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Experimental Investigation of Mixed Convection in aChannel With an Open CavityOronzio Manca a , Sergio Nardini a & Kambiz Vafai ba Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Università di Napoli, Aversa(CE), Italiab Department of Mechanical Engineering, University of California, Riverside, Riverside,California, USAPublished online: 20 Aug 2006.

To cite this article: Oronzio Manca , Sergio Nardini & Kambiz Vafai (2006): Experimental Investigation of Mixed Convection ina Channel With an Open Cavity, Experimental Heat Transfer: A Journal of Thermal Energy Generation, Transport, Storage, andConversion, 19:1, 53-68

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Experimental Heat Transfer, 19:53–68, 2006Copyright © Taylor & Francis, LLCISSN: 0891-6152 print/1521-0480 onlineDOI: 10.1080/08916150500318380

EXPERIMENTAL INVESTIGATION OF MIXEDCONVECTION IN A CHANNEL WITH AN OPEN CAVITY

Oronzio Manca and Sergio NardiniDipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Universitàdi Napoli, Aversa (CE), Italia

Kambiz VafaiDepartment of Mechanical Engineering, University of California, Riverside,Riverside, California, USA

Mixed convection in an open cavity with a heated wall bounded by a horizontally unheatedplate is investigated experimentally. The cavity has the heated wall on the inflow side. Mixedconvection fluid flow and heat transfer within the cavity is governed by the buoyancyparameter, Richardson number (Ri), and Reynolds number (Re). The results are reportedin terms of wall temperature profiles of the heated wall and flow visualization for Re =100 and 1000, Ri in the range 30–110 (for Re = 1000) and 2800–8700 (for Re = 100),the ratio of the length to the height of cavity (L/D) is in the range 0.5–1.5, and theratio of the channel height to cavity height (H/D) is in the range of 0.5 and 1.0. Thepresent results show that the maximum dimensional temperature rise values decrease asthe Reynolds and the Richardson numbers decrease. The flow visualization points out thatfor Re = 1000 there are two nearly distinct fluid motions: a parallel forced flow in thechannel and a recirculation flow inside the cavity. For Re = 100 the effect of a strongerbuoyancy determines a penetration of thermal plume from the heated plate wall into theupper channel. Nusselt numbers increase when L/D increase in the considered range ofRichardson numbers.

Keywords mixed convection, open cavity, channel flow, experimental visualization

INTRODUCTION

Mixed convection flow and heat transfer in open cavities have received great interestin recent years for their importance in a wide range of engineering areas such as nuclearreactors, solar collectors, crystal growth, geothermal energy systems, heat exchangers, andcooling of electronic systems. In thermal control of electronic systems, air cooling systemsare widely employed due to its simplicity in design and low maintenance cost. Theelectronic components are mounted on boards, which are often the vertical or horizontalwall in a U-shaped open cavity and the removal of the heat generated by the componentsis obtained by natural convection. The possible augmentation of heat transfer in thecavity can be achieved by an externally driven flow of cold air. The phenomenological

Received 7 February 2005; accepted 16 May 2005.This work was supported by MIUR with a 2003 PRIN grant.Address correspondence to Kambiz Vafai, Department of Mechanical Engineering, University of Cali-

fornia Riverside, A363 Bourns Hall, Riverside CA 92521-0425, USA. E-mail: vafai@engr.ucr.edu

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54 O. MANCA ET AL.

NOMENCLATURE

D height of the heated wall, mg gravitational acceleration, ms−2

Gr Grashof number, = gβqcD4/v2k

k thermal conductivity, Wm−1K−1

H height of the inflow and outflowopenings, m

Nu average Nusselt number, = qcTw−To

Dk

q heat flux, Wm−2

Re Reynolds number, = uiH/ν

Ri Richardson number, = Gr/Re2

T temperature, KT w average wall temperature, KTi ambient temperatureui inlet velocity, ms−1

x horizontal coordinate distance, my vertical coordinate distance, m

Greek Symbolsβ volumetric coefficient of expansion, K−1

φ tube diameter, mν kinematic viscosity, m2s−1

θ maximum dimensionless wall temperatureρ density, kgm−3

Subscriptc convectivek conductivei inflowo ambient airr radiativew wall� Ohmic dissipation

understanding of interaction between buoyancy-induced flow from the heated surfaces ofopen cavity and pressure-driven external flow becomes important in thermal design ofsystems.

