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Experimental study of flow and heat transfer characteristics of natural convection in an enclosure with horizontal parallel heated plates
International Journal of Heat and Mass Transfer 55 (2012) 7072–7078
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Experimental study of flow and heat transfer characteristics of natural convection in an enclosure with horizontal parallel heated plates Akihiko Horibe a, Rikio Shimoyama a,b,⇑, Naoto Haruki a, Akira Sanada b a b
Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama-shi, Okayama 700-8530, Japan Industrial Technology Center of Okayama Prefecture, 5301 Haga, Kita-ku, Okayama-shi, Okayama 701-1296, Japan
a r t i c l e
i n f o
Article history: Received 7 October 2011 Received in revised form 18 June 2012 Accepted 10 July 2012 Available online 4 August 2012 Keywords: Heat transfer Natural convection Parallel heated plates Enclosure Vortex motion Flow visualization
a b s t r a c t We conducted an experimental investigation of natural convection in an enclosure containing horizontal parallel heated plates. Our experimental setup was as follows: Two heated plates were arranged vertically in an enclosure. The temperature of the ceiling was maintained at a constant low temperature, while the other sides satisfied thermal insulation boundary conditions. We examined flow characteristics in the enclosure and heat transfer around the horizontal heated plates. In the region between the cooled ceiling and the upper heated surface, vortex motion occurred when the accompanying flow from the lower region interfered with the ascending flow. Heat transfer around the heated surface was enhanced by this vortex motion. In other regions, the flow circulated along the heated surfaces in all cases. Generally speaking, for each flow pattern, the Nusselt number was proportional to some power of the modified Rayleigh number. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The problem of natural convection heat transfer from horizontal parallel heated plates in enclosures has received much attention in recent years. In view of the increasing heat generation density inside electronic packages, issues related to thermal design are considered to be limiting factors in the performance of these devices. Although cooling is easily achieved by the use of fans, they often generate noise and decrease the reliability of electronic equipment. Therefore, natural convection has become a very important consideration in the thermal design of electronic packages. Due to the importance of certain features and designs, printed boards with heated elements tend to be oriented horizontally and arranged vertically. Moreover, outdoor electronic equipment is usually enclosed to provide waterproofing and dust resistance. Hence, the flow and heat transfer characteristics of this type of configuration significantly affect the thermal design of electronic packages. Over the years, numerous researchers have studied the problem of natural convection heat transfer in fluid layers confined between two horizontal plates, heated from below and cooled from above; see e.g. Chu and Goldstein [1], Tanaka and Miyata [2], Catton [3] and Pallares et al. [4]. Many other studies have fo⇑ Corresponding author at: Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama-shi, Okayama 700-8530, Japan. Tel.: +81 86 286 9600; fax: +81 86 286 9630. E-mail address: [email protected] (R. Shimoyama). 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.07.021
cused on natural convection around heated bodies in an enclosure; Mack and Hardee [5], Powe et al. [6], Yoon et al. [7] and Angeli et al. [8] investigated natural convective flow and heat transfer phenomena occurring between a heated body and an enclosure. However, these studies dealt only with individual spherical heated bodies. Liu and Tao [9] examined heat transfer and fluid flow characteristics around a channel in a rectangular enclosure. Barozzi and Carticelli [10] investigated natural convection in a cavity containing parallel heated plates. In each of these studies, the parallel plates were arranged vertically. Keyhani et al. [11] studied natural convection heat transfer in a rectangular enclosure with heat sources, but the heaters had a protruding shape and were mounted on a single vertical wall with uniform spacing. As noted above, to date no researchers have investigated natural convective flow and heat transfer phenomena in an enclosure containing horizontal parallel heated plates, and previous findings cannot be easily applied to this case. The main purpose of the present study was to describe hitherto unknown basic flow characteristics in an enclosure containing horizontal heated plates, and to determine the relationship between the flow and the heat transfer characteristics around the plates. The main focus was the effects of the interval between the heated plates and the heat flux, both of which strongly influence these characteristics. The experimental conditions were as follows: the enclosure was cylindrical, the two heated elements were arranged vertically, the heated surfaces were circular, the ceiling surface was maintained at a constant low
A. Horibe et al. / International Journal of Heat and Mass Transfer 55 (2012) 7072–7078
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Nomenclature a A g l1 l2
l3 Nu q Qloss r Ra⁄ T DTair
thermal diffusivity (m2/s) area of heated surface (m2) gravitational acceleration (m/s2) height of upper region (distance between cooling surface and upper heated surface of first layer) (m) height of middle region (distance between lower heated surface of first layer and upper heated surface of second layer) (m) height of lower region (distance between lower heated surface of second layer and bottom of enclosure) (m) Nusselt number, Nu = amlx/k heat flux on the heater (W/m2) heat loss from the enclosure (W) distance from the central axis of the enclosure (m) 4 modified Rayleigh number, Ra ¼ gbqm conv lx =kam temperature (K) temperature difference between the air at the center height of each region and the cooling surface (K)
temperature, and the other surfaces were insulated. These conditions were sufficiently simple to elucidate the basic characteristics. 2. Experimental apparatus and measurements The apparatus, schematically illustrated in Fig. 1, was comprised of an acrylic cylindrical enclosure, two heated elements, and a cooling plate. The heated elements were made of phenol foam insulation, 100 mm in diameter and 15 mm thick. Glass epoxy boards were glued onto the upper and lower surfaces of the phenol foam, with a 30-lm copper film on each board. The copper films were milled to a double spiral form with a width of 2 mm. Uniform heat flux conditions were realized by supplying electric power to the copper film. The amount of electric power provided to the heated surfaces per unit area q was varied from 95.5 to 293 W/m2. As Fig. 1 shows, the two heated elements were coaxially arranged in the acrylic cylindrical enclosure at the desired distances (18 mm < l1 < 93 mm, 20 mm < l2 < 87 mm, 18 mm < l3 < 88 mm), where l1 denotes the height of the upper region (the distance between the cooling surface and the upper heated surface of the first layer), l2 denotes the height of the middle region (the distance between the lower surface of the first layer and the upper surface of the second layer), and l3 denotes the height of the lower region (the distance between the lower surface of the second layer and the bottom of the enclosure). The heated elements were suspended on wires and oriented horizontally. The cooling plate was made from copper, and was maintained at Tc = 298 K by passing temperature-controlled water over the upper surface of the plate. The acrylic cylindrical enclosure was thermally insulated with glass wool and 80 mm of Styrofoam. Heat loss was estimated using thermocouples placed at the inner and outer surfaces of the Styrofoam, and was less than 17.1% of the total heat generated on the heaters. Heat transfer to the cooling plate was calculated using the difference between the cooling water temperatures at the inlet and outlet. The sum of the discharged heat and the heat transfer (calculated using the above methods) was estimated to be less than 5% of all generated heat. To estimate the heat transfer from the heated surfaces, the local temperatures of these surfaces Tr were measured using thermocouples with a diameter of 0.1 mm, which were spot-soldered to the surfaces at intervals along the radial direction (r = 0, 9,17,25,32,40,4_9 mm). The air temperature distribution in the enclosure was measured using
Greek symbols heat transfer coefficient (W/(m2K)) b volumetric thermal expansion coefficient (1/K) k thermal conductivity (W/(mK)) m kinematic viscosity (m2/s)
a
Subscripts c cooling surface conv convective m average mid middle region r location relative to the center on a heated surface rad radiative up upper region 1d lower surface of first layer 1u upper surface of first layer 2u upper surface of second layer
thermocouples of the same material and diameter as above. The thermocouples were fitted on bamboo traverses 2 mm in diameter, which were moved horizontally in the direction of the diameter at the central height of each region. The temperature of the heated surfaces and the air in the enclosure were observed to vary with time under certain experimental conditions, although the heat balance of the system
Fig. 1. Experimental apparatus.
