An Investigation of Natural Convection Heat Transfer

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An Investigation of Natural Convection Heat Transfer from a Horizontal Cooled Finned Tube a

M. Yaghoubi & M. Mahdavi

a

a

School of Mechanical Engineering, Shiraz University , Shiraz , Iran Accepted author version posted online: 04 Dec 2012.

To cite this article: M. Yaghoubi & M. Mahdavi (2013): An Investigation of Natural Convection Heat Transfer from a Horizontal Cooled Finned Tube, Experimental Heat Transfer: A Journal of Thermal Energy Generation, Transport, Storage, and Conversion, 26:4, 343-359 To link to this article: http://dx.doi.org/10.1080/08916152.2012.669809

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Experimental Heat Transfer, 26:343–359, 2013 Copyright © Taylor & Francis Group, LLC ISSN: 0891-6152 print/1521-0480 online DOI: 10.1080/08916152.2012.669809

AN INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFER FROM A HORIZONTAL COOLED FINNED TUBE M. Yaghoubi 1 and M. Mahdavi 1

Downloaded by [University of Windsor] at 11:27 14 June 2013

1 School

of Mechanical Engineering, Shiraz University, Shiraz, Iran

Natural convection and radiation heat transfer from annular mounted fins on a horizontal cylinder is studied experimentally and numerically. For experiments, surrounding air temperature is varied 22ı C–35ı C for fin bases 8ı C–15ı C. Airflow and thermal boundary layers descend around the fin tube. Heat transfer rates from surfaces of fins and tube base are measured and determined numerically, and good agreement is observed. Results show that cold air starts from the upper point and moves downward and that convection heat transfer is larger than radiation. A new correlation for predicting natural convection heat transfer is developed for the range of measurements. Keywords number

free convection, cold tube, laminar flow, annular fin, performance, Nusselt

INTRODUCTION Annular finned-tube heat exchangers are commonly used in refrigeration and airconditioning systems. For the design of finned-tube heat exchangers, it is necessary to find variations of local heat transfer for both natural and forced convection and flow distribution for the tube-fin geometry. For cooled surfaces, it is well known that a natural flow pattern within cold annular fins and tubes is very complex due to the plume of cooled air that descends between the fins and below the horizontal tube. For such geometry, the boundary layer over the cold tube starts to develop at the top of the fins and increases in thickness along the circumference of the tube. Due to the small space between fins, a boundary layer develops at a short distance from the top and air movement is not considerable between fins. Thus, there is a mixing of downward motion and circumferential air motion, which results in the variation of heat transfer coefficient both radially and circumferentially. Complex flow and heat transfer conditions for finned tubes have already been pointed out by Webb [1]. Some approximations for predicting heat transfer coefficient for the annular fin-tube are proposed when they are employed in heat exchangers. The phenomena of free and forced convection for a heat exchanger with finned tubes were reported in [2–4]. Chen and Chou [3] numerically and experimentally investigated natural Received 17 June 2011; accepted 25 January 2012. Address correspondence to Prof. Mahmood Yaghoubi, School of Mechanical Engineering, Shiraz University, Zand Ave., Shiraz, 7134851154 Iran. E-mail: [email protected] 343

344

M. YAGHOUBI AND M. MAHDAVI


NOMENCLATURE A At d D F h K Nu q Q r Ra s T v

(m2 )

area outer area of the steel tube (m2 ) outer diameter of the steel tube (m) fin outer diameter (m) view factor radiation heat transfer coefficient (W/m2 K) thermal conductivity (W/mK) Nusselt number heat flux (W/m2 ) heat (W) radius (m) Rayleigh number fin spacing (m) temperature (ı C) velocity (m/s)

Greek Symbols ˛ thermal diffusivity (m2 /s) ˇ volume expansion coefficient " emissivity factor

˛

dynamic viscosity (kg/ms) kinematic viscosity (m2 /s) density (kg/m3) Stefan–Boltzmann constant, 5:7 10 8 (W/m2 K4 )