Mixed convection in open cavities has been investigated in several applications asreviewed in [1] and more recently in [2–4]. Numerical results for flow in a cavity witha moving upper wall, which was either heated or cooled, so that flow due to shear andbuoyancy was induced within the cavity were carried out in [5]. In this investigation theReynolds number was equal to 100, the aspect ratio ranged from 0.5–2 and the range ofGrashof numbers, based on the width of the cavity, was from 0 to ± 106, with − forcooling and + for heating. The conditions for buoyancy or shear dominating were de-termined. Laminar thermal discharge of water from power plant into a reservoir wasanalyzed numerically in [6]. The reservoir had inflow and outflow openings on the leftand right vertical walls, respectively, whereas the surface was subjected to wind shear,solar radiation, evaporation, and convective heat transfer. Results were obtained for as-sisting and opposing wind conditions. Both cases of uniform initial temperature or initialstratification in the reservoir were considered. The recirculating flow in a thermally strat-ified, salt-gradient solar pond, into which fluid at different temperature was discharged,was studied numerically in [7]. The effect of buoyancy due to the temperature differenceson the flow was considered, dealing thus with mixed convection problem. Results forboth laminar and turbulent regimes were carried out.

The interaction between a through flow stream with a buoyancy flow induced bythe heated walls of a vertical cylindrical enclosure was studied in [8]. Results in termsof streamlines and isotherms at Reynolds number equal to 100 and a range of Rayleighnumbers from −106 to 106 were given. The effect of the forced flow, either aidingor opposing, on buoyancy force in a cavity with a uniformly heated, isothermal verticalwalls, and horizontal adiabatic walls was studied numerically in [9], using Galerkin finite-element method. The forced flow was considered to enter and leave the enclosure acrossthe cold wall. The numerical heat transfer results were obtained for various pertinent

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MIXED CONVECTION IN A CHANNEL WITH AN OPEN CAVITY 55

controlling parameters of the problem. A similar study was conducted in [10] on theinteraction between an injection and laminar natural convection in a thermally drivencavity. In this case, the forced flow was considered to enter the enclosure through thehot wall and leave through the opposite cold wall. Both aiding and opposing forced flowcases were investigated here. Mixed convection transport from an isolated heat sourcewith a uniform heat flux input within a rectangular enclosure was studied numericallyin [11]. The results showed that the average Nusselt number increases with an increasein the Richardson number at a fixed Reynolds number. An improvement in the heattransfer rate was found with an increase in the Reynolds number for a fixed value ofRichardson number. When natural convection heat transfer was dominant a rapid increasein heat transfer was observed with an increase in Richardson number. The effect of thethermal conductivity on the heat transfer in the cavity analyzed in [11] was studiedin [12]. The numerical results showed that the heat transfer from the source was higherif the solid wall thermal conductivity was higher. Numerical simulation for a turbulentflow in mixed convection in a cavity by k-ε model was carried out in [13]. Resultsfor Reynolds number equal to 1000 and 2000 in the range of Grashof number from5 × 107 to 5 × 108 were obtained. It was found that the effect of Reynolds numbers onNusselt number was small. A numerical study of an enclosure with a heated vertical platelocated in the cavity was carried out in [14]. Discrete heat sources were embedded on theplate and different orientations were considered. When the heat source was embeddedon the surface of the board opposite to forced flow inlet, the value of the convectiveNusselt number was found to be independent of the location of the heat source. Anumerical study of mixed convection in open-ended enclosure has been investigated in[15] for three different forced flow angle of attack. Results were obtained for Reynoldsnumbers in the range from 102 to 104, Grashof numbers between 102 and 105, andaspect ratio in the range from 0.25 to 1.0. It was shown that the average Nusselt numberson the lower and upper surface increased almost linearly with Reynolds numbers forthe three configurations at low Grashof numbers. A very interesting result was that thehorizontal flow could be used to insulate the cavity from the surrounding medium thusminimizing the heat transfer between the cavity and the surroundings. More recently, anumerical analysis of laminar mixed convection in an open cavity with a heated wallbounded by a horizontally insulated plate was presented in [16]. Three heating modeswere considered: assisting flow, opposing flow, and heating from below. Results forRichardson number equal to 0.1 and 100, Re = 100 and 1000, and aspect ratio in therange 0.1–1.5 were reported. It was shown that the maximum temperature values decreaseas the Reynolds and the Richardson numbers increase. The effect of the H/D ratio wasfound to play a significant role on streamline and isotherm patterns for different heatingconfigurations. The investigation showed that opposing forced flow configuration hasthe highest thermal performance, in terms of both maximum temperature and averageNusselt number.

