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Free convection in tilted rectangular enclosures heated at the bottom wall and vented by different slots-venting arrangements
Experimental Thermal and Fluid Science 28 (2004) 853–862 www.elsevier.com/locate/etfs
Free convection in tilted rectangular enclosures heated at the bottom wall and vented by different slots-venting arrangements S.A. Nada b
a,*
, M. Moawed
b
a Department of Mechanical Engineering, Benha High Institute of Technology, Benha 13512, Egypt Department of Mechanical Engineering, Faculty of Engineering, Zagazig University, Shoubra 108, Egypt
Received 24 July 2003; accepted 9 January 2004
Abstract Free convection from a tilted rectangular enclosure heated at the bottom wall and vented by uniform slots opening at different walls of the enclosure was experimentally investigated. The experiments were carried out to study the effects of venting arrangement, opening ratio and enclosure’s tilt angle on the passive cooling of the enclosure. The experiments were carried out at a constant heat flux of 250 W/m2 and for enclosure tilt angles ranging from 0 to 180. Three different venting arrangements of the air from the enclosure were studied: (1) top-venting arrangement, (2) side-venting arrangement, and (3) top and side-venting arrangement. Each venting arrangement was studied at different opening ratios of 1, 0.75, 0.5 and 0.25. The results showed that: (1) for top-venting arrangement, the Nusselt number decreases as the tilt angle of the enclosure increases, (2) for side-venting and side and top-venting arrangements, the Nusselt number increases as the tilt angle increases in the range [0, 90], then it decreases with the increase of the tilt angle, (3) for the three venting arrangements and at any tilt angle, the Nusselt number increases with the increase of the opening ratio of the slots, (4) for any tilt angle and at any opening ratio, the top and side-venting arrangement has the highest rate of cooling of the enclosure, and (5) for small tilt angles, the rate of cooling of the enclosure for top-venting arrangement was higher than that for side-venting arrangement, but with increasing tilt angle, the rate of cooling for side-venting arrangement becomes higher than that for top-venting arrangement. Correlations were developed for the three venting arrangements to predict the average Nusselt number of the enclosure in terms of the opening ratio and the enclosure tilt angle. 2004 Elsevier Inc. All rights reserved. Keywords: Free convection; Tilted enclosure; Venting arrangement; Opening ratio
1. Introduction Free convection from open cavity or vented enclosures has many engineering applications such as passive cooling of electronic equipment, energy conservations in building and solar heating and concentrating. Examples of the applications of the passive cooling of electronic equipments include compact power supplies, portable computers and telecommunications enclosures. The present study adds information on the area of the passive cooling of electronic equipments where heat transfer by free convection is the main cooling mechanism of the equipments. Many experimental and numerical studies have been carried out by previous investigators to study heat *
Corresponding author. Fax: +20-13-230297. E-mail address: [email protected] (S.A. Nada).
0894-1777/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2004.01.011
transfer in cavities or enclosures by free convection. The studies are classified either according to the type of the enclosure and if it was with or without venting or according to the heat source of the enclosure covered all or part of the area of one wall of the enclosure. For vented enclosures, most of the previous studies were carried out only for one wall of the enclosure (normally the top wall facing the bottom heated wall of the enclosure) fully open to the atmosphere. The other four walls of enclosure were adiabatically insulated. In these studies, the effects of the geometrical parameters of the enclosure on the cooling process were investigated. These geometrical parameters of the enclosure were: aspect ratio of the cavity, W =H (ratio of the width of the enclosure to the depth of the enclosure), opening ratio of the enclosure, OR (ratio between the area of the venting opening to the area of the heated wall); tilt angle of the enclosure (a), and the ratio of the area of the hot source
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Nomenclature A As F H h h I k kw L Nu DNu
area of a wall of the enclosure, m2 area of the heated board, m2 view factor, dimensionless depth of the enclosure, m local value of heat transfer coefficient, W/m2 K average value of heat transfer coefficient, W/m2 K electric current, A thermal conductivity of air, W/m K thermal conductivity of wall, W/m K length of enclosure, m average Nusselt number, dimensionless uncertainty in Nusselt number, dimensionless
to the area of the wall of the enclosure that has this hot source, (As =A). Also the effects of Grashof and Prandtl numbers on the heat transfer coefficient were investigated in many of these previous works. A summary of the studies on natural convection in electronic enclosures was provided by Lasance and Joshi [1]. Le Quere et al. [2], Penot [3], Showole and Tarasuk [4] and Angirasa et al. [5] studied numerically the heat transfer from fully open (OR ¼ 1) square cavity at different tilt angles. In these studies the four walls of the enclosure were isothermally at the same temperature. The studies were carried out for different ranges of Grashof number (Gr) between 103 and 107 and at different aspect ratio (As =A). The studies showed that the aspect ratio and the tilt angle affect the flow field within the cavity and the heat transfer coefficient. Chan and Tien [6,7], Angriasa et al. [8], Mohamad [9], Balaji and Venkateshan [10] and Lin and Xin [11] investigated numerically the heat transfer from fully open square horizontal cavity. In these studies the bottom horizontal wall of the cavity was isothermal at high temperature and the other walls were adiabatically insulated. Different ranges of Grashof number were studied. Miyamoto et al. [12] presented a two dimensional numerical study of the natural convection heat transfer from fully and partially open tilted cavity. Two opening ratios 0.5 and 1 were studied. All the walls of the cavity were isothermally at the same temperature. Chakroun et al. [13] investigated experimentally the effect of the opening ratio of the cavity on the heat transfer coefficient in a tilted partially open square cavity. In this study the bottom surface of the cavity was heated with a constant heat flux and the other side walls were adiabatically insulated. The opening in the top wall was one opening at the center. The study showed the increase of the heat transfer coefficient with increasing the opening ratio. Elsayed and Chakroun [14] studied experimentally the effect of the place of the
OR q qc qr T Ts t DT a e r
opening ratio, dimensionless heat transfer by free convection, W heat losses by conduction, W heat losses by radiation, W locale temperature of the heated board, C average surface temperature of the heated board, C thickness of enclosure’s wall, m temperature difference across enclosure wall thickness, C tilt angle of enclosure, rad emissivity of the heated board Stefan–Boltzmann constant
opening on the passive cooling process of a tilted partially open square cavity. The bottom surface of the cavity was heated with a constant heat flux and the other four side walls were adiabatically insulated. Four positions (centered, shifted to the top, shifted to the bottom and uniformly distributed) to the opening in the top wall was studied. Adams et al. [15] and Yu and Joshi [16] studied numerically and experimentally the process of passive cooling of discretely heated enclosures by combined conduction, convection and radiation. They found that both conduction and radiation affects the rate of cooling of the enclosure and cannot be neglected. More recently, Yu and Joshi [17] conducted an experimental flow visualizations and temperature measurements to investigate the passive air cooling of a discrete flush type heat source placed in a compact partially open horizontal enclosure. The effects of power levels, opening sizes, enclosure aspect ratios and opening configurations on the thermal performance of the enclosure were investigated. As shown above, most of the previous studies of vented cavity or enclosure had a common feature that the enclosure or the cavity was either top-vented or horizontally placed with the heat source placed at the bottom of the enclosure. Also, most of the studies considered the cavity or enclosure was vented by fully open or one partially opening at the center of the top wall or shifted from the center. To the author’s knowledge, none of these studies have covered the case when the enclosure is tilted at any angle and the opening of the enclosure is uniformly distributed using slots at the different walls of the enclosure. This geometry is of special importance in the applications of passive cooling of electronic equipments specially, in the design process. In the present work, the enclosure is tilted and partially open with uniformly distributed slots opening at the different walls of the enclosure. Three different arrange-
S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862
855
g q" OR=0.25
α
q" α
q"
q" OR=0.50
α
α
q" OR=0.75
α
α
q" α
α Top-venting
q" α
q"
q" OR=1.0
q"
α Side-venting
q" α Top and side-venting
Fig. 1. Venting arrangements and opening ratios that are considered in the present work.