A. Horibe et al. / International Journal of Heat and Mass Transfer 55 (2012) 7072–7078
3. Results and discussion 3.1. Visualization of flow fields in the enclosure This section describes typical examples of the flow field, which represents the flow characteristics. Fig. 2 presents the measured instantaneous velocity vectors at l1 = 53 mm, l2 = 45 mm, l3 = 33 mm, and q = 188 W/m2. In the upper region, the fluid flowed along the upper heated surface of the first layer, from the edge of the heated surface toward the center. The current gathered around the center and
l1= 53mm
Cooling Plate
Heated Element (1st Layer)
l2= 45mm
was maintained. Accordingly, the temperatures of the heated surfaces and the air in the enclosure were measured at 30-s intervals over 20 min, and were estimated based on average values. The validity of the experiments in this study were verified by comparison with the results of previous studies of natural convection in fluid layers in a circular cylinder [12] and between two horizontal plates [1], both heated from below and cooled from above. To obtain accurate estimates, the apparatus used in this study was temporarily modified as follows: the heated surface was placed only on the bottom of the cylindrical pipe. The diameter of the pipe was adjusted to that of the heater. The configuration of the heated surface, the cooling plate, the adiabatic material, the experimental method, and the estimation of heat transfer were not modified. In [12] and [1], the equations Nu = 0.188 Ra0.288 and Nu = 0.183 Ra0.278 were proposed. To compare the results for a uniform heat flux plate with those obtained from the above equations for isothermal plates, the results for Nu were transformed via the relationship Ra⁄ = Ra Nu, and compared with those of [12] and [1]. The greatest differences were less than 6.5% and 13%, respectively. The present results were in good agreement with those [12] obtained from the equation for a circular cylinder with the same aspect ratio as the apparatus used here, although small differences appeared between the present data and the results [1] for a fluid layer between two horizontal plates. Consequently, we can infer that the experimental apparatus and method used in this study are valid. The flow field of the measurements was constructed using a particle image velocimetry (PIV) system that allowed two-dimensional planar measurements. The laser light source was a doublepulsed YAG laser with a 50 mJ/pulse. The light sheet was adjusted to the central axis of the enclosure. To reduce the scattering and reflection of the laser sheet, the inner surface of the enclosure was masked with black paper. The particle image was tracked by a CCD camera in the direction normal to the laser sheet, with a spatial resolution of 4 mm. The interrogation area within 3 mm of the side surface was slightly strained by the lens effect, because the enclosure was cylindrical in shape. In contrast, almost no strain appeared in the areas necessary for estimating the flow characteristics around the heated elements. The seeding generator was a Laskin nozzle type and the seeding particle was dioctyl sebacate (DOS), with a mean particle diameter of about 1 lm and a specific gravity of 0.916. The measurement technique was as follows: The experimental system was set up in thermal equilibrium. The enclosure was then filled with seeding particles. After again reaching thermal equilibrium, measurements were taken without insulation. The flow field was observed to vary periodically under some conditions, although the heat balance of the system was maintained. Therefore, to describe the flow characteristics, instantaneous velocity vector results were employed. Moreover, since the flow and temperature fields in the enclosure were nearly axisymmetric, the measured velocity vectors were shown only in a range from the central axis to the side surface of the enclosure. To enhance the measurement accuracy and spatial resolution, the measured area was divided.
Heated Element (2nd Layer) l3= 33mm
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0.1m/s
Fig. 2. Velocity vector (l1 = 53 mm, l2 = 45 mm, l3 = 33 mm, q = 188 W/m2).
subsequently ascended to the cooling plate. The fluid then flowed along the cooling plate and subsequently descended to the middle region along the side of the enclosure. Over time, the ascending flow in the direction of the cooling plate was observed to fluctuate periodically in the horizontal direction. In the middle region, the fluid flowed along the upper surface of the second layer and then ascended to the lower surface of the first layer. This fluid flowed along the lower surface of the first layer and then ascended to the upper region. Along the side of the enclosure, descending flow (shown in Fig. 2) and ascending flow appeared alternately over time. Therefore, the flow field between the heated surfaces became unsteady, and the ascending flow fluctuated horizontally. In the lower region, fluid was observed along the lower surface of the second layer. This flow variability over time was more stable than in the other regions. Fig. 3 presents the instantaneous velocity vector at l1 = 33 mm, l2 = 65 mm, l3 = 33 mm, and q = 188 W/m2. Here, the heated element of the first layer was moved closer to the cooling plate; the other conditions were the same as those shown in Fig. 2. Under these conditions, the vortex was observed between the cooling surface and the upper heated surface of the first layer. As time progressed, the vortex repeatedly appeared and disappeared, and moved from the side of the enclosure toward the center. The generation of this vortex motion can be explained by comparison with Fig. 2, which shows the flow along the heated surface. The ascending flow from the middle region increased with the height of this region. In contrast, the flow caused by the temperature difference between the upper surface of the first layer and the cooling surface was inhibited by the decreased height of the upper region. This finding suggests that vortex motion occurs when the accompanying flow of the rising current from the middle region significantly interferes with the ascending flow in the upper region. In the middle and lower regions, the flow variability over time was similar to that described in Fig. 2.
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Fig. 5 presents the instantaneous velocity vector in the upper region at l1 = 43 mm, l2 = 55 mm, and l3 = 33 mm. The measurements shown in Fig. 5(a) and (b) were taken when q was 95.5 W/m2 and 293 W/m2, respectively. In Fig. 5(a), the fluid flowed along the heated surface. However, as shown in Fig. 5(b), vortex motion appeared in the upper region when the heat flux was increased from 95.5 W/m2 to 293 W/m2. An increase in heat flux promotes the ascending flow from the middle region, and gives rise to vortex motion. In the middle and lower region, the flow fields, which are omitted in Fig. 5, were similar to those in Figs. 2 and 3. In summary, the flow characteristics exhibited two distinctive patterns in the upper region: vortex motion and flow along the heated surface. In the other regions, the fluid flowed along the heated surface in all cases. Clearly, the occurrence of vortex motion is influenced by the heights of the upper and middle regions and the heat flux.
l1= 33mm
Cooling Plate
l2= 65mm
Heated Element (1st Layer)
3.2. Air temperature profiles in the enclosure
l3= 33mm
Heated Element (2nd Layer)
0.1m/s
Fig. 3. Velocity vector (l1 = 33 mm, l2 = 65 mm, l3 = 33 mm, q = 188 W/m2).
Fig. 6 presents air temperature profiles in the enclosure for each of the flow characteristics. Flow along the heated surface occurred for l1 = 53 mm and l2 = 45 mm, and vortex motion appeared for l1 = 33 mm and l2 = 65 mm. In each experiment, l3 and q were held constant at 33 mm and 188 W/m2, respectively. The experimental conditions were the same as those shown in Figs. 2 and 3. In Fig. 6, DTair represents the temperature difference between air at the center height of each region and the cooling surface. r is the distance measured from the central axis of the enclosure. The temperature difference DTair in the upper region for l1 = 53 mm and l2 = 45 mm increased linearly with decreasing r, reaching a maximum value in the central area. This occurred because heat transfer from the heated surface increases as approaching the central area. In contrast, DTair for l1 = 33 mm and l2 = 65 mm attained a mini-
l1= 33mm
Cooling Plate
l1= 43mm
Cooling Plate
l2= 20mm
Heated Element (1st Layer)
Heated Element (2nd Layer)
Heated Element (1st Layer)
0.1m/s
0.1m/s
(a) q = 95.5 W/m2 2
Fig. 4. Velocity vector (l1 = 33 mm, l2 = 20 mm, l3 = 78 mm, q = 188 W/m ).