To the authors’ knowledge, there is a lack of experimental investigation on mixedconvection in a channel with open cavity below. In this work mixed convection in a topupright cavity with a heated vertical wall at uniform heat flux is studied experimentally.A horizontal unheated plate is located at a distance above the cavity and the air flowsthrough the channel. A wall of the cavity experiences a uniform heat flux, while the otherwalls are unheated. This produces an interaction between a buoyancy-induced flow anda forced flow. The case of forced flow in the channel assisting the motion due to the

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56 O. MANCA ET AL.

natural convection within the cavity is investigated. Results in terms of wall temperatureprofiles and flow visualization of the air patterns for different significant parameters aregiven. Average Nusselt numbers and maximum dimensionless temperatures for differentsignificant parameters are reported.

In this article attention is given to the effect of L/D and Richardson number. Afuture investigation on the effect of Reynolds number is recommended.

EXPERIMENTAL APPARATUS

The experimental test section was made of a horizontal wall with a cavity below anda parallel adiabatic wall, as reported in Figure 1. The heated wall consisted of a 3.2 mmthick and 530 mm wide phenolic fiberboard plate, with a typical thermal conductivityof 0.17 W/mK. Its surface adjacent to the internal air was coated with a 16 µm thickcopper layer, which was the heater. The plate was heated by passing a direct electricalcurrent through it, which had a serpentine shape. Its runs were 4.9 mm wide with a gapof nearly 0.5 mm between each one, giving each heater a total length of 9.0 m and anexpected electric resistance of about 0.50 �. The narrow gaps between the runs, togetherwith the relatively high thickness of the resulting low-conductive fiberglass were suitableto maintain a nearly uniform heat flux at the plate surface. A direct electrical currentwas generated by using a Hewlett-Packard 6260B DC power supply. The electrical powersupplied by each heater was evaluated by measuring the voltage drop across the plate andthe current passing through them. The voltage drop was measured by a HP-3465A digitalmultimeter, whereas the current was calculated by the measured voltage drop across areference resistance. To avoid electrical contact resistances, thick copper bars solderedboth to the electric supply wire and to the ends of the heater were bolted together. Adirect electrical current was passed through the copper. The dissipated heat rate wasevaluated with an accuracy of ±2%, by measuring the voltage drop and the currentthrough the electrical resistance. A maximum variation of ±5% in the electrical resistivityof copper was evaluated under the worst conditions, when the maximum difference inwall temperatures was 20 K. Therefore, a uniform wall heat flux was assumed, witha ±5% maximum deviation from its average value. The typical time interval to attainsteady-state conditions after modifying the electric power supply was not greater than 1 hfor the minimum q� value. The other walls of the cavity were made of Plexiglas plates,

Figure 1. Geometry under consideration.

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MIXED CONVECTION IN A CHANNEL WITH AN OPEN CAVITY 57

which were machined to an accuracy of ±0.3 mm, in order to take pictures of the flowmotion. The wall spacing was measured to an accuracy of ±0.25 mm by a dial-gaugeequipped caliper. The total normal emissivity of the heated wall and unheated wallswas 0.1. It was obtained by sticking a 25 µm thick aluminum foil on the surfaces facingthe cavity. The emissivity was evaluated by means of radiometric direct measurements.The electric insulation between the copper surface and the aluminum foil was assured byuniformly spraying an electrically insulating varnish onto it before coating. A 150 mmPolystyrene block was affixed to the rear face of the plate in order to reduce conductiveheat losses.

The other walls of the channel were made of wood. The main channel was 1700mm long, 500 mm wide, and the height ranges between 10 and 200 mm. A blowerattached to the channel through a nozzle provides a variable mass flow rate. The entireapparatus was located within a room, sealed to eliminate extraneous air currents.