Subscripts 1, 2 inner and outer radius of the aluminum tube 3, 4 inner and outer radius of the steel tube Al one aluminum tube a, 1 air b fin base c conduction heat transfer h convection heat transfer r radiation heat transfer steel three steel tubes w fin wall wall chamber surface z, r, cylindrical coordinates

convection over a vertical square finned tube for various fin spacings. Their estimation showed that radiation heat transfer may be significant in natural convection and must be considered for heat transfer analysis. Sparrow et al. [5] experimented to determine heat transfer characteristics of a horizontally finned tube placed in a vertical channel that was open to the surroundings at the top and bottom. They measured heat transfer from the finned tubes by natural convection and radiation, and performances of the system are expressed as a function of three geometric parameters: vertical position of the tube in the channel, clearance between the fin tips and channel walls, and the height of the channel. Experiments were also carried out for the finned tube surrounded in a free space, and it was found that in-channel positioning of the tube gives a noticeably higher rate of heat transfer. Empirical correlations for a heated annular fin tube for natural convection were presented in [6, 7]. These relations were specified for only an isothermal fin for specified Rayleigh numbers. There have also been studies for local heat transfer coefficients on a plate fin [8–12]. Yildiz and Yuncu [13] experimentally explored the performance of annular fins on a horizontal cylinder in free convection with various fin spacings and diameters for various fin spacings at low temperature differences. Heat transfer rates have a slight reduction, but it increases for high temperature differences. It was also found that by increasing the fin spacing, the convection heat transfer rate approaches that of a horizontal cylinder. They showed that for a fixed diameter, the rate of heat transfer increases to a maximum and then starts to decrease when the fin spacing increases. Chen and Hsu [14] estimated the heat transfer coefficient on the fins of a heated annular finned tube for natural convection of various fin spacings by measuring temperature variations on the fin. They showed that resistance to natural convective airflow from the fin arrays increases with decreasing the fin spacing. They illustrated that this resistance has no effect


NATURAL CONVECTION FROM HORIZONTAL FINNED TUBE

345

on the average heat transfer coefficient and fin efficiency as the fin spacing enlarges to infinity. They also reported that the heat transfer coefficient varied around the fin and was found to be high on the fin bottom and minimum on the fin top when the tube was hotter than the ambient air. They also introduced a new correlation for isothermal and non-isothermal finned tubes, where the minimum fin spacing considered was 5 mm. Results of measurements on free convection around horizontal annular finned tubes have also been published by [15–17]. Kayansaya and Karabacak [15] experimentally studied natural convection heat transfer coefficients for a horizontal cylinder with vertically attached circular fins. They showed that for low fin spacing (minimum of 12.5 mm), the radiation heat transfer is not significant. A correlation for a finned tube with a circular fin of high fin spacing was presented by Gesellschaft et al. [16]. It was found that the proposed correlation is not suitable for an annular slender fin with very low fin spacing. Literature shows that almost all analyses were done for hot tubes, and no studies are available for a cold annular fin tube, where the flow direction is along the gravity. For a cold horizontal cylinder, Tahavvor and Yaghoubi [18] analyzed natural convection heat transfer using an artificial neural network as well as fluid flow experimentally by flow visualization. They showed that natural convection from a cold cylinder aids the flow because of gravity, but natural convection from a hot cylinder is an opposing flow. They found slight differences of natural convection of a cold cylinder compared with a hot cylinder. This study attempts to find natural convection heat transfer from a cold annular finned tube without any phase change. The fin spacing is small compared to the previous studies, and the tube diameter and Rayleigh numbers are changed to illustrate the cold plume motion descending around the cold tube. Based on the measurements, a new correlation is developed for natural convection from a cold and compact finned tube. Results are compared with a relation of [14] that takes into account the fin spacing; their correlation is found to be suitable for certain cases.