Fig. 4 presents a portion of the instantaneous velocity vector at l1 = 33 mm, l2 = 20 mm, l3 = 78 mm, and q = 188 W/m2. Here, the second layer was moved closer to the cooling plate; the other conditions remained the same as in Fig. 2. In the upper region, although the typical fluid flow was along the heated surface, the vortex was observed from time to time, as shown Fig. 4. Vortex motion was inadequately developed because the ascending flow to the upper region was inhibited by the decreased height of the middle region. The occurrence of vortex motion appears to be influenced by the height of the middle region, as well as the height of the upper region. In the middle region, the flow along the heated surface was observed to be the same as in Figs. 2 and 3. In the lower region, the flow field, which is omitted in Fig. 4, was similar to those in Figs. 2 and 3.
l1= 43mm
Cooling Plate
Heated Element (1st Layer)
0.1m/s
(b) q = 293 W/m2 Fig. 5. Velocity vector (l1 = 43 mm, l2 = 55 mm, l3 = 33 mm): (a) q = 95.5 W/m2; (b) q = 293 W/m2.
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loss Qloss_rad from the total heat loss Qloss, then dividing the result by the number of heated surfaces: Qloss_conv = (Qloss Qloss_rad)/4. The convective heat loss was estimated to average 13.8% of the total heat generated on the heaters. The local heat transfer coefficient is defined by the following equation:
30 q = 188 W/m2
25
l3 = 33 mm
ΔTair [K]
20 15 r=0
10 Cooler
Upper
Heater
5
Middle Lower
[mm] l1 l2
ar ¼ qr Upper Middle Lower
53 45 33 65
0 0
10
20
30
40 50 r [mm]
60
70
80
Fig. 6. Air temperature in the enclosure.
mum value in the central area. This occurred because the vortex, which is cooled by the cooling plate, moves toward the central region. In each case, in the middle and lower regions, DTair increased with decreasing r and reached a maximum value in the central area. Moreover, in the middle region, DTair was lower for l2 = 65 mm than for l2 = 45 mm. In contrast, in the lower region, the results for l3 = 33 mm were at the same level. Comparable experiments were performed using various heater layouts and heat fluxes, and the results were similar to those obtained above. Therefore, we can infer that the air temperature in the enclosure is strongly influenced by the flow characteristics and the height of the adjacent air space. 3.3. Local heat transfer characteristics The relevance of the flow to heat transfer characteristics was demonstrated with typical results. This section begins by describing our technique for estimating the local heat transfer coefficient of the heated surfaces. We obtained the local convective heat flux qr_conv by subtracting the local radiative heat flux on the heater qr_rad and the convective constituent of the heat loss through the acrylic enclosure per unit of heated surface area Qloss_conv/A from the amount of electric power provided to the heated surfaces per unit area q, as follows:
qr
conv
¼ q qr
rad
Q loss
conv =A:
ð1Þ
The local radiative heat flux qr_rad was simulated by the discrete transfer radiation method (DTRM) [13], using the STAR-CD commercial software. The thermal boundary conditions were defined as follows: The measured temperature profile of each heated surface was approximately expressed by a second- or third-order equation. The temperatures of the cooling surface and the side and bottom of the enclosure were set to the respective measured mean temperatures. Adiabatic conditions were applied to the side surfaces of the heated elements. The emissivity of each surface was also measured, and the results were: 0.21 for the upper and lower surfaces of the heated elements (copper films) and the inside surface of the cooling plate; 0.95 for the inside surfaces of the acrylic enclosure; and 0.73 for the side surfaces of the heated elements (phenol foam). Our findings confirm that local radiative heat flux is not significantly influenced by the position and orientation of the heated surface, and is independent of the heated surface temperature. Radiative heat transfer from the heaters was estimated to average 18.9% of the total heat generated on the heaters. Heat loss by conduction from the enclosure to the insulation Qloss was estimated for the measured temperature difference between the inside and outside of the Styrofoam. The radiative constituent of the heat loss Qloss_rad was calculated using the above simulation. The convective constituent of the heat loss Qloss_conv was obtained by subtracting the radiative constituent of the heat
conv =ðT r
TcÞ
ð2Þ
where Tr is the local heated surface temperature, and Tc denotes the cooling surface temperature, which is industrially useful. To determine the relevance of flow to heat transfer characteristics, we examined how the location of the first heated element affects heat transfer from the heated surfaces. Fig. 7 presents the local heat transfer coefficients relative to r for each heated surface and various values of l1 and l2. In all cases, l3 and q were held constant at 33 mm and 188 W/m2, respectively. Fig. 7(a) presents the results for the upper heated surface of the first layer. When l1 was greater than 53 mm, the local heat transfer coefficients were greatest at the edge of the heated surface, and decreased monotonically with r to a minimum value at r = 0. This occurred because the air temperature around the heater increased as approaching the center area. Conversely, below l1 = 43 mm, the heat transfer coefficients exceeded the values obtained above l1 = 53 mm, and the difference was notable in the center area. This occurred because the vortex, which is cooled by the cooling plate, moves toward the central region. Moreover, below l1 = 38 mm, the heat transfer coefficients remained almost constant, and the values were greater than those obtained for l1 = 43 mm. We can infer that the vortex motion does not develop adequately in the case of l1 = 43 mm. In other words, the flow field consists of both current along the heated surface and vortex motion. Fig. 7(b) presents the local heat transfer coefficients for the lower heated surface of the first layer for various values of l1 and l2. The coefficients generally decreased with decreasing r, because the fluid flowed along the heated surfaces in the middle region. Because increasing l2 led to an increase in the flow in the middle region, heat transfer was enhanced with increasing l2. These effects were especially noticeable in the center area, where the ascending flow was concentrated. Fig. 7(c) and (d) present the local heat transfer coefficients for the upper and lower heated surfaces of the second layer, respectively. In each case, the coefficients generally decreased with decreasing r. These results are similar to those shown in Fig. 7(b), with the current flowing along the heater. Moreover, Fig. 7(c) shows that increasing l2 tends to enhance heat transfer. In contrast, Fig. 7(d) presents coefficients that remain constant for various values of l1 and l2. This occurred because the regions adjacent to the heaters were varied in Fig. 7(c), but were held constant in Fig. 7(d). The following conclusions can be inferred from the above results: Vortex motion enhances heat transfer from the heated surfaces, especially in the center area. Heat transfer via the current flowing along a heated surface is influenced by the heights of the adjacent regions, and the effect of other regions is negligible. Comparable experiments were conducted using various heater layouts and heat fluxes, and the heat transfer characteristics were found to be similar to those described above. 3.4. Average heat transfer characteristics The heat transfer characteristics of the heated surfaces are estimated in terms of dimensionless numbers for each of the flow patterns. First, the method for distinguishing the flow pattern is presented. In the upper region, the flow characteristics exhibited two distinctive patterns: vortex motion and flow along the heated surface. In the other regions, the fluid flowed along the heated surfaces in all cases. Therefore, we focused on the conditions that pro-
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middle region interfered with the ascending flow in the upper region. The generation of vortex motion was affected by the flow fields of the upper and middle regions. Angeli et al. [8] and Quere [14] estimated the flow regimes for Ra and addressed the mechanism of flow transition. Consequently, the flow regimes of the upper and middle region were estimated using the following equations:
5
2
αr [W/m K]
4 3 l = 33 mm 2
l
Cooler 1
l 2 l
1
r
3
q = 188 W/m2 0 0
10
l1 l2
[mm] l1 l2
18 80 33 65 38 60
43 55 53 45 73 25
1st_top
20
30 r
40
50
Raup ¼ gbqm
60
Cooler
2
αr [W/m K]
1st_bottom
r
3
3
q = 188 W/m2 l = 33 mm
0 0
10
20
l1 l2
[mm] l1 l2
18 80 33 65 38 60
43 55 53 45 73 25
30 r
40
50
60
[mm]
(b) 1st_bottom 5 l
4
Cooler 1
l 2 l
r
3
2
conv 1d
þ qm
4 conv 2u Þ=2Þl2 =ka
m
ð4Þ
Ramid ¼ 1:9 102 Ra0:68 up : 2 1
αr [W/m K]
Ramid ¼ gbððqm