ments of venting the air from the enclosure were studied: (1) top-venting arrangement (slots are uniformly distributed in the top wall of the enclosure), (2) side-venting arrangement (slots are uniformly distributed in two opposite side walls of the enclosure), and (3) top and sideventing arrangement (slots are uniformly distributed in the top and two opposite side walls of the enclosure). For each venting arrangement, four different opening ratios (ratio between the openings area of the enclosure to the area of the bottom heated wall of the enclosure) were examined (OR ¼ 0.25, 0.5, 0.75 and 1). The different venting arrangements and the opening ratios of the enclosure that were considered in the present work are shown in Fig. 1. For the different venting arrangements and the opening ratios, the experiments were carried out at tilt angle a (measured from the horizontal) varies from 0 to 180 with an increment of 30. The heat flux was kept constant for all experiments at 250 W/m2 .
2. Experimental setup and procedure 2.1. Experimental setup The experimental setup is shown in Fig. 2. It consists of a rectangular enclosure of internal dimensions
W ¼ 200 mm, H ¼ 160 mm and L ¼ 320 mm. The bottom side of the enclosure, where the heat source is fixed, was made of two sandwiched layers. The internal layer was made of 10 mm thick Baklite plate having a thermal conductivity of 0.21 W/m K and the outer layer was made of 8 mm thick Plexiglass plate having a thermal conductivity of 0.192 W/m K. A heated printed wiring board having dimensions 200 · 320 mm and emissivity 0.15 was mounted internally on the bottom wall of the enclosure. The other walls of the enclosure were made of Plexiglass of 8 mm thick. All walls of the enclosure, except the wall having the slot openings, were thermally insulated with a 5-cm thick glass wool to minimize heat losses from the enclosure. The enclosure was mounted on a rotatable frame to vary the tilt angle of the enclosure. The tilt angle was measured using a protractor fixed on the frame. To obtain a natural convection environment by preventing any wind to affect natural convection during the tests, the experimental set up was placed inside 1-m wide plastic square box which was open from the two sides normal to the direction of gravity. The printed wiring board was connected with a DC power supply to control the power input to the board. The voltage and the current supplied to the board were measured by a digital voltmeter and an ammeter of
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S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862 slots
protractor
W= 2
0
00
32
H=160
L=
enclosure rotating axis
stand
least 4 h before steady state conditions were achieved. The steady state condition was considered to be achieved when the differences in the measured temperatures were not changed by more than 0.2 C over 20 min. When steady state conditions were established, the readings of all thermocouples, the input power and the ambient temperature were recorded. The rate of heat losses by radiation and conduction through the sides of the enclosure were calculated and subtracted from the input power to obtain the rate of heat transfer by free convection through the openings of the enclosure. For each venting arrangement and each opening ratio shown in Fig. 1, seven experimental runs were carried out at different tilt angles varies from 0 to 180 at increments of 30.
3. Data reduction The energy balance for the enclosure gives
Fig. 2. Schematic diagram of the experimental set up.
VI ¼ q þ qc þ qr y
1 2 3 4 5 6
heated board bakalit Plexiglass wall slots opening glass wall insulation thermocouple junction
4 3
x
6 2
1
cross sectional view
5
thermocouple locations
Fig. 3. Cross-sectional view and thermocouples locations along the test section.
accuracy 0.025%. The surface temperature distribution of the board was measured using 11 thermocouples (type k) distributed equally spaced along the axes of the board (see Fig. 3). To estimate the heat losses across the walls of the enclosure, two thermocouples (type k) were fixed across the thickness of each blind wall of the enclosure (see Fig. 3). The ambient temperature outside the enclosure was measured by a separate thermocouple (type k) placed at the bottom of the plastic box containing the set up. All the thermocouples were calibrated in a constant temperature path and a measurement accuracy of ±0.2 C was obtained. All the temperature signals were acquired with a data acquisition system and sent into a PC for data recording. 2.2. Experimental procedure After adjusting the input power for an experiment at 250 W/m2 , the experiment was allowed to run for at
ð1Þ
where I and V are the electric current and the voltage input to the electric board, q is the heat transfer by free convection from the board through the openings of the enclosure, qc is the heat losses by conduction through the walls of the enclosure and qr is the heat transfer by radiation from the electric board to the surroundings as seen through the openings of the enclosure. The conduction heat losses through the walls of the enclosure are the sum of the heat losses through the bottom heated wall of the enclosure and the heat losses through the other blind walls of the enclosure. This is expressed as X qc ¼ kw Aj DTj =t ð2Þ where j is the wall identification number, kw is the thermal conductivity of the wall of the enclosure, A is the area of a side wall of the enclosure, t is the thickness of the walls of the enclosure, and DTj is the temperature difference between the inner and outer surfaces of the jth wall, respectively. The radiation heat loss from the board through the opening wall of the enclosure was estimated as follows: h i 4 4 Ar T s þ 273 ðT1 þ 273Þ qr ¼ ð3Þ ð1 eÞ=ðeÞ þ 1=Fs where A is the area of the board, T s is the average temperature of the board, e is its emissivity and Fs is the view factor between the board and the opening wall of the enclosure. In the last equation it was assumed that the opening surface of the enclosure (surrounding) is a black body at T1 . The view factors Fs between the board and the opening wall of the enclosure was calculated from the graphs and expressions given by Incropera and De Witt [18] and Suryanarayana [19]. The conduction
S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862
heat losses through the enclosure walls and the radiation heat losses were within 12% and 4% of the input heat, respectively. The local heat transfer coefficient between the board and surrounding is given by: q h¼ ð4Þ AðTs T1 Þ where Ts is the local temperature of the board and T1 is the ambient temperature measured at the bottom of the plastic box containing the experimental set up. Temperature measurements showed that the variation of the temperature of the board was very negligible along the x-axis and varies slightly along the y-axis in a manner depending on the venting arrangement and the tilt angle. Therefore, in calculating the average heat transfer coefficient the board was divided into 6-equal sections along the y-axis as shown in Fig. 3. The average heat transfer coefficient can be expressed as ð5Þ
where Ts;i is the temperature of the ith section of the board which was taken as the average of the two thermocouple reading on the boundary of this section along the y-axis. The average Nusselt number is defined as Nu ¼
hH k
measurement, 0.5% for the thermal conductivity of air, 2% for the thermal conductivity of plexiglass, and 5% for the emissivity of the wiring board. It was found that the uncertainty for the data of Nu ranges from 5% to 10%.