EXPERIMENTAL APPARATUS AND TECHNIQUES Experimental Set-Up Free convection heat transfer over a horizontal finned tube of 25.4 mm diameter in a control chamber is carried out when the fins are circular with a height of 15.3 mm, spacing of 2 mm, and thickness of 0.4 mm. For the experiments, ambient conditions, such as air temperature and humidity, are controlled in the test room, which is equipped with cooling and heating systems and could simulate free convection condition. A schematic diagram of the test chamber and the apparatuses is illustrated in Figure 1. This figure explains that temperature of the tube surface is controlled by a refrigeration cycle Ttype thermocouples attached to the cylinder surface and fins that measure temperature at various positions. All measured data are recorded by a data acquisition unit that is connected to a PC. The test room consists of two blocks—a test room and an equipment room, which are separated by an isolated wall. In the equipment room, the air cooling and air heating units operate until the air reaches the desired temperature and relative humidity. An on–off fan blows air for a very limited time in the space between the roof and suspended ceiling, as shown in Figure 1. Air flows into the ceiling, opposite wall, and outlet holes with reduced air velocity. The air velocity at the outlet is less than


346


Figure 1. Schematic diagram of test room and experimental equipment.

0.4 m/s when the fan is on, and free convection condition is maintained in the position of the horizontal cylinder. The fan only runs when the air needs conditioning; for the most of time, which is greater than 90% of the experimental period, the fan is off, and air does not have any circulation. Control room surfaces temperatures are also measured at two positions to check the radiation heat transfer between the test surface and control chamber walls. Test Section The test section is shown in Figure 2. The inner cylinder is an aluminum cylinder with 30 cm of length, and the outside diameter is 19 mm; 12 T-type thermocouples are attached to the cylinder to measure its surface temperature. Four thermocouples are attached to a fin: two thermocouples are attached on the fin base and two thermocouples are attached to the fin tip (Figure 2) with ˙ 0.2ı C accuracy. The outer cylinder is carbon steel, and aluminum fins are attached on it. The thermocouples are placed in the middle cross-section of the cylinder, as illustrated in Figure 2. For measuring heat flux and temperature distribution along the test section, thermocouples are placed on both sides of the test section (six thermocouples in each side), as shown is Figure 3. The value of the wall temperature is taken as the average of the thermocouples in each cylinder (aluminum and steel). To achieve a high temperature difference and more accurate heat flux, an insulated layer with the thermal conductivity of about 0.17 W/m K is placed between the aluminum and steel layers. Figure 4 shows the test section, probes, and instruments around it that measure air temperature. A TUV Brandenburg, DWM CMPLAD, GmbH, (Germany) cooling unit is



347

Figure 2. Position of wall and surface thermocouples (section of fin tube).

used for cooling the test room (Figure 1), with the ability to cool the ambient air to 0ıC. The air heating unit consists of three thermal elements with 2,000 watts in power. These have the capacity to reach the test room air temperature to 50ıC. To achieve a low constant temperature on the fin base, ethylene-glycol antifreeze solution is pumped through the cylinder, causing the temperature of the cylinder to drop to the desired temperature.

Figure 3. Test section with three layers and position of thermocouples at the end section. (color figure available online)


348


Figure 4. Test section: finned tube, thermocouples sensors, Samsung SHC-735 camera. (color figure available online)

Measurements Experimental measurements are made for three sets of thermocouple probes as follows: cold surface temperature, test room air temperature, and test chamber surface temperature. Tube surface and ambient air temperature are kept constant during each experiment.

Heat Flux Measurement For steady-state condition, surface temperature distribution reveals that heat conduction along the axis of the cylinder is negligible in comparison with the heat flux along the radial direction. Thus, in this study, axial variation of the tube surface temperature is less than 2%, and therefore, axial heat conduction is neglected. According to the geometry of the test section, radial heat flux is calculated by Eq. (1): qc D

Qc .Tsteel TAl/ ; D d Ln.r2 =r1 / d Ln.r3 =r2 / d Ln.r4 =r3 / At C C 2 K1 2 K2 2 K3

(1)

where k1 , k2 , and k3 are the thermal conductivity of aluminum, insulator, and steel cylinder; their values are, respectively, k1 D 200, k2 D 0:17, and k3 D 50 W/mK. Measuring heat flux includes conduction and radiation heat transfer, as illustrated in Figure 5. As a result, total heat flux to the base tube can be expressed as qc D

Qh Qr C D qh C qr ) qh D qc At At

qr ;

where qh and qr are convection and radiation heat flux, respectively.

