jet region is to be taken into account, it has evidently a co-current pattern (figure 5B). If we also assume constant heat flux on heat exchange surface, thus logarithmic mean temperature difference can be used as an acting temperature gradient between two fluids. It can be written as: T h ' T c ' T h " T c "
T
ln
Th ' Tc '
Th "Tc "
(4)
Than total amount of heat transferred can be written as: Q kA T
(5)
Knowing the fact that in tested heat exchanger flow pattern is identical thus heat transfer surface is identical for both fluids (fig 5). Thus it allows us to write the overall heat transfer coefficient k simply as : 1
k
1
c
1
1
h
(6)
Heat transfer correlations usually are presented in a dimensionless Nusselt number and are formed based on Dittus-Boelter [27] correlation: Nu C 0 Re
n
Pr
m
(7)
where C0, n, m are experimental correlation factors, and Nusselt, Reynolds and Prandtl numbers are described as: Nu
Re
Pr
D
,
VD S D c p
,
.
Page 9 of 25
After rearranging eq.(7) takes form: Vd C 0 S D
n
c p
m
D
(8)
For given flow geometry and assuming constant fluid properties in given temperature range, eq.(8) can be simplified to : C 1V
n
(9)
Where C1 is a constant and
V
is fluids volumetric flow rate. Description of heat transfer
coefficient of a cold fluid by eq.(9), with maintaining constant flow parameters on hot circuit side, can be written by rearranged eq.(6): 1 k
a n Vc
where
b
a 1
(10)
Cc
,
b
1 k
1
2
.
Therefore the heat transfer coefficient is a linear function of volumetric flow rate of cold fluid, where coefficient a is functions gradient and b is an ordinate as depicted on figure 6.
Based on experimental data and given data reduction procedure it is possible to calculate heat transfer coefficient on hot fluid side. The n parameter to which flow rate is raised, usually equals to 0.8, but best results are given for experimental fit of this coefficient. The value of b ordinate is calculated by extrapolation of experimental data to the vertical axis, which corresponds to infinite heat transfer coefficient of cold fluid. With neglible low thermal resistance of a membrane b is a HTC of hot fluid.
Experimental results
In tested heat exchanger, transferred heat can be calculated based on temperature raise of flowing medium both for hot and cold side as written in eq. (11) and (12). Q c m c c pc T c
(11)
Q h m h c ph T h
(12)
Based on calculated heat flux, total heat transfer coefficient is calculated from eq. (5). Due to minor loses heat flux values calculated by eq. (11) and (12) differ. Difference was typically less than 2%, after accommodating heat loses to ambient calculated with eq. (1-3). For further
Page 10 of 25
calculations heat absorbed by cold medium (11) was taken into account. The heat exchanger was capable of exchanging up to 800W of thermal energy at LMTD of 60 K. Figures 7 and 8 present experimental data series for calculating HTC with Wilsons plot method, for constant cold fluid velocity, and 14.5oC supply temperature. As can be expected higher velocities result in lower thermal resistance, corresponding to total heat transfer coefficient of k=14 kW/m2K for Re=2290 and k=8.5 kW/m2K for Re=1150. Figure 9 presents linear regression values for experimental series grouped in constant cold fluid velocities. The resulting heat transfer coefficient of cold fluid from experimental data was calculated by eq. (6). The heat transfer coefficient calculations by Wilson’s method were conducted for the plate thickness of 1 mm. The plate material (the aluminum alloy) has the thermal conductivity λ equal to 207 W/mK. Similarly,
figures 10 and 11 present experimental data series for calculating HTC with
Wilsons plot method, for constant hot fluid velocity. Because in general, inlet fluid parameters and the nozzle diameter is assumed as characteristic length and fluid properties in Reynolds number, thus despite constant flow rate Reynolds numbers can vary significantly with hot water supply temperature. Experimental data were collected for hot water was supply for three constant temperature levels i.e. 45, 62 and 82oC. As in in previous series, higher velocities result in lower thermal resistance, corresponding to total heat transfer coefficient of k=20 kW/m2K for v=4.5m/s and k=12.8 kW/m2K for v=2.2m/s. Figure 12 presents linear regression values for experimental series grouped in constant hot fluid velocities.