4. Results and discussions The experimental work was performed to study the effects of the venting arrangement, the opening ratio and the tilt angle of the enclosure on the heat transfer coefficient by free convection from the enclosure. For each venting arrangement and slot opening ratio, the heat transfer coefficient was obtained for tilt angle varies from 0 to 180 with increments of 30. The average temperature of the heated board and the average Nusselt number was found to be dependent on the tilt angle, the opening ratio and the venting arrangement. Figs. 4–9 include the variation of the average temperature of the board and the average Nusselt number with the tilt angle for various venting arrangements and different opening ratios.
40
ð6Þ
where H is the height of the enclosure and k is the thermal conductivity of the air in the enclosure. Combining Eqs. (1)–(6) together, the expression of Nu is as follows: 2 i¼6 X H X 1 4VI Nu ¼ kw Aj DTj =ðtj Þ 6Ak i¼1 Ts;i T1 3 4 4 Ar T s þ 273 ðT1 þ 273Þ 5 þ ð7Þ ð1 eÞ=ðeÞ þ 1=Fs
30
20
10 correlation OR=1.0
The last equation is in the form
OR=0.75
60
OR=0.50
ð8Þ
where x1 to xn are all the variable that affect the experimental determination of Nu. The uncertainty DNu in the value of Nu was estimated based on the procedure of Holman and Gajda [20] and is expressed as follows
2 i¼n 2 X oNu DNu ¼ Dxi ð9Þ oxi i¼1 where Dxi is the uncertainty in the xi variable. The uncertainty in the various variables used in the determination of the Nusselt number were: 0.25% for the electric current I, 0.25% for the electric volt V , 0.2 C for any temperature measurement, 0.001 m for any distance
OR=0.25 Nusselt Number
Nu ¼ f ðx1 ; x2 ; x3 ; . . . ; xn Þ
Top-venting
Ts-T∞,°C
i¼6 1 X q h¼ 6A i¼1 ðTs;i T1 Þ
857
40
20
0
30
60 90 120 enclosure tilt angle, deg.
150
180
Fig. 4. Variation of wall temperature and Nusselt number with tilt angle for top-venting.
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Side-venting
Top and side-venting
40
30
Ts-T∞,°C
Ts-T∞,°C
30
20
20
correlation
10
correlation
10
OR=1.0
OR=1.0
OR=0.75 60
OR=0.75
OR=0.50
60
40
Nusselt Number
Nusselt Number
OR=0.25
OR=0.50
40
20
20 0
30
60
90
120
150
180
enclosure tilt angle, deg.
Fig. 5. Variation of wall temperature and Nusselt number with tilt angle for side-venting.
0
30
60
90
120
150
180
enclosure tilt angle, deg.
Fig. 6. Variation of wall temperature and Nusselt number with tilt angle for top and side-venting.
4.1. Effect of tilt angle Figs. 4–6 present the variation of the average temperature difference between the board and the surrounding, and the average Nusselt number versus the tilt angle of the enclosure with the opening ratio as a parameter for the three cases of venting arrangements. For top-venting arrangement, Fig. 4 shows that: (i) for a < 90 the change in the tilt angle has negligible effect on the average temperature and Nusselt number at OR ¼ 1.0 and 0.75, however at OR ¼ 0.25 and 0.5 the average Nusselt number decreases very slowly with the increase of tilt angle, and (ii) for a > 90, the average wall temperature increases and the average Nusselt number decreases more rapidly with the increase of the tilt angle. These variations can be attributed to the buoyancy driven flow which causes the heat transfer from the enclosure. For a < 90, free convection occurs upward the heated board and the flow is driven by descending and ascending parcels of the fluid, respectively as shown in Fig. 10(a). This circulation of the air in the enclosure causes heat transfer in the same direction of the buoyancy force (upward direction). For a > 90 heat is transferred in the downward direction
opposite to the direction of the buoyancy force and a stagnant zone of air starts to exist at the top of the enclosure (see Fig. 10(a)). This reduces the fraction of the surface area of the heated wall that derives the flow through the enclosure which leads to high wall temperature and low Nusselt number. As the tilt angle increases the stagnant zone of the air in the enclosure increases and this decreases the fraction of the surface area of the heated wall to derive the flow through the enclosure which leads to the decrease of the Nusselt number. Figs. 5 and 6 show that for side-venting and top and side-venting arrangements and at any opening ratio the average temperature of the board decreases and the average Nusselt number increases with the increase of the tilt angle of the enclosure from 0 to 90, then the average temperature increases and the average Nusselt number decreases with the increase of the tilt angle of the enclosure from 90 to 180. The rate of decreasing of the temperature and the rate of increasing of Nusselt number with the increase of the tilt angle from 0 to 90 is small and becomes more rapidly with the increase of the tilt angle from 90 to 180. These variations of the average temperature and the average Nusselt number
S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862 OR=1.0
OR=0.5
correlation
correlation 60
60
Top-venting
Top-venting Side-venting
Side-venting
top and side-venting Nusselt Number
Nusselt Number
top and side-venting 40
40
20
20
0
30
60 90 120 enclosure tilt angle, deg.
150
180
Fig. 7. Variation of Nusselt number with tilt angle for different venting arrangements at OR ¼ 0.5.
OR=0.75 correlation 60
Top-venting Side-venting top and side-venting
Nusselt Number
859
40
20
0
30
60 90 120 enclosure tilt angle, deg.
150
180
Fig. 8. Variation of Nusselt number with tilt angle for different venting arrangements at OR ¼ 0.75.
with the tilt angle can be attributed to buoyancy driven flow which causes the heat transfer from the enclosure. Starting from a ¼ 0, like top-venting enclosure, free convection occurs upward the heated wall. In this case the buoyancy driven force is normal to the heated wall and the flow is driven by descending and ascending parcels of the fluid. In the case of side-venting arrangement, the upward motion of the hot air is resisted by the blind top wall of the enclosure. This makes air to change its direction horizontally to escape from the top portion of the openings in the side walls (see Fig. 10(b)). But in the case of top and side-venting this hot air escape directly from the openings in the top wall (see Fig. 10(c)). As the tilt angle increases to approach 90 (vertical enclosure), the heated board inclined to ap-
0
30
60 90 120 enclosure tilt angle, deg.
150
180
Fig. 9. Variation of Nusselt number with tilt angle for different venting arrangements at OR ¼ 1.0.
proach the direction of the buoyancy driving force and this increases the convection currents from the heated board and increases the rate of heat transfer. At the same time, the resistance of the convection currents caused by the blind top wall of the enclosure in the case of side-venting decreases with increasing the tilt angle in the range 0 < a < 90, and this also causes the increase of the rate of heat transfer. Increasing the tilt angle beyond 90 the problems becomes similar to free convection from a downward-facing heated inclined surface, and the rate of heat transfer decreases as a increases in the range 90 < a < 180 (see Suryanarayana [19]). At a ¼ 180 the problems becomes similar to free convection from downward-facing heated horizontal plate and in this case the buoyancy force is normal to the surface, and the tendency of the hot air ascend is impeded by the plate. The air must move horizontally before it can ascend from the slot openings of the side walls (see Fig. 10(b) and (c)). 4.2. Effect of opening ratio Figs. 4–6 show the effect of opening ratio on the average temperature of the board and the average Nusselt number for the three venting arrangements. As shown in the figures, for any venting arrangement the average temperature of the board decreases and the average Nusselt number increases as the opening ratio of the slots increases. When the opening ratio decreases, the resistance to the circulation motion of the air in the enclosure (i.e. the resistance to the convection currents to escape from the enclosure) increases and this leads to slower replacement of the hot air by cold air and this result in an increase of the average temperature of the board and a decrease of the heat transfer coefficient.