(2)



349

Figure 5. Heat fluxes on fin and tube base. (color figure available online)

Flow Visualization Flow visualization is made by passing hydrocarbon smoke over the finned tube. The cold plume flow of air is recorded by an automatic digital Canon S3IS camera (0023332, Great Britain) and Samsung camera SHC-735 (South Korea), as addressed in Figure 1. RADIATION HEAT TRANSFER Heat transfer takes place by natural convection and radiation from the finned tube. Radiation heat flux is calculated by 4 FA" Twall Tw4 qr D ; (3) At where Tw and Twall are averaged the fin cold surface and room average surface temperature. F , ", and are the view factor, emissivity, and the Stefan–Boltzmann constant, respectively. At is the steel tube outer area. The emissivity factor for industrial aluminum is " D 0:09. For low fin spacing, experimental and numerical results show that temperature difference is insignificant between base and tip fin (less than ˙ 0.5ı C). For analysis of radiation heat loss, the fins within adequate engineering accuracy can be assumed to have a uniform temperature, which is estimated as the average of the base tube and the fin tip values. As shown in Figure 6, an enclosure confined by two closest fins, the band between fins, and an imaginary black surface for S1, complete the unit cell for radiation analysis. According to [19], for concentric cylinders, the view factor between


350


Figure 6. Unit enclosure for radiation heat flux examination (S2 and S3 are fins inner surfaces).

tube surface (between fins) and room wall is very low and can be neglected. Also, the view factor between the fin surface and room walls is F D 0:0877, and the view factor between fin tip and room wall is F D 1. MATHEMATICAL MODELING Governing Equations The governing equations for fluid flow around the finned tube are given by Eqs. (4)– (9). Figure 7 shows the configuration of finned tube with grid distribution for the numerical model. Axial heat flux is neglected due to nearly uniform surface temperature. For numerical scheme, two half fins and fin spacing is selected as shown in Figure 7. The governing equations include continuity, momentum, and energy for the three-dimensional steady-state fluid flow condition. The Boussinesq approximation is used for density with a limitation of ˇ.T T1 / 1 [20], where ˇ is volume expansion coefficient of air: 1 @ Š 1 Œ1 ˇ.T T1 /; ˇD ; (4) @T p @vr vr 1 @v @vz C C C D 0; (5) @r r r @ @z v2 @vr v @vr @vz @p vr C C vz D C r 2 vr C gˇ.T T1 / cos./; (6) @r r @ r @z @r @v v @v v vr @v 1 @p vr C C C vz D C r 2 v C gˇ.T T1 / sin./; (7) @r r @ r @z r @



351

Figure 7. Circular finned tube: (a) physical geometry and (b) grid distribution. (color figure available online)

v @vz @vz @vz vr C C vz D @r r @ @z vr

@p C r 2 vz ; @z

@T v @T @T 1 @ @T 1 @2 T @2 T C C vz D˛ r C 2 2 C 2 : @r r @ @z r @r @r r @ @z

(8)

(9)

Numerical Method An available discretized computational fluid dynamics (CFD) code is used to find fluid flow and thermal field of the configuration shown in Figure 7. The governing equations in Eqs. (5)–(9) are solved by the control volume scheme. This method is derived on the spatial integration of the conservation equations over finite control volumes, altering the governing equations to a set of algebraic equations. It solves the systems of equations resulting from the discretization method using the finite-volume scheme. The convergence criteria 10 8 are designated for all dependent variable quantities. Some grid dimensions are examined to find grid-independent results. Several tests are made between grid dimensions of 80 40 8, 120 80 16, and 170 130 20 nodes along the radial, tangential, and axial directions, respectively. Results in terms of averaged convection heat transfer found that a 120 80 16 grid distribution is suitably fine to ensure a grid-independent solution with less than 3% differences with the lowest grid size.