The heat flux in Eq. (4) was calculated by averaging qm_conv_1d and qm_conv_2u, which are the values for the heated surfaces adjacent to the middle region. The calculated Raup and Ramid at which the transitions from flow along the heated surface to vortex motion were observed, are plotted as denoted black circles in Fig. 8. Additionally, the flow patterns were distinguished by the visualizations of the flow fields. The results were expressed by the following equation:
1
l 2 l
ð3Þ
[mm]
5 l
m
and
(a) 1st_top
4
4 conv 1u l1 =ka
2nd_top
3 2 q = 188 W/m2 l = 33 mm
1 0 0
10
20
l1 l2
[mm] l1 l2
18 80 33 65 38 60
43 55 53 45 73 25
30 r
40
50
ð5Þ
In this study, it was obvious that the generation and enhancement of vortex motion are strongly affected by l1 and l2. Therefore, results obtained for various values of l1 and l2 are plotted in Fig. 8 as examples to estimate the flow transition. In all cases, l3 and q were held constant at 33 mm and 188 W/m2, respectively. The fluid flowed along the heated surface for l1 = 73 mm and l2 = 25 mm, and for l1 = 53 mm and l2 = 45 mm. The vortex was observed from time to time for l1 = 43 mm and l2 = 55 mm. The vortex appeared periodically and moved toward the center for l1 = 38 mm and l2 = 60 mm, and for l1 = 33 mm and l2 = 65 mm. As described above, the vortex developed with decreasing l1 and increasing l2. This is because the vortex occurs when the flow from the middle region significantly interferes with the ascending flow in the upper region. The vortex was almost stable for l1 = 18 mm and l2 = 80 mm, because little fluid flowed in the region between the cooling and heated surface when l1 decreased to 18 mm. Comparable estimations were conducted using various heater layouts and heat fluxes, and the flow patterns were determined within the range 2 104 < Raup < 1 107 as follows:
60
[mm]
l1 l2
(c) 2nd_top
Flow field
18 80 With Vortex Motion (Almost Stable) 33 65 With Vortex Motion (Developed) 38 60 With Vortex Motion (Developed)
5 l
4
53 45 Along Heated Surface
1
l 2 l
10 r
3
8
73 25 Along Heated Surface
2nd_bottom
Eq. (5) Conditions at Flow Transition
3
q = 188 W/m2
1
l3 = 33 mm 0 0
10
20
30 r
l1 l2
[mm] l1 l2
18 80 33 65 38 60
43 55 53 45 73 25
40
50
10
7
10
6
10
5
10
4
Flow with Vortex Motion *
2
Ra mid
2
αr [W/m K]
43 55 With Vortex Motion (Inadequately Developed)
Cooler
60
Flow along Heated Surface
[mm]
(d) 2nd_bottom Fig. 7. Local heat transfer coefficients for variable l1 and l2: (a) 1st_top; (b) 1st_bottom; (c) 2nd_top; (d) 2nd_bottom.
10
4
10
5
10
6
10
*
duced the vortex motion in the upper region. Vortex motion occurred when the flow that accompanied the rising flow from the
Ra up Fig. 8. Relationship between Raup and Ramid for flow regimes.
7
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differences in the height H and diameter R of the enclosure within the range 100 mm < H < 160 mm and 150 mm < R < 190 mm. The purpose of this study was to examine the relationship between flow and heat transfer characteristics in an enclosure containing parallel heaters. Accordingly, we focused on how the characteristics were affected by varying the interval between the heated plates and the heat flux without varying the height H or the diameter R of the enclosure. Within the range 1 104 < Ra⁄ < 3 107, we obtained the following conclusions:
20 Akino et al. [12] Chu et al. [1]
Nu
10
Flow with Vortex Motion Flow along Heated Surface 1 4
5
10
10
10
6
7
10
8
10
*
Ra
Fig. 9. Relationship between Num and Ra⁄.
(1) vortex motion,
upper region : Ramid > 1:9 102 Ra0:68 up
ð6Þ
(2) flow along the heated surfaces, upper region: regions excluding Eq. (6), middle and lower region.
(1) Flow characteristics exhibit two distinctive patterns: vortex motion and flow along the heated surface. (2) In the upper region, vortex motion occurs when the flow that accompanies the rising flow from the middle region interferes with the ascending flow from the upper heated surface of the first layer. The generation of vortex motion is influenced by the height of the upper and middle regions and the heat flux. (3) In the middle and lower regions, the flow circulates along the heated surfaces in all cases. (4) In the upper region, heat transfer is enhanced by the vortex motion. In the flow field along a heated surface, heat transfer generally increases with the heights of the adjacent region. (5) We defined an equation to determine flow characteristics. For each flow pattern, the Nusselt number is proportional to some power of the modified Rayleigh number.
The Nusselt number Nu and the modified Rayleigh number Ra⁄ were respectively normalized using the following equations:
Nu ¼ am lx =k
ð7Þ
and
Ra ¼
4 gbqm conv lx =ka
m
ð8Þ
where am is defined as the area integral average of the local heat transfer coefficients and lx is the height of the region adjacent to the heated surface. In fact, the characteristic lengths are l1 (for the upper heated surface of the first layer), l2 (for the lower surface of the first layer and the upper surface of the second layer), and l3 (for the lower heated surface of the second layer). The uncertainties of the experimental results were analyzed using the error propagation method [15]. The errors in Nu and Ra⁄ were less than 6.7% and 5.5%, respectively. Fig. 9 presents the relationships between Nu and Ra⁄ for the cases of vortex motion and flow along the heated surface, respectively. The flow patterns were distinguished by the above conditions. The results were within the range 1 104 < Ra⁄ < 3 107 for 18 mm < l1 < 93 mm, 20 mm < l2 < 87 mm, 18 mm < l3 < 88 mm, and 95.5 W/m2 < q < 293 W/m2. For each flow pattern, the Nusselt number was proportional to some power of the modified Rayleigh number. In the case of vortex motion, Nu was greater than the value for flow along the heated surface. Moreover, in the latter case, the relationships between Nu and Ra⁄ were similar to the results of previous studies of natural convection in fluid layers in a circular cylinder [12] and between two horizontal plates [1]. 4. Conclusions In this study, we experimentally investigated the heat transfer and flow characteristics of natural convection from horizontal parallel heated plates in an enclosure. In another experiment, we confirmed that the flow characteristics are only minimally affected by
References [1] T.Y. Chu, R.J. Goldstein, Turbulent convection in a horizontal layer of water, J. Fluid Mech. 60 (1) (1973) 141–159. [2] H. Tanaka, H. Miyata, Turbulent natural convection in a horizontal water layer heated from below, Int. J. Heat Mass Transfer 23 (9) (1980) 1273–1281. [3] Ivan Catton, The effect of insulating vertical walls on the onset of motion in a fluid heated from below, Int. J. Heat Mass Transfer 15 (4) (1972) 665–672. [4] J. Pallares, M.P. Arroyo, F.X. Grau, F. Giralt, Experimental laminar RayleighBénard convection in a cubical cavity at moderate Rayleigh and Prandtl numbers, Exp. Fluids 31 (2) (2001) 208–218. [5] Lawrence R. Mack, Harry C. Hardee, Natural convection between concentric spheres at low Rayleigh numbers, Int. J. Heat Mass Transfer 11 (3) (1968) 387– 396. [6] Ralph E. Powe, Robert O. Warrington, Jack A. Scanlan, Natural convective flow between a body and its spherical enclosure, Int. J. Heat Mass Transfer 23 (10) (1980) 1337–1350. [7] H.S. Yoon, D.H. Yu, M.Y. Ha, Y.G. Park, Three-dimensional natural convection in an enclosure with a sphere at different vertical locations, Int. J. Heat Mass Transfer 53 (15–16) (2010) 3143–3155. [8] D. Angeli, G.S. Barozzi, M.W. Collons, O.M. Kamiyo, A critical review of buoyancy – induced flow transition in horizontal annuli, Int. J. Thermal Sci. 49 (2010) 2231–2241. [9] J.P. Liu, W.Q. Tao, Numerical analysis of natural convection around a vertical channel in a rectangular enclosure, Heat Mass Transfer 31 (5) (1996) 313–321. [10] G.S. Barozzi, M.A. Corticelli, Natural convection in cavities containing internal sources, Heat Mass Transfer 36 (6) (2000) 473–480. [11] M. Keyhani, L. Chen, D.R. Pitts, The aspect ratio effect on natural convection in an enclosure with protruding heat sources, J. Heat Transfer 113 (4) (1991) 883–891. [12] N. Akino, T. Kunugi, Y. Shiina, M. Seki, Y. Okamoto, Natural convection in a horizontal silicone oil layer in a circular cylinder heated from below and cooled from above, Trans. JSME (ser. B) 55 (509) (1989) 152–158. [13] F.C. Lockwood, N.G. Shah, A new radiation solution method for incorporation in general combustion prediction procedures, in: Symposium (international) on combustion, vol. 18, no. 1, 1981, pp. 1405–1414. [14] P.L. Quere, Onset of unsteadiness, routes to chaos and simulation of chaotic flows in cavities heated from the side: a review of present status, in: G.F. Hewitt (Ed.), Proceeding of the Tenth International Heat Transfer Conference, vol. 1, Hemisphere Publishing Corporation, Brighton, UK, 1994, pp. 281–296. [15] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Fluid Sci. 1 (1988) 3–17.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental study of flow and heat transfer characteristics of natural convection in an enclosure with horizontal parallel heated plates Akihiko Horibe a, Rikio Shimoyama a,b,⇑, Naoto Haruki a, Akira Sanada b a b
Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama-shi, Okayama 700-8530, Japan Industrial Technology Center of Okayama Prefecture, 5301 Haga, Kita-ku, Okayama-shi, Okayama 701-1296, Japan
a r t i c l e
i n f o
Article history: Received 7 October 2011 Received in revised form 18 June 2012 Accepted 10 July 2012 Available online 4 August 2012 Keywords: Heat transfer Natural convection Parallel heated plates Enclosure Vortex motion Flow visualization
a b s t r a c t We conducted an experimental investigation of natural convection in an enclosure containing horizontal parallel heated plates. Our experimental setup was as follows: Two heated plates were arranged vertically in an enclosure. The temperature of the ceiling was maintained at a constant low temperature, while the other sides satisfied thermal insulation boundary conditions. We examined flow characteristics in the enclosure and heat transfer around the horizontal heated plates. In the region between the cooled ceiling and the upper heated surface, vortex motion occurred when the accompanying flow from the lower region interfered with the ascending flow. Heat transfer around the heated surface was enhanced by this vortex motion. In other regions, the flow circulated along the heated surfaces in all cases. Generally speaking, for each flow pattern, the Nusselt number was proportional to some power of the modified Rayleigh number. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The problem of natural convection heat transfer from horizontal parallel heated plates in enclosures has received much attention in recent years. In view of the increasing heat generation density inside electronic packages, issues related to thermal design are considered to be limiting factors in the performance of these devices. Although cooling is easily achieved by the use of fans, they often generate noise and decrease the reliability of electronic equipment. Therefore, natural convection has become a very important consideration in the thermal design of electronic packages. Due to the importance of certain features and designs, printed boards with heated elements tend to be oriented horizontally and arranged vertically. Moreover, outdoor electronic equipment is usually enclosed to provide waterproofing and dust resistance. Hence, the flow and heat transfer characteristics of this type of configuration significantly affect the thermal design of electronic packages. Over the years, numerous researchers have studied the problem of natural convection heat transfer in fluid layers confined between two horizontal plates, heated from below and cooled from above; see e.g. Chu and Goldstein [1], Tanaka and Miyata [2], Catton [3] and Pallares et al. [4]. Many other studies have fo⇑ Corresponding author at: Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama-shi, Okayama 700-8530, Japan. Tel.: +81 86 286 9600; fax: +81 86 286 9630. E-mail address: [email protected] (R. Shimoyama). 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.07.021
cused on natural convection around heated bodies in an enclosure; Mack and Hardee [5], Powe et al. [6], Yoon et al. [7] and Angeli et al. [8] investigated natural convective flow and heat transfer phenomena occurring between a heated body and an enclosure. However, these studies dealt only with individual spherical heated bodies. Liu and Tao [9] examined heat transfer and fluid flow characteristics around a channel in a rectangular enclosure. Barozzi and Carticelli [10] investigated natural convection in a cavity containing parallel heated plates. In each of these studies, the parallel plates were arranged vertically. Keyhani et al. [11] studied natural convection heat transfer in a rectangular enclosure with heat sources, but the heaters had a protruding shape and were mounted on a single vertical wall with uniform spacing. As noted above, to date no researchers have investigated natural convective flow and heat transfer phenomena in an enclosure containing horizontal parallel heated plates, and previous findings cannot be easily applied to this case. The main purpose of the present study was to describe hitherto unknown basic flow characteristics in an enclosure containing horizontal heated plates, and to determine the relationship between the flow and the heat transfer characteristics around the plates. The main focus was the effects of the interval between the heated plates and the heat flux, both of which strongly influence these characteristics. The experimental conditions were as follows: the enclosure was cylindrical, the two heated elements were arranged vertically, the heated surfaces were circular, the ceiling surface was maintained at a constant low
A. Horibe et al. / International Journal of Heat and Mass Transfer 55 (2012) 7072–7078
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Nomenclature a A g l1 l2
l3 Nu q Qloss r Ra⁄ T DTair
thermal diffusivity (m2/s) area of heated surface (m2) gravitational acceleration (m/s2) height of upper region (distance between cooling surface and upper heated surface of first layer) (m) height of middle region (distance between lower heated surface of first layer and upper heated surface of second layer) (m) height of lower region (distance between lower heated surface of second layer and bottom of enclosure) (m) Nusselt number, Nu = amlx/k heat flux on the heater (W/m2) heat loss from the enclosure (W) distance from the central axis of the enclosure (m) 4 modified Rayleigh number, Ra ¼ gbqm conv lx =kam temperature (K) temperature difference between the air at the center height of each region and the cooling surface (K)
temperature, and the other surfaces were insulated. These conditions were sufficiently simple to elucidate the basic characteristics. 2. Experimental apparatus and measurements The apparatus, schematically illustrated in Fig. 1, was comprised of an acrylic cylindrical enclosure, two heated elements, and a cooling plate. The heated elements were made of phenol foam insulation, 100 mm in diameter and 15 mm thick. Glass epoxy boards were glued onto the upper and lower surfaces of the phenol foam, with a 30-lm copper film on each board. The copper films were milled to a double spiral form with a width of 2 mm. Uniform heat flux conditions were realized by supplying electric power to the copper film. The amount of electric power provided to the heated surfaces per unit area q was varied from 95.5 to 293 W/m2. As Fig. 1 shows, the two heated elements were coaxially arranged in the acrylic cylindrical enclosure at the desired distances (18 mm < l1 < 93 mm, 20 mm < l2 < 87 mm, 18 mm < l3 < 88 mm), where l1 denotes the height of the upper region (the distance between the cooling surface and the upper heated surface of the first layer), l2 denotes the height of the middle region (the distance between the lower surface of the first layer and the upper surface of the second layer), and l3 denotes the height of the lower region (the distance between the lower surface of the second layer and the bottom of the enclosure). The heated elements were suspended on wires and oriented horizontally. The cooling plate was made from copper, and was maintained at Tc = 298 K by passing temperature-controlled water over the upper surface of the plate. The acrylic cylindrical enclosure was thermally insulated with glass wool and 80 mm of Styrofoam. Heat loss was estimated using thermocouples placed at the inner and outer surfaces of the Styrofoam, and was less than 17.1% of the total heat generated on the heaters. Heat transfer to the cooling plate was calculated using the difference between the cooling water temperatures at the inlet and outlet. The sum of the discharged heat and the heat transfer (calculated using the above methods) was estimated to be less than 5% of all generated heat. To estimate the heat transfer from the heated surfaces, the local temperatures of these surfaces Tr were measured using thermocouples with a diameter of 0.1 mm, which were spot-soldered to the surfaces at intervals along the radial direction (r = 0, 9,17,25,32,40,4_9 mm). The air temperature distribution in the enclosure was measured using
Greek symbols heat transfer coefficient (W/(m2K)) b volumetric thermal expansion coefficient (1/K) k thermal conductivity (W/(mK)) m kinematic viscosity (m2/s)
a
Subscripts c cooling surface conv convective m average mid middle region r location relative to the center on a heated surface rad radiative up upper region 1d lower surface of first layer 1u upper surface of first layer 2u upper surface of second layer
thermocouples of the same material and diameter as above. The thermocouples were fitted on bamboo traverses 2 mm in diameter, which were moved horizontally in the direction of the diameter at the central height of each region. The temperature of the heated surfaces and the air in the enclosure were observed to vary with time under certain experimental conditions, although the heat balance of the system
Fig. 1. Experimental apparatus.