860
S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862
g
q" α
(a)
q"
(b)
q"
(c) Fig. 10. A sketch of the convection current from the enclosure. (a) Top-venting arrangement, (b) side-venting arrangement, (c) top and side-venting arrangement.
Also Figs. 4–6 show that the curves of the Nusselt number for the different opening ratios converge to each other as the tilt angle increases from 90 to 180. This means that the effect of the opening ratio on the Nusselt number decreases as the tilt angle increases from 90 to 180. This can be attributed to the increase of the stagnant zone of the air in this range of tilt angle. The effect of the opening ratio vanishes at a ¼ 180 where the air is completely stagnant for any opening ratio and the air at the bottom of the enclosure must moves horizontally before it can ascend from the bottom edges of the side walls of the enclosure. 4.3. Effect of venting arrangement Figs. 7–9 show the effect of the venting arrangements on the average Nusselt number for opening ratios of 0.5, 0.75 and 1, respectively. The figures show that at any tilt angle and opening ratio the Nusselt numbers for top and side-venting arrangement are larger than those for topventing and for side-venting arrangements. The figures
also show that at small a the differences between the Nusselt numbers for top-venting and side-venting are within the experimental uncertainty but the trend shows that the Nusselt numbers for top-venting is always larger than that for side-venting. Increasing a the Nusselt number for top-venting decreases and that for side venting increases and the two Nusselt numbers equalized at a certain a lies in the range 0 6 a 6 90. Beyond this tilt angle the Nusselt number for side-venting arrangement becomes larger than that for top-venting arrangement. This effect of the venting arrangements on Nusselt number can be attributed to the resistance of the circulation motion of air through the cavity. This air circulation resistance is small for the case of top and side-venting arrangement. For smaller a: the resistance of air circulation for top-venting arrangement is smaller than that for side-venting arrangement. As a increase the resistance in top-venting arrangement increases but that for side-venting arrangement decreases until equalization is obtained then the resistance for topventing becomes larger than that for side-venting.
S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862
5. Empirical correlations Three different empirical correlations were developed to fit the experimental data in Figs. 4–6 for the three venting arrangements. The expressions for these correlations are as follows:
Nu ¼ ð14:97 11:34ðcos2 0:5a 3:67 cos 0:5aÞÞOR0:19 ð10Þ (b) Side-venting arrangement (0:25 6 OR 6 1:0) Nu ¼ ð17:98 51:29 cos 0:5aðcos2 0:5a 0:67 ð11Þ
(c) Top and side-venting arrangement (0:5 6 OR 6 1:0) Nu ¼ ð17:65 54:7 cos 0:5aðcos2 0:5a 0:608 cos 0:5a 0:878ÞÞOR0:12
Rayleigh number ¼ 9.5 · 108 while that of Elsayed and Chakroun [14] was at 3.9 · 108 . Therefore, the difference agrees with the fact that the Nusselt number increases exponentially with the increase of Rayleigh number.
7. Conclusions
(a) Top-venting arrangement (0:25 6 OR 6 1:0)
cos 0:5a 0:75ÞÞOR0:085
861
ð12Þ
Figs. 4–6 depict comparisons between these correlations and experimental data. The agreement between these correlations and the corresponding experimental data is within the experimental uncertainty. The above correlations are valid only for W =H ¼ 1:25 and As =A ¼ 1 and at thermally insulated enclosure walls and input heat flux of 250 W/m2 . More experimental data are needed to cover a wide range of W =H , As =A and heat flux. It was possible, however, to use these correlations in addition to correlations of previous works which relate Nusselt number with W =H , As =A and heat flux to approximately predict Nusselt number at different conditions than the tested ones.
6. Comparison with literature Comparison of the present work with that in the literature is difficult. The reason is that the present work was carried out at boundary conditions, geometrical conditions, and venting arrangements different from those available in the literature. It was possible, however, to compare the trend of the present data of topventing arrangement with that of Elsayed and Chakroun [14] who carried out experimental work for the determination of Nusselt number for top-vented tilted partially open cavity. Both works showed the decrease of the Nusselt number with the increase of tilt angle and the decrease of the opening ratio. The Nusselt number of the present work was higher than that of Elsayed and Chakroun [14] by 25–100% according to the tilt angle and the opening ratio. This difference can be explained based on the Rayleigh numbers at which both works were carried out. The present work was carried out at
Free convection heat transfer from rectangular, tilted partially open enclosures has been investigated experimentally. Three different venting arrangements were presented; top-venting, side-venting, and top and sideventing. In the three cases, the openings were on the form of slots distributed uniformly along the walls of the enclosure having the venting. For each venting arrangement, the experiments were carried out at four different opening ratios 0.25, 0.5, 0.75 and 1.0 and for enclosure tilt angles ranging from 0 to 180 at increments of 30 and at a constant heat flux of 250 W/m2 . Conduction and radiation losses are taken into account in the determination of the average Nusselt number of the enclosure. For the top-venting arrangement, the Nusselt number decreases as the tilt angle increases. For side-venting and top and side-venting arrangements, the Nusselt number increases slightly as the tilt angle increases until the tilt angle reaches 90, then it decreases with the increase of the tilt angle. For the three venting arrangements, the Nusselt number increases with the increase in opening ratio. For any opening ratio and at any tilt angle the Nusselt number for top and sideventing arrangement was higher than those of topventing and side-venting arrangements. For any opening ratio and at smaller tilt angle, the Nusselt number of top-venting arrangement was higher than that for sideventing arrangement, and the opposite is true at higher tilt angle. Three empirical correlations were developed for the three venting arrangements to give the average Nusselt number in terms of the opening ratio and tilt angle.
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S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862 inclined open cavities, ASME Journal of Heat Transfer 115 (1993) 592–605. D. Angirasa, M.J.B.M. Pourquie, F.T.M. Nieuwstadt, Numerical study of transient and steady laminar buoyancy-driven flows and heat transfer in a square open cavity, Numerical Heat Transfer, Part A 22 (1992) 223–239. Y.L. Chan, C.L. Tien, A numerical study of two dimensional laminar natural convection in shallow open cavities, International Journal of Heat and Mass Transfer 28 (1985) 603–612. Y.L. Chan, C.L. Tien, Laminar natural coin shallow open cavities, ASME Journal of Heat Transfer 108 (1986) 305–309. D. Angirasa, I.G. Eggels, F.T.M. Nieuwstadt, Numerical simulation of transient natural convection from an isothermal cavity open on a side, Numerical Heat Transfer, Part A 28 (1995) 755–768. A.A. Mohamad, Natural convection in open cavities and slots, Numerical Heat Transfer, Part A 27 (1995) 705–716. C. Balaji, S.P. Venkateshan, Correlations for free convection and surface radiation in a square cavity, International Journal of Heat and Fluid Flow 15 (3) (1994) 249–251. C.X. Lin, M.D. Xin, Transient turbulent free convection in an open cavity, Institution of Chemical Engineers Symposium Series 1 (1992) 515–521. M. Miyamoto, T.H. Kuehn, R.J. Goldstein, Y. Katoh, Two dimensional laminar natural convection heat transfer from a fully or partially open square cavity, Numerical Heat Transfer 15 (A) (1989) 411–430.