352



Table 1. Conditions of the tests Test no.

Tb (ı C)

Ta (ı C)

Twall (ı C)

1 2 3 4 5 6 7 8 9

8 8 8 12 12 12 15 15 15

22 27 33 22 27 33 22 27 33

21.5 26.5 32 21.5 26.5 32 21.5 26.5 32

RESULTS AND DISCUSSIONS To study convection and radiation heat transfer from an annular finned tube, experiments are performed to reach a steady-state condition by means of uniform thermocouple temperatures output. All tests are recorded in Table 1. For each test, heat flux is determined from Eq. (1), convection heat transfer is determined from Eq. (2), and radiation heat flux is obtained from Eq. (3). The mean experimental heat transfer coefficient is obtained from the measured heat transfer rate for a single annular fin introduced by [21]. On the basis of Eq. (3), radiation heat flux is calculated for two geometries and illustrated in Figure 8. First, radiation heat flux is calculated by use of fin and tube base geometry, as illustrated in the “Radiation” section (black lines in Figure 8). Second,

Figure 8. Comparison of radiation heat flux by two procedures.



353

radiation heat flux can be determined with assumption of an aluminum tube with outer diameter of 56 mm (equal to fin outside diameter). Figure 8 shows that radiation is equal by two considerations: that fin spacing is very small and that radiation heat transfer has a low effect from surfaces of the fin to ambient air for the range of present measurements. A comparison of convection and radiation heat flux is illustrated Figure 9. This figure illustrates that radiation heat flux is very low with respect to convection heat transfer, and it is less than 10% of total heat conduction from tube. This is due to the small temperature difference between the tube and control room walls. For a fixed air temperature, by increasing the temperature difference, the relative radiation heat transfer decreases and the value of convection heat transfer increases. With decreasing the tube surface temperature, a cold plume flows around the fin tube with higher velocity and heat transfer coefficient enhances; therefore, convection exceeds more than radiation. Such experiences were reported in [16]. Figures 10 and 11 show the effect of tube surface and air temperature on the mean free convection coefficient (without radiation). These figures illustrate that with increasing ambient air temperature or decreasing tube surface temperature, free convection coefficient increases; however, the effect of tube surface temperature is more pronounced than the ambient air temperature rise. Such a condition may be due to higher airflow, which accelerates by the induced air force created by reducing the tube surface temperature. Also these figures show that average heat transfer coefficient is very low, which may be due to the trapped air between fins, as reported in [14] in terms of higher resistance that acts as an insulation layer. Therefore, these figures show that fins make the heat transfer coefficient significantly lower than a bare tube of the same outer diameter for free convection condition. Figures 10 and 11 also show that there is good agreement between experimental and numerical results with slight underestimation with an average error less than 5%. Results of streamlines, velocity, and isothermal lines of the numerical analysis are illustrated in Figures 12–14. Figure 13 illustrates the experimental flow visualization,

Figure 9. Comparison of convection and radiation heat flux from a finned tube for Ta D 33ı C.


354


Figure 10. Effect of tube surface temperature on mean free convection coefficient.

and Figure 14 presents an isothermal line from the base tube surface to ambient air. As shown in Figure 12b, there is very slight air movement between fins and a lot of air passes over the fin tip. Afterward, airflow accelerates under the finned tube because it is aligned with gravity. At the vicinity of the fin tip, a few air leaks between fins and causes the streamlines to combine at the bottom of the finned tube. No strong flow separation of the cooled plume is observed, both experimentally and numerically, for the range of tests carried out in this study. The flow of the cooled plume is also shown

Figure 11. Effect of ambient temperature on free convection coefficient.