A. Horibe et al. / International Journal of Heat and Mass Transfer 55 (2012) 7072–7078
3. Results and discussion 3.1. Visualization of flow fields in the enclosure This section describes typical examples of the flow field, which represents the flow characteristics. Fig. 2 presents the measured instantaneous velocity vectors at l1 = 53 mm, l2 = 45 mm, l3 = 33 mm, and q = 188 W/m2. In the upper region, the fluid flowed along the upper heated surface of the first layer, from the edge of the heated surface toward the center. The current gathered around the center and
l1= 53mm
Cooling Plate
Heated Element (1st Layer)
l2= 45mm
was maintained. Accordingly, the temperatures of the heated surfaces and the air in the enclosure were measured at 30-s intervals over 20 min, and were estimated based on average values. The validity of the experiments in this study were verified by comparison with the results of previous studies of natural convection in fluid layers in a circular cylinder [12] and between two horizontal plates [1], both heated from below and cooled from above. To obtain accurate estimates, the apparatus used in this study was temporarily modified as follows: the heated surface was placed only on the bottom of the cylindrical pipe. The diameter of the pipe was adjusted to that of the heater. The configuration of the heated surface, the cooling plate, the adiabatic material, the experimental method, and the estimation of heat transfer were not modified. In [12] and [1], the equations Nu = 0.188 Ra0.288 and Nu = 0.183 Ra0.278 were proposed. To compare the results for a uniform heat flux plate with those obtained from the above equations for isothermal plates, the results for Nu were transformed via the relationship Ra⁄ = Ra Nu, and compared with those of [12] and [1]. The greatest differences were less than 6.5% and 13%, respectively. The present results were in good agreement with those [12] obtained from the equation for a circular cylinder with the same aspect ratio as the apparatus used here, although small differences appeared between the present data and the results [1] for a fluid layer between two horizontal plates. Consequently, we can infer that the experimental apparatus and method used in this study are valid. The flow field of the measurements was constructed using a particle image velocimetry (PIV) system that allowed two-dimensional planar measurements. The laser light source was a doublepulsed YAG laser with a 50 mJ/pulse. The light sheet was adjusted to the central axis of the enclosure. To reduce the scattering and reflection of the laser sheet, the inner surface of the enclosure was masked with black paper. The particle image was tracked by a CCD camera in the direction normal to the laser sheet, with a spatial resolution of 4 mm. The interrogation area within 3 mm of the side surface was slightly strained by the lens effect, because the enclosure was cylindrical in shape. In contrast, almost no strain appeared in the areas necessary for estimating the flow characteristics around the heated elements. The seeding generator was a Laskin nozzle type and the seeding particle was dioctyl sebacate (DOS), with a mean particle diameter of about 1 lm and a specific gravity of 0.916. The measurement technique was as follows: The experimental system was set up in thermal equilibrium. The enclosure was then filled with seeding particles. After again reaching thermal equilibrium, measurements were taken without insulation. The flow field was observed to vary periodically under some conditions, although the heat balance of the system was maintained. Therefore, to describe the flow characteristics, instantaneous velocity vector results were employed. Moreover, since the flow and temperature fields in the enclosure were nearly axisymmetric, the measured velocity vectors were shown only in a range from the central axis to the side surface of the enclosure. To enhance the measurement accuracy and spatial resolution, the measured area was divided.
Heated Element (2nd Layer) l3= 33mm
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0.1m/s
Fig. 2. Velocity vector (l1 = 53 mm, l2 = 45 mm, l3 = 33 mm, q = 188 W/m2).
subsequently ascended to the cooling plate. The fluid then flowed along the cooling plate and subsequently descended to the middle region along the side of the enclosure. Over time, the ascending flow in the direction of the cooling plate was observed to fluctuate periodically in the horizontal direction. In the middle region, the fluid flowed along the upper surface of the second layer and then ascended to the lower surface of the first layer. This fluid flowed along the lower surface of the first layer and then ascended to the upper region. Along the side of the enclosure, descending flow (shown in Fig. 2) and ascending flow appeared alternately over time. Therefore, the flow field between the heated surfaces became unsteady, and the ascending flow fluctuated horizontally. In the lower region, fluid was observed along the lower surface of the second layer. This flow variability over time was more stable than in the other regions. Fig. 3 presents the instantaneous velocity vector at l1 = 33 mm, l2 = 65 mm, l3 = 33 mm, and q = 188 W/m2. Here, the heated element of the first layer was moved closer to the cooling plate; the other conditions were the same as those shown in Fig. 2. Under these conditions, the vortex was observed between the cooling surface and the upper heated surface of the first layer. As time progressed, the vortex repeatedly appeared and disappeared, and moved from the side of the enclosure toward the center. The generation of this vortex motion can be explained by comparison with Fig. 2, which shows the flow along the heated surface. The ascending flow from the middle region increased with the height of this region. In contrast, the flow caused by the temperature difference between the upper surface of the first layer and the cooling surface was inhibited by the decreased height of the upper region. This finding suggests that vortex motion occurs when the accompanying flow of the rising current from the middle region significantly interferes with the ascending flow in the upper region. In the middle and lower regions, the flow variability over time was similar to that described in Fig. 2.
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Fig. 5 presents the instantaneous velocity vector in the upper region at l1 = 43 mm, l2 = 55 mm, and l3 = 33 mm. The measurements shown in Fig. 5(a) and (b) were taken when q was 95.5 W/m2 and 293 W/m2, respectively. In Fig. 5(a), the fluid flowed along the heated surface. However, as shown in Fig. 5(b), vortex motion appeared in the upper region when the heat flux was increased from 95.5 W/m2 to 293 W/m2. An increase in heat flux promotes the ascending flow from the middle region, and gives rise to vortex motion. In the middle and lower region, the flow fields, which are omitted in Fig. 5, were similar to those in Figs. 2 and 3. In summary, the flow characteristics exhibited two distinctive patterns in the upper region: vortex motion and flow along the heated surface. In the other regions, the fluid flowed along the heated surface in all cases. Clearly, the occurrence of vortex motion is influenced by the heights of the upper and middle regions and the heat flux.
l1= 33mm
Cooling Plate
l2= 65mm
Heated Element (1st Layer)
3.2. Air temperature profiles in the enclosure
l3= 33mm
Heated Element (2nd Layer)
0.1m/s
Fig. 3. Velocity vector (l1 = 33 mm, l2 = 65 mm, l3 = 33 mm, q = 188 W/m2).