[13] W. Chakroun, M.M. Elsayed, S.F. Al-Fahd, Experimental measurements of heat transfer coefficient in a partially/fully opened tilted cavity, ASME Journal of Solar Energy Engineering 119 (1997) 298–303. [14] M.M. Elsayed, W. Chakroun, Effect of aperture geometry on heat transfer in tilted partially open cavities, ASME Journal of Heat Transfer 121 (1999) 819–827. [15] V.H. Adams, Y. Joshi, D.L. Blackburn, Three-dimensional study of combined conduction, radiation, and natural convection from discrete heat sources in a horizontal narrow-aspect-ratio enclosure, ASME Journal of Heat Transfer 121 (1999) 992– 1001. [16] E. Yu, Y.K. Joshi, Heat transfer in discretely heated side-vented compact enclosures by combined conduction, natural convection, and radiation, ASME Journal of Heat Transfer 121 (1999) 1002– 1010. [17] E. Yu, Y.K. Joshi, Natural convection air cooling of electronic components in partially open compact horizontal enclosures, IEEE Transaction on Components and Packaging Technologies 23 (1) (2000) 14–22. [18] F.P. Incropera, D.P. De Witt, Introduction to Heat Transfer, Wiley, New York, 1990. [19] N.V. Suryanarayana, Engineering Heat Transfer, West Publishing Company, New York, 1995. [20] J.P. Holman, W.J. Gajda, Experimental Methods for Engineers, McGraw Hill, New York, 1989.
Free convection in tilted rectangular enclosures heated at the bottom wall and vented by different slots-venting arrangements S.A. Nada b
a,*
, M. Moawed
b
a Department of Mechanical Engineering, Benha High Institute of Technology, Benha 13512, Egypt Department of Mechanical Engineering, Faculty of Engineering, Zagazig University, Shoubra 108, Egypt
Received 24 July 2003; accepted 9 January 2004
Abstract Free convection from a tilted rectangular enclosure heated at the bottom wall and vented by uniform slots opening at different walls of the enclosure was experimentally investigated. The experiments were carried out to study the effects of venting arrangement, opening ratio and enclosure’s tilt angle on the passive cooling of the enclosure. The experiments were carried out at a constant heat flux of 250 W/m2 and for enclosure tilt angles ranging from 0 to 180. Three different venting arrangements of the air from the enclosure were studied: (1) top-venting arrangement, (2) side-venting arrangement, and (3) top and side-venting arrangement. Each venting arrangement was studied at different opening ratios of 1, 0.75, 0.5 and 0.25. The results showed that: (1) for top-venting arrangement, the Nusselt number decreases as the tilt angle of the enclosure increases, (2) for side-venting and side and top-venting arrangements, the Nusselt number increases as the tilt angle increases in the range [0, 90], then it decreases with the increase of the tilt angle, (3) for the three venting arrangements and at any tilt angle, the Nusselt number increases with the increase of the opening ratio of the slots, (4) for any tilt angle and at any opening ratio, the top and side-venting arrangement has the highest rate of cooling of the enclosure, and (5) for small tilt angles, the rate of cooling of the enclosure for top-venting arrangement was higher than that for side-venting arrangement, but with increasing tilt angle, the rate of cooling for side-venting arrangement becomes higher than that for top-venting arrangement. Correlations were developed for the three venting arrangements to predict the average Nusselt number of the enclosure in terms of the opening ratio and the enclosure tilt angle. 2004 Elsevier Inc. All rights reserved. Keywords: Free convection; Tilted enclosure; Venting arrangement; Opening ratio
1. Introduction Free convection from open cavity or vented enclosures has many engineering applications such as passive cooling of electronic equipment, energy conservations in building and solar heating and concentrating. Examples of the applications of the passive cooling of electronic equipments include compact power supplies, portable computers and telecommunications enclosures. The present study adds information on the area of the passive cooling of electronic equipments where heat transfer by free convection is the main cooling mechanism of the equipments. Many experimental and numerical studies have been carried out by previous investigators to study heat *
Corresponding author. Fax: +20-13-230297. E-mail address: [email protected] (S.A. Nada).
0894-1777/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2004.01.011
transfer in cavities or enclosures by free convection. The studies are classified either according to the type of the enclosure and if it was with or without venting or according to the heat source of the enclosure covered all or part of the area of one wall of the enclosure. For vented enclosures, most of the previous studies were carried out only for one wall of the enclosure (normally the top wall facing the bottom heated wall of the enclosure) fully open to the atmosphere. The other four walls of enclosure were adiabatically insulated. In these studies, the effects of the geometrical parameters of the enclosure on the cooling process were investigated. These geometrical parameters of the enclosure were: aspect ratio of the cavity, W =H (ratio of the width of the enclosure to the depth of the enclosure), opening ratio of the enclosure, OR (ratio between the area of the venting opening to the area of the heated wall); tilt angle of the enclosure (a), and the ratio of the area of the hot source
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Nomenclature A As F H h h I k kw L Nu DNu
area of a wall of the enclosure, m2 area of the heated board, m2 view factor, dimensionless depth of the enclosure, m local value of heat transfer coefficient, W/m2 K average value of heat transfer coefficient, W/m2 K electric current, A thermal conductivity of air, W/m K thermal conductivity of wall, W/m K length of enclosure, m average Nusselt number, dimensionless uncertainty in Nusselt number, dimensionless
to the area of the wall of the enclosure that has this hot source, (As =A). Also the effects of Grashof and Prandtl numbers on the heat transfer coefficient were investigated in many of these previous works. A summary of the studies on natural convection in electronic enclosures was provided by Lasance and Joshi [1]. Le Quere et al. [2], Penot [3], Showole and Tarasuk [4] and Angirasa et al. [5] studied numerically the heat transfer from fully open (OR ¼ 1) square cavity at different tilt angles. In these studies the four walls of the enclosure were isothermally at the same temperature. The studies were carried out for different ranges of Grashof number (Gr) between 103 and 107 and at different aspect ratio (As =A). The studies showed that the aspect ratio and the tilt angle affect the flow field within the cavity and the heat transfer coefficient. Chan and Tien [6,7], Angriasa et al. [8], Mohamad [9], Balaji and Venkateshan [10] and Lin and Xin [11] investigated numerically the heat transfer from fully open square horizontal cavity. In these studies the bottom horizontal wall of the cavity was isothermal at high temperature and the other walls were adiabatically insulated. Different ranges of Grashof number were studied. Miyamoto et al. [12] presented a two dimensional numerical study of the natural convection heat transfer from fully and partially open tilted cavity. Two opening ratios 0.5 and 1 were studied. All the walls of the cavity were isothermally at the same temperature. Chakroun et al. [13] investigated experimentally the effect of the opening ratio of the cavity on the heat transfer coefficient in a tilted partially open square cavity. In this study the bottom surface of the cavity was heated with a constant heat flux and the other side walls were adiabatically insulated. The opening in the top wall was one opening at the center. The study showed the increase of the heat transfer coefficient with increasing the opening ratio. Elsayed and Chakroun [14] studied experimentally the effect of the place of the
OR q qc qr T Ts t DT a e r
opening ratio, dimensionless heat transfer by free convection, W heat losses by conduction, W heat losses by radiation, W locale temperature of the heated board, C average surface temperature of the heated board, C thickness of enclosure’s wall, m temperature difference across enclosure wall thickness, C tilt angle of enclosure, rad emissivity of the heated board Stefan–Boltzmann constant
opening on the passive cooling process of a tilted partially open square cavity. The bottom surface of the cavity was heated with a constant heat flux and the other four side walls were adiabatically insulated. Four positions (centered, shifted to the top, shifted to the bottom and uniformly distributed) to the opening in the top wall was studied. Adams et al. [15] and Yu and Joshi [16] studied numerically and experimentally the process of passive cooling of discretely heated enclosures by combined conduction, convection and radiation. They found that both conduction and radiation affects the rate of cooling of the enclosure and cannot be neglected. More recently, Yu and Joshi [17] conducted an experimental flow visualizations and temperature measurements to investigate the passive air cooling of a discrete flush type heat source placed in a compact partially open horizontal enclosure. The effects of power levels, opening sizes, enclosure aspect ratios and opening configurations on the thermal performance of the enclosure were investigated. As shown above, most of the previous studies of vented cavity or enclosure had a common feature that the enclosure or the cavity was either top-vented or horizontally placed with the heat source placed at the bottom of the enclosure. Also, most of the studies considered the cavity or enclosure was vented by fully open or one partially opening at the center of the top wall or shifted from the center. To the author’s knowledge, none of these studies have covered the case when the enclosure is tilted at any angle and the opening of the enclosure is uniformly distributed using slots at the different walls of the enclosure. This geometry is of special importance in the applications of passive cooling of electronic equipments specially, in the design process. In the present work, the enclosure is tilted and partially open with uniformly distributed slots opening at the different walls of the enclosure. Three different arrange-
S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862
855
g q" OR=0.25
α
q" α
q"
q" OR=0.50
α
α
q" OR=0.75
α
α
q" α
α Top-venting
q" α
q"
q" OR=1.0
q"
α Side-venting
q" α Top and side-venting
Fig. 1. Venting arrangements and opening ratios that are considered in the present work.