355

(a)

(b) Figure 12. Streamlines around finned tube and between fins: (a) Tb D 12ı C, Ta D 27ı C and (b) Tb D 8ı C, Ta D 33ı C. (color figure available online)


356


Figure 13. Flow visualization around finned tube of natural convection for Tb D 8ı C, Ta D 33ı C: (a) side view and (b) aligned with finned tube. (color figure available online)

Figure 14. Isothermal lines of fin and air for: (a) Tb D 12ı C, Ta D 27ı C and (b) Tb D 8ı C, Ta D 33ı C.


357


by flow visualization in Figure 13. Air falls over the fin tips but is trapped between fins. Such an air layer acts as a thermal resistance [14]. This can be seen in Figure 14, where no remarkable temperature distribution is observed on the fins from base to tip. Such temperature variation also depends on the fin material [4, 21], but for most heat exchanger fins, their thermal conductivity is high, similar to that selected in the present analysis. All available correlations of heat transfer from finned tubes in literature are proposed for hot finned-tube geometries, where gravitational acceleration has an opposite direction with the plume. For cooled plumes, gravitational acceleration has the same direction with the plume flow and aids flow around the finned tubes. To predict convection heat transfer coefficient, Chen and Hsu [14] introduced a correlation for an isothermal circular finned tube with minimum fin spacing of 5 mm: Nu D 0:667 Ra0:25

0:516;

(10)

where the Rayleigh number Ra and the mean Nusselt number Nu are defined as Ra D

gˇ.Tw Ta /s 3 s ; ˛ D

(11)

Nu D

hs : k

(12)

In Eq. (11), properties ˇ, ˛, k, and denote volumetric thermal expansion coefficient, thermal diffusivity, heat conduction coefficient, and kinematic viscosity of air at a cold wall temperature, respectively. Comparison is made between some experimental results of this study and Eq. (11) in Figure 15. This figure shows that for very low Rayleigh numbers, the results of the present study are higher than the correlation by Chen and Hsu [14]. This is probably due to the fact that for free convection on a cold surface, airflow direction is the same with gravity, and it aids to accelerate airflow, thus increasing the heat transfer coefficient. A new correlation is derived from the data of the present experimental measurements for natural convection from a cold horizontal finned tube based on the relations in Eqs. (11) and (12) as Nu D 11:04 Ra4 C 18:63 Ra3

11:24 Ra2 C 2:898 Ra

0:224

(13)

for Rayleigh number ranges 0:1 < Ra < 0:7, with R2 equal to 0.96.

Uncertainty Analysis During experiments, errors may present from various terms, making it necessary to find the uncertainty of each item. The accuracy of thermocouples is about ˙ 0.2ı C, and measuring length error is ˙ 0.02 mm. Thus, an uncertainty of heat flux is determined according to [22, 23], and it is found to be less than 7.1%, and the uncertainty of Nu from Eq. (13) was less than 7.5%.


358


Figure 15. Variation of Nu with Ra.

CONCLUSION In this study, natural convection heat transfer from a cold horizontal compact finned tube is studied experimentally and numerically. Based on the results, the following conclusions are found. Fluid flow between fins is very weak, and average convection heat transfer coefficient is very small relative to a bar tube. For low fin spacing, the radiation view factor of the finned tube is very small. The finned tube acts similarly to a tube equal with the fin outside diameter. The fraction of radiation heat transfer from total heat transfer is very low and less than 10% for the range of experiments. Airflow between fins is very limited, and it makes the fin have an almost uniform temperature. The relative amount of convection heat transfer increases more than radiation heat transfer with decreasing the tube surface temperature. Flow visualization showed that fluid flow is laminar and does not have any significant separation. For the range of experiments, good agreements are observed for convection heat transfer with a numerical solution. For cold finned tubes, Nusselt number is slightly greater than that of a hot finned tube. REFERENCES 1. R. L. Webb, Principles of Enhanced Heat Transfer, Wiley, New York, pp. 125–153, 1994.



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