5. Impinging jets heat transfer correlations Values of heat transfer coefficient are crucial in calculations of heat exchanger dimensions. In order to validate the applicability of experimental correlations to design and build microjet heat exchangers experimental results were compared to literature correlations for impinging jets heat transfer. The heat transfer with impinging jets depends on many factors, which are usually grouped into two main categories of fluid properties and geometric characteristics. The fluid properties include both thermal and dynamic characteristics, which can be conveniently expressed with the Prandtl, Pr, and the Reynolds, Re, numbers. The geometric parameters include the nozzle geometry, diameter D, nozzle-to-nozzle spacing, and nozzle to surface distance, H. Generally,
Page 11 of 25
the dimensionless quantities H/D, and d/D are considered. In general, the nozzle diameter is assumed as characteristic length in Nusselt and Reynolds numbers. Table 2 presents the correlations developed for microjet cooling based on a vast number of experimental data.
Direct comparison of experimentally obtained values of HTC in form of dimensionless Nusselt numbers is presented on figures 13 and 14 We need to observe that given literature correlations from table 2 are developed for average heat transfer rate on test surface. As can be clearly seen experimentally obtained values of heat transfer are lower than predictions. A very large discrepancies between prediction given in literature are visible. A best consistency is obtained for Lytle and Webb correlation [22], but still obtained results differ greatly from predictions. Unfortunately the difference between predictions and experimental data is higher for nozzle diameter of 0.4mm as can be seen on figure 14. Overall the increase of HTC with higher liquid jet velocities, gives a similar trend as their predictions. Difference may be attributed to different setup of outlet manifold in tested heat exchanger, thus different flow pattern than in specified test facilities. Which indicates that flow arrangement has significant influence on obtained results, and that given correlations are limited in validity to specific working fluids and ranges of operating parameters for the data upon which these models are based. Due to large differences between experimental and predicted data, depicted in table 3 and calculated as:
Nu
eq
Nu
Nu
exp
100 %
(13)
exp
Authors proposed own empirical correlation based on similarity theory [23] The experimentally collected heat transfer coefficient was approximated using the multiple regression method to yield the following relation:
Page 12 of 25
Nu 5 . 55 Re
0 . 65
Pr
0 .4
D d
2 .3
H d
1 .4
(14)
The developed correlation has a simple form, dependent only of Reynolds number (-) and diameter of the nozzle (expressed in m) ratio to equivalent wetted surface diameter (m). The Prandtl number is for the sake of capturing the change of specific properties of cooling fluid. Comparisons against authors own experimental data are presented in fig. 15. Experimental values of heat transfer coefficient were determined directly from Wilsons plot method, presented in the previous section.
6. Conclusions A prototype heat exchanger was built and tested. It incorporates very effective method of enhancing the heat transfer by means of impinging microjets. Modular configuration allows to carry out a series of tests with various working fluids, for both single phase and convective heat transfer and two phase boiling/condensation flow. The research allows the determination of the heat exchanger thermal performance, and to determine the usefulness of the intensification of heat exchange method in the refrigeration and air conditioning systems. Tested design has a great number of potential applications in a variety of machines and devices.
The Wilson plot method was successfully applied to determine the heat transfer coefficients in the laminar and transition flow regimes of a liquid-to-liquid heat exchanger. The heat exchanger is capable of exchanging 800W of thermal energy at LMTD of 60 K. The obtained overall heat transfer coefficient reaches over 10000 W/m2K.
Average Nu predictions of the Lytle and Webb [22] correlation were in best agreement with the experimentally determined average Nusselt numbers for Reynolds numbers in the range 700 < Re < 3000. Better correlation of the data was produced by Eq. (14). In the whole tested flow range, Nusselt numbers were not well correlated by any of the correlations from the literature and the experimentally determined Nusselt numbers were considerably lower than expected. In authors opinion the reason for this was due to narrow range of given literature correlations applicability. These discrepancies may be due to variations in the jet velocity along the flow path on both sides of the heat exchanger. New correlation was suggested, predicting the experimental results within 30%.
Page 13 of 25
The heat exchanger design will be further pursuit in the optimization with respect to the spacing and quantity of nozzles to reduce the pressure drop and increase heat transfer rates.