ments of venting the air from the enclosure were studied: (1) top-venting arrangement (slots are uniformly distributed in the top wall of the enclosure), (2) side-venting arrangement (slots are uniformly distributed in two opposite side walls of the enclosure), and (3) top and sideventing arrangement (slots are uniformly distributed in the top and two opposite side walls of the enclosure). For each venting arrangement, four different opening ratios (ratio between the openings area of the enclosure to the area of the bottom heated wall of the enclosure) were examined (OR ¼ 0.25, 0.5, 0.75 and 1). The different venting arrangements and the opening ratios of the enclosure that were considered in the present work are shown in Fig. 1. For the different venting arrangements and the opening ratios, the experiments were carried out at tilt angle a (measured from the horizontal) varies from 0 to 180 with an increment of 30. The heat flux was kept constant for all experiments at 250 W/m2 .
2. Experimental setup and procedure 2.1. Experimental setup The experimental setup is shown in Fig. 2. It consists of a rectangular enclosure of internal dimensions
W ¼ 200 mm, H ¼ 160 mm and L ¼ 320 mm. The bottom side of the enclosure, where the heat source is fixed, was made of two sandwiched layers. The internal layer was made of 10 mm thick Baklite plate having a thermal conductivity of 0.21 W/m K and the outer layer was made of 8 mm thick Plexiglass plate having a thermal conductivity of 0.192 W/m K. A heated printed wiring board having dimensions 200 · 320 mm and emissivity 0.15 was mounted internally on the bottom wall of the enclosure. The other walls of the enclosure were made of Plexiglass of 8 mm thick. All walls of the enclosure, except the wall having the slot openings, were thermally insulated with a 5-cm thick glass wool to minimize heat losses from the enclosure. The enclosure was mounted on a rotatable frame to vary the tilt angle of the enclosure. The tilt angle was measured using a protractor fixed on the frame. To obtain a natural convection environment by preventing any wind to affect natural convection during the tests, the experimental set up was placed inside 1-m wide plastic square box which was open from the two sides normal to the direction of gravity. The printed wiring board was connected with a DC power supply to control the power input to the board. The voltage and the current supplied to the board were measured by a digital voltmeter and an ammeter of
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protractor
W= 2
0
00
32
H=160
L=
enclosure rotating axis
stand
least 4 h before steady state conditions were achieved. The steady state condition was considered to be achieved when the differences in the measured temperatures were not changed by more than 0.2 C over 20 min. When steady state conditions were established, the readings of all thermocouples, the input power and the ambient temperature were recorded. The rate of heat losses by radiation and conduction through the sides of the enclosure were calculated and subtracted from the input power to obtain the rate of heat transfer by free convection through the openings of the enclosure. For each venting arrangement and each opening ratio shown in Fig. 1, seven experimental runs were carried out at different tilt angles varies from 0 to 180 at increments of 30.
3. Data reduction The energy balance for the enclosure gives
Fig. 2. Schematic diagram of the experimental set up.
VI ¼ q þ qc þ qr y
1 2 3 4 5 6
heated board bakalit Plexiglass wall slots opening glass wall insulation thermocouple junction
4 3
x
6 2
1
cross sectional view
5
thermocouple locations
Fig. 3. Cross-sectional view and thermocouples locations along the test section.
accuracy 0.025%. The surface temperature distribution of the board was measured using 11 thermocouples (type k) distributed equally spaced along the axes of the board (see Fig. 3). To estimate the heat losses across the walls of the enclosure, two thermocouples (type k) were fixed across the thickness of each blind wall of the enclosure (see Fig. 3). The ambient temperature outside the enclosure was measured by a separate thermocouple (type k) placed at the bottom of the plastic box containing the set up. All the thermocouples were calibrated in a constant temperature path and a measurement accuracy of ±0.2 C was obtained. All the temperature signals were acquired with a data acquisition system and sent into a PC for data recording. 2.2. Experimental procedure After adjusting the input power for an experiment at 250 W/m2 , the experiment was allowed to run for at
ð1Þ
where I and V are the electric current and the voltage input to the electric board, q is the heat transfer by free convection from the board through the openings of the enclosure, qc is the heat losses by conduction through the walls of the enclosure and qr is the heat transfer by radiation from the electric board to the surroundings as seen through the openings of the enclosure. The conduction heat losses through the walls of the enclosure are the sum of the heat losses through the bottom heated wall of the enclosure and the heat losses through the other blind walls of the enclosure. This is expressed as X qc ¼ kw Aj DTj =t ð2Þ where j is the wall identification number, kw is the thermal conductivity of the wall of the enclosure, A is the area of a side wall of the enclosure, t is the thickness of the walls of the enclosure, and DTj is the temperature difference between the inner and outer surfaces of the jth wall, respectively. The radiation heat loss from the board through the opening wall of the enclosure was estimated as follows: h i 4 4 Ar T s þ 273 ðT1 þ 273Þ qr ¼ ð3Þ ð1 eÞ=ðeÞ þ 1=Fs where A is the area of the board, T s is the average temperature of the board, e is its emissivity and Fs is the view factor between the board and the opening wall of the enclosure. In the last equation it was assumed that the opening surface of the enclosure (surrounding) is a black body at T1 . The view factors Fs between the board and the opening wall of the enclosure was calculated from the graphs and expressions given by Incropera and De Witt [18] and Suryanarayana [19]. The conduction
S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862
heat losses through the enclosure walls and the radiation heat losses were within 12% and 4% of the input heat, respectively. The local heat transfer coefficient between the board and surrounding is given by: q h¼ ð4Þ AðTs T1 Þ where Ts is the local temperature of the board and T1 is the ambient temperature measured at the bottom of the plastic box containing the experimental set up. Temperature measurements showed that the variation of the temperature of the board was very negligible along the x-axis and varies slightly along the y-axis in a manner depending on the venting arrangement and the tilt angle. Therefore, in calculating the average heat transfer coefficient the board was divided into 6-equal sections along the y-axis as shown in Fig. 3. The average heat transfer coefficient can be expressed as ð5Þ
where Ts;i is the temperature of the ith section of the board which was taken as the average of the two thermocouple reading on the boundary of this section along the y-axis. The average Nusselt number is defined as Nu ¼
hH k
measurement, 0.5% for the thermal conductivity of air, 2% for the thermal conductivity of plexiglass, and 5% for the emissivity of the wiring board. It was found that the uncertainty for the data of Nu ranges from 5% to 10%.