Fig. 6 presents air temperature profiles in the enclosure for each of the flow characteristics. Flow along the heated surface occurred for l1 = 53 mm and l2 = 45 mm, and vortex motion appeared for l1 = 33 mm and l2 = 65 mm. In each experiment, l3 and q were held constant at 33 mm and 188 W/m2, respectively. The experimental conditions were the same as those shown in Figs. 2 and 3. In Fig. 6, DTair represents the temperature difference between air at the center height of each region and the cooling surface. r is the distance measured from the central axis of the enclosure. The temperature difference DTair in the upper region for l1 = 53 mm and l2 = 45 mm increased linearly with decreasing r, reaching a maximum value in the central area. This occurred because heat transfer from the heated surface increases as approaching the central area. In contrast, DTair for l1 = 33 mm and l2 = 65 mm attained a mini-
l1= 33mm
Cooling Plate
l1= 43mm
Cooling Plate
l2= 20mm
Heated Element (1st Layer)
Heated Element (2nd Layer)
Heated Element (1st Layer)
0.1m/s
0.1m/s
(a) q = 95.5 W/m2 2
Fig. 4. Velocity vector (l1 = 33 mm, l2 = 20 mm, l3 = 78 mm, q = 188 W/m ).
Fig. 4 presents a portion of the instantaneous velocity vector at l1 = 33 mm, l2 = 20 mm, l3 = 78 mm, and q = 188 W/m2. Here, the second layer was moved closer to the cooling plate; the other conditions remained the same as in Fig. 2. In the upper region, although the typical fluid flow was along the heated surface, the vortex was observed from time to time, as shown Fig. 4. Vortex motion was inadequately developed because the ascending flow to the upper region was inhibited by the decreased height of the middle region. The occurrence of vortex motion appears to be influenced by the height of the middle region, as well as the height of the upper region. In the middle region, the flow along the heated surface was observed to be the same as in Figs. 2 and 3. In the lower region, the flow field, which is omitted in Fig. 4, was similar to those in Figs. 2 and 3.
l1= 43mm
Cooling Plate
Heated Element (1st Layer)
0.1m/s
(b) q = 293 W/m2 Fig. 5. Velocity vector (l1 = 43 mm, l2 = 55 mm, l3 = 33 mm): (a) q = 95.5 W/m2; (b) q = 293 W/m2.
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loss Qloss_rad from the total heat loss Qloss, then dividing the result by the number of heated surfaces: Qloss_conv = (Qloss Qloss_rad)/4. The convective heat loss was estimated to average 13.8% of the total heat generated on the heaters. The local heat transfer coefficient is defined by the following equation:
30 q = 188 W/m2
25
l3 = 33 mm
ΔTair [K]
20 15 r=0
10 Cooler
Upper
Heater
5
Middle Lower
[mm] l1 l2
ar ¼ qr Upper Middle Lower
53 45 33 65
0 0
10
20
30
40 50 r [mm]
60
70
80
Fig. 6. Air temperature in the enclosure.
mum value in the central area. This occurred because the vortex, which is cooled by the cooling plate, moves toward the central region. In each case, in the middle and lower regions, DTair increased with decreasing r and reached a maximum value in the central area. Moreover, in the middle region, DTair was lower for l2 = 65 mm than for l2 = 45 mm. In contrast, in the lower region, the results for l3 = 33 mm were at the same level. Comparable experiments were performed using various heater layouts and heat fluxes, and the results were similar to those obtained above. Therefore, we can infer that the air temperature in the enclosure is strongly influenced by the flow characteristics and the height of the adjacent air space. 3.3. Local heat transfer characteristics The relevance of the flow to heat transfer characteristics was demonstrated with typical results. This section begins by describing our technique for estimating the local heat transfer coefficient of the heated surfaces. We obtained the local convective heat flux qr_conv by subtracting the local radiative heat flux on the heater qr_rad and the convective constituent of the heat loss through the acrylic enclosure per unit of heated surface area Qloss_conv/A from the amount of electric power provided to the heated surfaces per unit area q, as follows:
qr
conv
¼ q qr
rad
Q loss
conv =A:
ð1Þ
The local radiative heat flux qr_rad was simulated by the discrete transfer radiation method (DTRM) [13], using the STAR-CD commercial software. The thermal boundary conditions were defined as follows: The measured temperature profile of each heated surface was approximately expressed by a second- or third-order equation. The temperatures of the cooling surface and the side and bottom of the enclosure were set to the respective measured mean temperatures. Adiabatic conditions were applied to the side surfaces of the heated elements. The emissivity of each surface was also measured, and the results were: 0.21 for the upper and lower surfaces of the heated elements (copper films) and the inside surface of the cooling plate; 0.95 for the inside surfaces of the acrylic enclosure; and 0.73 for the side surfaces of the heated elements (phenol foam). Our findings confirm that local radiative heat flux is not significantly influenced by the position and orientation of the heated surface, and is independent of the heated surface temperature. Radiative heat transfer from the heaters was estimated to average 18.9% of the total heat generated on the heaters. Heat loss by conduction from the enclosure to the insulation Qloss was estimated for the measured temperature difference between the inside and outside of the Styrofoam. The radiative constituent of the heat loss Qloss_rad was calculated using the above simulation. The convective constituent of the heat loss Qloss_conv was obtained by subtracting the radiative constituent of the heat
conv =ðT r
TcÞ
ð2Þ
where Tr is the local heated surface temperature, and Tc denotes the cooling surface temperature, which is industrially useful. To determine the relevance of flow to heat transfer characteristics, we examined how the location of the first heated element affects heat transfer from the heated surfaces. Fig. 7 presents the local heat transfer coefficients relative to r for each heated surface and various values of l1 and l2. In all cases, l3 and q were held constant at 33 mm and 188 W/m2, respectively. Fig. 7(a) presents the results for the upper heated surface of the first layer. When l1 was greater than 53 mm, the local heat transfer coefficients were greatest at the edge of the heated surface, and decreased monotonically with r to a minimum value at r = 0. This occurred because the air temperature around the heater increased as approaching the center area. Conversely, below l1 = 43 mm, the heat transfer coefficients exceeded the values obtained above l1 = 53 mm, and the difference was notable in the center area. This occurred because the vortex, which is cooled by the cooling plate, moves toward the central region. Moreover, below l1 = 38 mm, the heat transfer coefficients remained almost constant, and the values were greater than those obtained for l1 = 43 mm. We can infer that the vortex motion does not develop adequately in the case of l1 = 43 mm. In other words, the flow field consists of both current along the heated surface and vortex motion. Fig. 7(b) presents the local heat transfer coefficients for the lower heated surface of the first layer for various values of l1 and l2. The coefficients generally decreased with decreasing r, because the fluid flowed along the heated surfaces in the middle region. Because increasing l2 led to an increase in the flow in the middle region, heat transfer was enhanced with increasing l2. These effects were especially noticeable in the center area, where the ascending flow was concentrated. Fig. 7(c) and (d) present the local heat transfer coefficients for the upper and lower heated surfaces of the second layer, respectively. In each case, the coefficients generally decreased with decreasing r. These results are similar to those shown in Fig. 7(b), with the current flowing along the heater. Moreover, Fig. 7(c) shows that increasing l2 tends to enhance heat transfer. In contrast, Fig. 7(d) presents coefficients that remain constant for various values of l1 and l2. This occurred because the regions adjacent to the heaters were varied in Fig. 7(c), but were held constant in Fig. 7(d). The following conclusions can be inferred from the above results: Vortex motion enhances heat transfer from the heated surfaces, especially in the center area. Heat transfer via the current flowing along a heated surface is influenced by the heights of the adjacent regions, and the effect of other regions is negligible. Comparable experiments were conducted using various heater layouts and heat fluxes, and the heat transfer characteristics were found to be similar to those described above. 3.4. Average heat transfer characteristics The heat transfer characteristics of the heated surfaces are estimated in terms of dimensionless numbers for each of the flow patterns. First, the method for distinguishing the flow pattern is presented. In the upper region, the flow characteristics exhibited two distinctive patterns: vortex motion and flow along the heated surface. In the other regions, the fluid flowed along the heated surfaces in all cases. Therefore, we focused on the conditions that pro-