ACKNOWLEDGMENTS The work presented in the paper was partially funded by statuary activity of faculty of Mechanical Engineering of Gdansk University of Technology NOMENCLATURE A
surface of heat transfer [m2]
a
coefficient, function gradient []
Ar
area ratio []
b
ordinate []
C0
experimental factor, []
cp
specific heat, [J/kgK]
d/D
diameter [m]
g
gravitational acceleration [m/s2]
H
nozzle to impinged surface distance [m]
k
total heat transfer [W/m2K]
L
channel length [m]
LMTD logarithmic mean temperature difference [K] m
experimental factor, [] mass flow of fluid, [kg/s]
n
experimental factor []
Nu
Nusselt number []
P
pressure [Pa]
Pr
Prandtl number []
P
pressure drop [Pa]
Re
Reynolds number []
Ri
thermal resistance [mK/W]
T
temperature [K]
U
uncertainity [%]
v
velocity [m/s] volumetric flow rate [m3/s]
Page 14 of 25
q
heat flux [W/m2] heat flow [W]
Greek symbols heat transfer coefficient [W/m2K] thickness of membrane [m]
density [kg/m3]
l
liquid density [kg/m3]
λ
thermal conductivity [W/mK]
μ
dynamic viscosity [Pas]
kinematic viscosity [m2/s]
Superscripts air
air
c
cold
eq
equation
exp
experimental
h
hot
w
wall
LITERATURE [1] Gupta A., Uniyal M.: Review of heat transfer augmentation through different passive intensifier methods. IOSR Journal of Mechanical and Civil Engineering, vol. 1, pp. 14-21, 2012. [2] Webb R. L.: Principles of enhanced heat transfer. Wiley-Interscience, New York, 1994. [3] Stone. K.M.: Review of literature on heat transfer enhancement in compact heat exchangers. Air Conditioning and Refrigeration Center Technical Reports, 1996. [4] Sun Y., Zhang L., Xu H., Zhong X., Flow boiling enhancement of FC-72 from microporous surfaces, Experimental Thermal and Fluid Science, vol. 35 (2011), 1418-1426 [5] Wang H., Peterson R.B., Enhanced boiling heat transfer in parallel microchannels with diffusion brazed wire mesh, IEEE Transactions on Components and Packing Technology, vol. 33 (2010), 784-793 [6] Jones, B.J., McHale, J.P.&Garimella, S.V., The Influence of Surface Roughness on Nucleate Pool Boiling Heat Transfer, Journal of Heat Transfer, 131, 2009 [7] Dovic D., Palm B., Svaic S.: Generalized correlations for predicting heat transfer and pressure drop in plate heat exchanger channels of arbitrary geometry. International Journal of Heat and Mass Transfer, vol. 52, pp. 4553–4563, 2009.
Page 15 of 25
[8] Galeazzo F.C.C., Tadini C.C., Gut J.A.W.: The effect of flow arrangement on the pressure drop of plate heat exchangers. Chemical Engineering Science, vol. 63, pp. 5386-5393, 2008. [9] Kanaris A.G., Mouza A.A., Paras S.V.: Optimal design of a plate heat exchanger with undulated surfaces. International Journal of Thermal Sciences, vol. 48, pp. 1184–1195, 2009. [10] Wang L., Sunden B.: Optimal design of plate heat exchangers with and without pressure drop specifications. Applied Thermal Engineering, vol. 23, pp. 295–311, 2003. [11] Wang E.N., Zhang L., Goodson K.E., Kenny T.W., Micromachined jets for liquid impingement cooling of VLSI chips, J. Microelectromech. Syst. 2004. [12] Wolf D.H., Incropera F.P., and Viskanta R., Local jet impingement boiling heat transfer, Int. J. Heat Mass Transfer,1996 [13] Garimella S.V., Rice R.A., Confined and submerged liquid jet impingement heattransfer, J. Heat Transfer,1995 [14] Muszyński T., Andrzejczyk R.: Zastosowanie korelacji opisujących wymianę ciepła w obszarze pęczków mikrostrug do projektowania kompaktowych wymienników ciepła: cz.1. Budowa modelowego