4. Results and discussions The experimental work was performed to study the effects of the venting arrangement, the opening ratio and the tilt angle of the enclosure on the heat transfer coefficient by free convection from the enclosure. For each venting arrangement and slot opening ratio, the heat transfer coefficient was obtained for tilt angle varies from 0 to 180 with increments of 30. The average temperature of the heated board and the average Nusselt number was found to be dependent on the tilt angle, the opening ratio and the venting arrangement. Figs. 4–9 include the variation of the average temperature of the board and the average Nusselt number with the tilt angle for various venting arrangements and different opening ratios.
40
ð6Þ
where H is the height of the enclosure and k is the thermal conductivity of the air in the enclosure. Combining Eqs. (1)–(6) together, the expression of Nu is as follows: 2 i¼6 X H X 1 4VI Nu ¼ kw Aj DTj =ðtj Þ 6Ak i¼1 Ts;i T1 3 4 4 Ar T s þ 273 ðT1 þ 273Þ 5 þ ð7Þ ð1 eÞ=ðeÞ þ 1=Fs
30
20
10 correlation OR=1.0
The last equation is in the form
OR=0.75
60
OR=0.50
ð8Þ
where x1 to xn are all the variable that affect the experimental determination of Nu. The uncertainty DNu in the value of Nu was estimated based on the procedure of Holman and Gajda [20] and is expressed as follows
2 i¼n 2 X oNu DNu ¼ Dxi ð9Þ oxi i¼1 where Dxi is the uncertainty in the xi variable. The uncertainty in the various variables used in the determination of the Nusselt number were: 0.25% for the electric current I, 0.25% for the electric volt V , 0.2 C for any temperature measurement, 0.001 m for any distance
OR=0.25 Nusselt Number
Nu ¼ f ðx1 ; x2 ; x3 ; . . . ; xn Þ
Top-venting
Ts-T∞,°C
i¼6 1 X q h¼ 6A i¼1 ðTs;i T1 Þ
857
40
20
0
30
60 90 120 enclosure tilt angle, deg.
150
180
Fig. 4. Variation of wall temperature and Nusselt number with tilt angle for top-venting.
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S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862 40
Side-venting
Top and side-venting
40
30
Ts-T∞,°C
Ts-T∞,°C
30
20
20
correlation
10
correlation
10
OR=1.0
OR=1.0
OR=0.75 60
OR=0.75
OR=0.50
60
40
Nusselt Number
Nusselt Number
OR=0.25
OR=0.50
40
20
20 0
30
60
90
120
150
180
enclosure tilt angle, deg.
Fig. 5. Variation of wall temperature and Nusselt number with tilt angle for side-venting.
0
30
60
90
120
150
180
enclosure tilt angle, deg.
Fig. 6. Variation of wall temperature and Nusselt number with tilt angle for top and side-venting.
4.1. Effect of tilt angle Figs. 4–6 present the variation of the average temperature difference between the board and the surrounding, and the average Nusselt number versus the tilt angle of the enclosure with the opening ratio as a parameter for the three cases of venting arrangements. For top-venting arrangement, Fig. 4 shows that: (i) for a < 90 the change in the tilt angle has negligible effect on the average temperature and Nusselt number at OR ¼ 1.0 and 0.75, however at OR ¼ 0.25 and 0.5 the average Nusselt number decreases very slowly with the increase of tilt angle, and (ii) for a > 90, the average wall temperature increases and the average Nusselt number decreases more rapidly with the increase of the tilt angle. These variations can be attributed to the buoyancy driven flow which causes the heat transfer from the enclosure. For a < 90, free convection occurs upward the heated board and the flow is driven by descending and ascending parcels of the fluid, respectively as shown in Fig. 10(a). This circulation of the air in the enclosure causes heat transfer in the same direction of the buoyancy force (upward direction). For a > 90 heat is transferred in the downward direction
opposite to the direction of the buoyancy force and a stagnant zone of air starts to exist at the top of the enclosure (see Fig. 10(a)). This reduces the fraction of the surface area of the heated wall that derives the flow through the enclosure which leads to high wall temperature and low Nusselt number. As the tilt angle increases the stagnant zone of the air in the enclosure increases and this decreases the fraction of the surface area of the heated wall to derive the flow through the enclosure which leads to the decrease of the Nusselt number. Figs. 5 and 6 show that for side-venting and top and side-venting arrangements and at any opening ratio the average temperature of the board decreases and the average Nusselt number increases with the increase of the tilt angle of the enclosure from 0 to 90, then the average temperature increases and the average Nusselt number decreases with the increase of the tilt angle of the enclosure from 90 to 180. The rate of decreasing of the temperature and the rate of increasing of Nusselt number with the increase of the tilt angle from 0 to 90 is small and becomes more rapidly with the increase of the tilt angle from 90 to 180. These variations of the average temperature and the average Nusselt number
S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862 OR=1.0
OR=0.5
correlation
correlation 60
60
Top-venting
Top-venting Side-venting
Side-venting
top and side-venting Nusselt Number
Nusselt Number
top and side-venting 40
40
20
20
0
30
60 90 120 enclosure tilt angle, deg.
150
180
Fig. 7. Variation of Nusselt number with tilt angle for different venting arrangements at OR ¼ 0.5.
OR=0.75 correlation 60
Top-venting Side-venting top and side-venting
Nusselt Number
859
40
20
0
30
60 90 120 enclosure tilt angle, deg.
150
180
Fig. 8. Variation of Nusselt number with tilt angle for different venting arrangements at OR ¼ 0.75.
with the tilt angle can be attributed to buoyancy driven flow which causes the heat transfer from the enclosure. Starting from a ¼ 0, like top-venting enclosure, free convection occurs upward the heated wall. In this case the buoyancy driven force is normal to the heated wall and the flow is driven by descending and ascending parcels of the fluid. In the case of side-venting arrangement, the upward motion of the hot air is resisted by the blind top wall of the enclosure. This makes air to change its direction horizontally to escape from the top portion of the openings in the side walls (see Fig. 10(b)). But in the case of top and side-venting this hot air escape directly from the openings in the top wall (see Fig. 10(c)). As the tilt angle increases to approach 90 (vertical enclosure), the heated board inclined to ap-
0
30
60 90 120 enclosure tilt angle, deg.