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middle region interfered with the ascending flow in the upper region. The generation of vortex motion was affected by the flow fields of the upper and middle regions. Angeli et al. [8] and Quere [14] estimated the flow regimes for Ra and addressed the mechanism of flow transition. Consequently, the flow regimes of the upper and middle region were estimated using the following equations:
5
2
αr [W/m K]
4 3 l = 33 mm 2
l
Cooler 1
l 2 l
1
r
3
q = 188 W/m2 0 0
10
l1 l2
[mm] l1 l2
18 80 33 65 38 60
43 55 53 45 73 25
1st_top
20
30 r
40
50
Raup ¼ gbqm
60
Cooler
2
αr [W/m K]
1st_bottom
r
3
3
q = 188 W/m2 l = 33 mm
0 0
10
20
l1 l2
[mm] l1 l2
18 80 33 65 38 60
43 55 53 45 73 25
30 r
40
50
60
[mm]
(b) 1st_bottom 5 l
4
Cooler 1
l 2 l
r
3
2
conv 1d
þ qm
4 conv 2u Þ=2Þl2 =ka
m
ð4Þ
Ramid ¼ 1:9 102 Ra0:68 up : 2 1
αr [W/m K]
Ramid ¼ gbððqm
The heat flux in Eq. (4) was calculated by averaging qm_conv_1d and qm_conv_2u, which are the values for the heated surfaces adjacent to the middle region. The calculated Raup and Ramid at which the transitions from flow along the heated surface to vortex motion were observed, are plotted as denoted black circles in Fig. 8. Additionally, the flow patterns were distinguished by the visualizations of the flow fields. The results were expressed by the following equation:
1
l 2 l
ð3Þ
[mm]
5 l
m
and
(a) 1st_top
4
4 conv 1u l1 =ka
2nd_top
3 2 q = 188 W/m2 l = 33 mm
1 0 0
10
20
l1 l2
[mm] l1 l2
18 80 33 65 38 60
43 55 53 45 73 25
30 r
40
50
ð5Þ
In this study, it was obvious that the generation and enhancement of vortex motion are strongly affected by l1 and l2. Therefore, results obtained for various values of l1 and l2 are plotted in Fig. 8 as examples to estimate the flow transition. In all cases, l3 and q were held constant at 33 mm and 188 W/m2, respectively. The fluid flowed along the heated surface for l1 = 73 mm and l2 = 25 mm, and for l1 = 53 mm and l2 = 45 mm. The vortex was observed from time to time for l1 = 43 mm and l2 = 55 mm. The vortex appeared periodically and moved toward the center for l1 = 38 mm and l2 = 60 mm, and for l1 = 33 mm and l2 = 65 mm. As described above, the vortex developed with decreasing l1 and increasing l2. This is because the vortex occurs when the flow from the middle region significantly interferes with the ascending flow in the upper region. The vortex was almost stable for l1 = 18 mm and l2 = 80 mm, because little fluid flowed in the region between the cooling and heated surface when l1 decreased to 18 mm. Comparable estimations were conducted using various heater layouts and heat fluxes, and the flow patterns were determined within the range 2 104 < Raup < 1 107 as follows:
60
[mm]
l1 l2
(c) 2nd_top
Flow field
18 80 With Vortex Motion (Almost Stable) 33 65 With Vortex Motion (Developed) 38 60 With Vortex Motion (Developed)
5 l
4
53 45 Along Heated Surface
1
l 2 l
10 r
3
8
73 25 Along Heated Surface
2nd_bottom
Eq. (5) Conditions at Flow Transition
3
q = 188 W/m2
1
l3 = 33 mm 0 0
10
20
30 r
l1 l2
[mm] l1 l2
18 80 33 65 38 60
43 55 53 45 73 25
40
50
10
7
10
6
10
5
10
4
Flow with Vortex Motion *
2
Ra mid
2
αr [W/m K]
43 55 With Vortex Motion (Inadequately Developed)
Cooler
60
Flow along Heated Surface
[mm]
(d) 2nd_bottom Fig. 7. Local heat transfer coefficients for variable l1 and l2: (a) 1st_top; (b) 1st_bottom; (c) 2nd_top; (d) 2nd_bottom.
10
4
10
5
10
6
10
*
duced the vortex motion in the upper region. Vortex motion occurred when the flow that accompanied the rising flow from the
Ra up Fig. 8. Relationship between Raup and Ramid for flow regimes.
7
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A. Horibe et al. / International Journal of Heat and Mass Transfer 55 (2012) 7072–7078
differences in the height H and diameter R of the enclosure within the range 100 mm < H < 160 mm and 150 mm < R < 190 mm. The purpose of this study was to examine the relationship between flow and heat transfer characteristics in an enclosure containing parallel heaters. Accordingly, we focused on how the characteristics were affected by varying the interval between the heated plates and the heat flux without varying the height H or the diameter R of the enclosure. Within the range 1 104 < Ra⁄ < 3 107, we obtained the following conclusions:
20 Akino et al. [12] Chu et al. [1]
Nu
10
Flow with Vortex Motion Flow along Heated Surface 1 4
5
10
10
10
6
7
10
8
10
*
Ra
Fig. 9. Relationship between Num and Ra⁄.
(1) vortex motion,
upper region : Ramid > 1:9 102 Ra0:68 up
ð6Þ
(2) flow along the heated surfaces, upper region: regions excluding Eq. (6), middle and lower region.
(1) Flow characteristics exhibit two distinctive patterns: vortex motion and flow along the heated surface. (2) In the upper region, vortex motion occurs when the flow that accompanies the rising flow from the middle region interferes with the ascending flow from the upper heated surface of the first layer. The generation of vortex motion is influenced by the height of the upper and middle regions and the heat flux. (3) In the middle and lower regions, the flow circulates along the heated surfaces in all cases. (4) In the upper region, heat transfer is enhanced by the vortex motion. In the flow field along a heated surface, heat transfer generally increases with the heights of the adjacent region. (5) We defined an equation to determine flow characteristics. For each flow pattern, the Nusselt number is proportional to some power of the modified Rayleigh number.
The Nusselt number Nu and the modified Rayleigh number Ra⁄ were respectively normalized using the following equations:
Nu ¼ am lx =k
ð7Þ
and
Ra ¼
4 gbqm conv lx =ka
m
ð8Þ
where am is defined as the area integral average of the local heat transfer coefficients and lx is the height of the region adjacent to the heated surface. In fact, the characteristic lengths are l1 (for the upper heated surface of the first layer), l2 (for the lower surface of the first layer and the upper surface of the second layer), and l3 (for the lower heated surface of the second layer). The uncertainties of the experimental results were analyzed using the error propagation method [15]. The errors in Nu and Ra⁄ were less than 6.7% and 5.5%, respectively. Fig. 9 presents the relationships between Nu and Ra⁄ for the cases of vortex motion and flow along the heated surface, respectively. The flow patterns were distinguished by the above conditions. The results were within the range 1 104 < Ra⁄ < 3 107 for 18 mm < l1 < 93 mm, 20 mm < l2 < 87 mm, 18 mm < l3 < 88 mm, and 95.5 W/m2 < q < 293 W/m2. For each flow pattern, the Nusselt number was proportional to some power of the modified Rayleigh number. In the case of vortex motion, Nu was greater than the value for flow along the heated surface. Moreover, in the latter case, the relationships between Nu and Ra⁄ were similar to the results of previous studies of natural convection in fluid layers in a circular cylinder [12] and between two horizontal plates [1]. 4. Conclusions In this study, we experimentally investigated the heat transfer and flow characteristics of natural convection from horizontal parallel heated plates in an enclosure. In another experiment, we confirmed that the flow characteristics are only minimally affected by
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