wymiennika ciepła i jego charakterystyka// Pomiary Automatyka Kontrola. -Vol. 60., nr. 11 (2014), s.1021-1024 [15] Fabbri, M; Dhir, V. K. Optimized heat transfer for high power electronic cooling using arrays of microjets. Journal of heat transfer, 2005, 127.7: 760-769. Womac, D. J., Incropera, F. P., and Ramadhyani, S., 1994, “Correlating Equations for [16] Impingement Cooling of Small Heat Sources With Multiple Circular Liquid Jets,” ASME J. Heat Transfer, 1162, pp. 482–486. [17] Gregory J. Michna, Eric A. Browne, Yoav Peles, Michael K. Jensen, Single-Phase Microscale Jet Stagnation Point Heat Transfer, Journal of Heat Transfer, NOVEMBER 2009, Vol. 131, [18] Martin, H. Heat and Mass Transfer between Impinging Gas Jets and Solid Surfaces (1977) Advances in Heat Transfer, 13 (C), pp. 1-60. [19] Li C-Y, Garimella S. V. Prandtl-number effects and generalized correlations for confined and submerged jet impingement International Journal of Heat and Mass Transfer, Volume 44, Issue 18, September 2001, Pages 3471-3480 [20] Wen MY, Jang KJ (2003) An impingement cooling on a flat surface by using circular jet with longitudinal swirling strips. Int J Heat Mass Transf 46:4657–4667 [21] Meola C. A New Correlation of Nusselt Number for Impinging Jets Heat Transfer Engineering, 30(3):221–228, 2009 [22] D. Lytle, B.W. Webb, Air jet impingement heat transfer at low nozzle–plate spacings, Int. J. Heat Mass Transfer 37 (1994) 1687–1697. [23] T. Muszynski, R. Andrzejczyk, Heat transfer characteristics of hybrid microjet microchannel cooling module, Applied Thermal Engineering, Volume 93, pp 1360-1366, 2016 [24] Florschuetz, L. W., Truman, C. R., and Metzger, D. E., 1981, “Streamwise Flow and Heat Transfer Distributions for Jet Array Impingement With Cross- flow,” ASME J. Heat Transfer, 1032, pp. 111–134
Page 16 of 25
[25] B.N. Taylor, C.E. Kuyatt Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results National Institute of Standards and Technology Technical Note 1297 (1994) [26] John W. Rose, Heat-transfer coefficients, Wilson plots and accuracy of thermal measurements, Experimental Thermal and Fluid Science 28 (2004) 77–86, [27] Dittus, F.W., Boelter, L.M.K., 1930. Publications on Engineering, vol. 2. University of California, Berkeley, s. 443.
Page 17 of 25
Fig.1. Schematic of a test facility: 1- heat exchanger, 2 - Corriolis mass flow meter, 3 pulsation free gear pump, 4 - filter, 5 - inspection glass, 6 - fluid tank , 7 - heater, 8 - chiller
Fig. 2. View on microjet heat exchanger
Page 18 of 25
Fig. 3. Schematic of microjet HX
160 4x0.6mm 4x0.4mm
p [kPa]
120
80
40
0 0
500
1000
1500
Re [-]
2000
2500
Fig. 4. Hydraulic Characteristics of tested heat exchanger
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Fig. 5. A) Possible flow pattern in tested heat exchanger, B) Flow pattern and temperature distribution of impinging jet
Fig. 6. Graphical scheme for calculating heat transfer coefficient by Wilsons plot method
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
5.0x10-5 0.0 0
104
2x104
wh [(m /s) ] n
3
3x104
4x104
n
Fig. 7. Graphical scheme for calculating heat transfer coefficient by Wilsons plot method, for case of cold fluid jet velocity of v=4.5m/s corresponding to Re=2290
Page 20 of 25
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
5.0x10-5 0.0 0
104
2x104
whn[(m3/s)n]
3x104
4x104
Fig. 8. Graphical scheme for calculating heat transfer coefficient by Wilsons plot method, for case of cold fluid jet velocity of v=1.6m/s corresponding to Re=1150