150
180
Fig. 9. Variation of Nusselt number with tilt angle for different venting arrangements at OR ¼ 1.0.
proach the direction of the buoyancy driving force and this increases the convection currents from the heated board and increases the rate of heat transfer. At the same time, the resistance of the convection currents caused by the blind top wall of the enclosure in the case of side-venting decreases with increasing the tilt angle in the range 0 < a < 90, and this also causes the increase of the rate of heat transfer. Increasing the tilt angle beyond 90 the problems becomes similar to free convection from a downward-facing heated inclined surface, and the rate of heat transfer decreases as a increases in the range 90 < a < 180 (see Suryanarayana [19]). At a ¼ 180 the problems becomes similar to free convection from downward-facing heated horizontal plate and in this case the buoyancy force is normal to the surface, and the tendency of the hot air ascend is impeded by the plate. The air must move horizontally before it can ascend from the slot openings of the side walls (see Fig. 10(b) and (c)). 4.2. Effect of opening ratio Figs. 4–6 show the effect of opening ratio on the average temperature of the board and the average Nusselt number for the three venting arrangements. As shown in the figures, for any venting arrangement the average temperature of the board decreases and the average Nusselt number increases as the opening ratio of the slots increases. When the opening ratio decreases, the resistance to the circulation motion of the air in the enclosure (i.e. the resistance to the convection currents to escape from the enclosure) increases and this leads to slower replacement of the hot air by cold air and this result in an increase of the average temperature of the board and a decrease of the heat transfer coefficient.
860
S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862
g
q" α
(a)
q"
(b)
q"
(c) Fig. 10. A sketch of the convection current from the enclosure. (a) Top-venting arrangement, (b) side-venting arrangement, (c) top and side-venting arrangement.
Also Figs. 4–6 show that the curves of the Nusselt number for the different opening ratios converge to each other as the tilt angle increases from 90 to 180. This means that the effect of the opening ratio on the Nusselt number decreases as the tilt angle increases from 90 to 180. This can be attributed to the increase of the stagnant zone of the air in this range of tilt angle. The effect of the opening ratio vanishes at a ¼ 180 where the air is completely stagnant for any opening ratio and the air at the bottom of the enclosure must moves horizontally before it can ascend from the bottom edges of the side walls of the enclosure. 4.3. Effect of venting arrangement Figs. 7–9 show the effect of the venting arrangements on the average Nusselt number for opening ratios of 0.5, 0.75 and 1, respectively. The figures show that at any tilt angle and opening ratio the Nusselt numbers for top and side-venting arrangement are larger than those for topventing and for side-venting arrangements. The figures
also show that at small a the differences between the Nusselt numbers for top-venting and side-venting are within the experimental uncertainty but the trend shows that the Nusselt numbers for top-venting is always larger than that for side-venting. Increasing a the Nusselt number for top-venting decreases and that for side venting increases and the two Nusselt numbers equalized at a certain a lies in the range 0 6 a 6 90. Beyond this tilt angle the Nusselt number for side-venting arrangement becomes larger than that for top-venting arrangement. This effect of the venting arrangements on Nusselt number can be attributed to the resistance of the circulation motion of air through the cavity. This air circulation resistance is small for the case of top and side-venting arrangement. For smaller a: the resistance of air circulation for top-venting arrangement is smaller than that for side-venting arrangement. As a increase the resistance in top-venting arrangement increases but that for side-venting arrangement decreases until equalization is obtained then the resistance for topventing becomes larger than that for side-venting.
S.A. Nada, M. Moawed / Experimental Thermal and Fluid Science 28 (2004) 853–862
5. Empirical correlations Three different empirical correlations were developed to fit the experimental data in Figs. 4–6 for the three venting arrangements. The expressions for these correlations are as follows:
Nu ¼ ð14:97 11:34ðcos2 0:5a 3:67 cos 0:5aÞÞOR0:19 ð10Þ (b) Side-venting arrangement (0:25 6 OR 6 1:0) Nu ¼ ð17:98 51:29 cos 0:5aðcos2 0:5a 0:67 ð11Þ
(c) Top and side-venting arrangement (0:5 6 OR 6 1:0) Nu ¼ ð17:65 54:7 cos 0:5aðcos2 0:5a 0:608 cos 0:5a 0:878ÞÞOR0:12
Rayleigh number ¼ 9.5 · 108 while that of Elsayed and Chakroun [14] was at 3.9 · 108 . Therefore, the difference agrees with the fact that the Nusselt number increases exponentially with the increase of Rayleigh number.
7. Conclusions
(a) Top-venting arrangement (0:25 6 OR 6 1:0)
cos 0:5a 0:75ÞÞOR0:085
861
ð12Þ
Figs. 4–6 depict comparisons between these correlations and experimental data. The agreement between these correlations and the corresponding experimental data is within the experimental uncertainty. The above correlations are valid only for W =H ¼ 1:25 and As =A ¼ 1 and at thermally insulated enclosure walls and input heat flux of 250 W/m2 . More experimental data are needed to cover a wide range of W =H , As =A and heat flux. It was possible, however, to use these correlations in addition to correlations of previous works which relate Nusselt number with W =H , As =A and heat flux to approximately predict Nusselt number at different conditions than the tested ones.
6. Comparison with literature Comparison of the present work with that in the literature is difficult. The reason is that the present work was carried out at boundary conditions, geometrical conditions, and venting arrangements different from those available in the literature. It was possible, however, to compare the trend of the present data of topventing arrangement with that of Elsayed and Chakroun [14] who carried out experimental work for the determination of Nusselt number for top-vented tilted partially open cavity. Both works showed the decrease of the Nusselt number with the increase of tilt angle and the decrease of the opening ratio. The Nusselt number of the present work was higher than that of Elsayed and Chakroun [14] by 25–100% according to the tilt angle and the opening ratio. This difference can be explained based on the Rayleigh numbers at which both works were carried out. The present work was carried out at
Free convection heat transfer from rectangular, tilted partially open enclosures has been investigated experimentally. Three different venting arrangements were presented; top-venting, side-venting, and top and sideventing. In the three cases, the openings were on the form of slots distributed uniformly along the walls of the enclosure having the venting. For each venting arrangement, the experiments were carried out at four different opening ratios 0.25, 0.5, 0.75 and 1.0 and for enclosure tilt angles ranging from 0 to 180 at increments of 30 and at a constant heat flux of 250 W/m2 . Conduction and radiation losses are taken into account in the determination of the average Nusselt number of the enclosure. For the top-venting arrangement, the Nusselt number decreases as the tilt angle increases. For side-venting and top and side-venting arrangements, the Nusselt number increases slightly as the tilt angle increases until the tilt angle reaches 90, then it decreases with the increase of the tilt angle. For the three venting arrangements, the Nusselt number increases with the increase in opening ratio. For any opening ratio and at any tilt angle the Nusselt number for top and sideventing arrangement was higher than those of topventing and side-venting arrangements. For any opening ratio and at smaller tilt angle, the Nusselt number of top-venting arrangement was higher than that for sideventing arrangement, and the opposite is true at higher tilt angle. Three empirical correlations were developed for the three venting arrangements to give the average Nusselt number in terms of the opening ratio and tilt angle.
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