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
Linear fit Re=840 Linear fit Re=1150 Linear fit Re=1660 Linear fit Re=1910 Linear fit Re=2110 Linear fit Re=2290
5.0x10-5 0.0 0
104
2x104
whn[(m3/s)n]
3x104
4x104
Fig. 9 Linear regression of experimental data for calculating heat transfer coefficient by Wilsons plot method, for varying hot and constant cold fluid jet velocity
Page 21 of 25
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
5.0x10-5 0.0 0
104
2x104
wc [(m /s) ] n
3
3x104
4x104
n
Fig. 10. Graphical scheme for calculating heat transfer coefficient by Wilsons plot method, for case of cold fluid jet velocity of v=2.2m/s corresponding to Re=2200-3800
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
5.0x10-5 0.0 0
104
2x104
wc [(m /s) ] n
3
3x104
4x104
n
Fig. 11. Graphical scheme for calculating heat transfer coefficient by Wilsons plot method, for case of cold fluid jet velocity of v=4.5m/s corresponding to Re=4400-7600
Page 22 of 25
2.5x10-4
k-1 [m2K/kW]
2.0x10-4 1.5x10-4 -4
10
Linear fit v=4.5m/s Linear fit v=4.2m/s Linear fit v=3.8m/s Linear fit v=3.2m/s Linear fit v=2.2m/s Linear fit v=1.6m/s
5.0x10-5 0.0 0
104
2x104
wc [(m /s) ] n
3
3x104
4x104
n
Fig. 12 Linear regression of experimental data for calculating heat transfer coefficient by Wilsons plot method, for varying cold and constant hot fluid jet velocity
400
Exp. Meola 2009 Wen i Jang 2003 Li i Garimella 2001 Lytle i Web 1994 Womac 1993 Martin 1977
Nu [-]
300
200
100
0 0
500
1000
1500
Re [-]
2000
2500
Fig. 13 Comparison between predicted and experimental average Nusselt numbers for 4x0.4mm geometry.
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80
Meola 2009 Wen & Jang 2003 Li & Garimella 2001
Lytle & Web 1994 Womac 1993 Martin 1977
Nu [-]
60
40
20
0 0
500
1000
1500
Re [-]
2000
2500
Fig. 14 Comparison between predicted and experimental average Nusselt numbers for 4x0.6mm geometry.
25
+30% 4x0.6mm 4x0.4mm
Nueq [-]
20
15
-30%
10
5
0 0
5
10
15
Nuexp [-]
20
25
Fig. 15 Comparison between experimental and predited values of nusselt number based on eq. (14)
Page 24 of 25
Table 1. Measurement uncertainties. Variable
Uncertainty (%)
Accuracy
0.5%
±0.5 g/s
ΔT
2.1%
±1.44 K
vjet
1.41%
±0.02 m/s
1.0%
±4 kW/m2
α
2.5%
±0.05 kW/m2K
Re
2.5%
±18
Table 2. Literature correlations for impinging jets heat transfer Source
Correlation
Exp. range
Martin [18]
Nu 2 Re
Womac [16]
Re D 1 200
0 , 55
0 ,5 D
Nu 0 , 509 Re
L*
0 ,5
Pr
D
0 ,5
1 1 ,1 D D R R 1 0 ,1 H 6 D D R
A r , w 0 , 0363 Re
0,4
2 L / 2 1 .9 D L / 2 1 .9 D
0 ,8 L*
D L*
1
Pr
Re
2000 0 , 42
A r , w Pr
D
400000
2 ,5 R / D 7 ,5 2 H / D 12
water 0,4
Re
d
50000
1, 65 d 6 , 55 mm
3 , 5 H / D 10
water, FC77
2
Li & Garimella [19] Wen & Jang [20] Lytle & Web [22]
Nu 0 ,160 Re
0 , 695
Nu 0 , 442 Re
Nu 0 , 726 Re
Pr
D
0 , 696 D
0 , 53 D
Pr
0 , 68 D
0 , 56
CF
1/3
h D
Meola [21]
Nu 0 , 3 Re
0,4
h D h D
0 , 11
0 , 20
d D
0 , 11
d /2 D
Re D 23000
1, 59 D 12 , 5 mm 1 H /D 5 0 , 41
500 Re
D
,air, water, FC77
27000
3 H / D 16
,
air 3600
0 , 191
D H
4000
Re
D
27600
0 . 1 H / D 10
,
air 250 Re
0 ,3 0 , 15
Ar
Pr
0 , 42
D
98000
0 . 39 D 50 mm
,
air, water
Table 3 – Relative error between predicted and experimental average Nusselt numbers Correlation Martin [18] Womac [16] Lytle& Web [19] Li & Garimella [20] Wen & Jang [22] Meola [21]
Min
Max
357% 770% 94% 456%
998% 2200% 348% 1178%
645% 221%
1612% 641%
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