Wall temperature was measured by means of 0.50 mm OD ungrounded iron-constantan (J-type) thermocouples embedded in the fiberboard plate in the very proximityof the backside of the copper layer and bonded with a 3M epoxy glue. The distance be-tween the thermocouple and external surface of the heated plate was less than 0.1 mm. Assuch, the temperature difference between the measured value and the surface temperaturewas estimated to be less than 0.1 K. They were run horizontally, parallel to the surfaces,thereby lying along isotherms in order to minimize conduction heat losses in the leads.Ten equally spaced thermocouples were placed in the centerline of the heated wall. Thefirst was placed 5.0 mm downstream the lower edge, the distance between two successivethermocouples being 10 mm. At 75 mm from the lower edge the heated wall, 8 additionalthermocouples were located horizontally at ±75, ±100, ±125, and ±150 mm from thecenterline, in order to provide indications of the horizontal variation of the wall tem-perature. Fifteen thermocouples were affixed to the rear surface of the heated wall andembedded in the Polystyrene block, in order to evaluate the conductive heat losses. Theambient air temperature was measured by a shielded thermocouple placed near the leadingedge of the channel. Thermocouples voltages were recorded to 1 µV. Each thermocouplewas calibrated in a ±0.01 K thermostatic bath by means of a reference standard ther-mometer (Pt100). Calibration of the temperature measuring system showed an estimatedprecision of the thermocouple-readout system of ±0.1 K. A Kaye instrument K170 icepoint was used as a reference for thermocouple junctions. A National Instruments SCXImodule data acquisition system and a PC were used for the data collection and reduction.The data acquisition was performed through the LabviewTM software. Tests showed thewall temperature to be independent of the z coordinate within z = ±100 mm, since inthis region its maximum deviation from the centerline temperature was found to be notlarger than 1.0◦C when the latter was 65◦C.

Mass flow rate was calculated by measuring the velocity by means of a Pitottube. The sensor was located at 2500 mm from the inlet section of a circular duct witha diameter of 40 mm in order to have a laminar fully developed motion, (Figure 2a).Furthermore, the Pitot tube was at about 6 m from the outlet rectangular section of the testsection. Velocity uncertainty was ±2%, the error on the measurement of the duct diameterwas ±1%, and the uncertainty of the location of the sensor was ±4%. Downstream thePitot tube a thermocouple was located in order to measure the flow temperature. Its valuewas nearly equal to the temperature of the air at the inlet of the test section in each case.For this reason the value of the average velocity at the inlet section was 0.5 times the

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58 O. MANCA ET AL.

(a)

(b)

Figure 2. (a) Schematic layout of the experimental apparatus. (b) Side view of the test section.

velocity value measured by the Pitot tube times the ratio between the area of the sectionof the circular duct and the area of section upstream the cavity.

Smoke for visualization was generated by burning incense sticks in a steel tube,connected to a compressor. The smoke was injected through a glass heat exchangerto reduce the temperature of the smoke. The smoke was sent into a plenum and itstemperature was controlled by means of a thermocouple. This value was close to that ofthe air ambient incoming into the channel. Then it was driven in the test section througha small slot situated along the lower edge of the heated wall. The visualization was madepossible by means of a laser sheet, generated by a He-Ne laser source. The laser sheetwas produced by placing a mirror near the end of the test section with an angle of 45◦respect to the direction of the main flow, after which a cylindrical lens was placed toenlarge the beam as needed. The pictures were taken by means of the still digital cameraNikon D-100.

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MIXED CONVECTION IN A CHANNEL WITH AN OPEN CAVITY 59

DATA REDUCTION

The governing parameters in the problem are the buoyancy parameter, RichardsonRi = Gr/Re2, the Reynolds number, Re, and the Prandtl number, Pr. The Reynolds andGrashof numbers are defined as follows:

Re = uiH

ν, Gr = gβqcD

4

ν2k(1)

where qc is the spatially-averaged convective heat flux on the heated wall

qc = 1

D

∫ D

0qc(x)dx. (2)

The Nusselt number is based on the difference between the wall and the inlet fluidtemperatures. The average Nusselt number is defined as the following:

Nu = qc

Tw − ToD

k(3)

where the average wall temperature is defined as follows:

Tw = 1

D

∫ D

0Tw(x)dx (4)

Dimensionless maximum wall temperature can be defined as

θ = (Tw,max − To)/(qcD/k). (5)

The thermophysical properties of the air are evaluated at the reference temperature(Tw + To)/2.

Local convective heat flux, qc(x), was not uniform because of radiation and con-duction. Experimental data were reduced by first introducing the convective local heatflux in the equations presented above

qc(x) = q�(x)− qk(x)− qr(x) (6)

where q�(x) was the local heat flux due to Ohmic dissipation, which was assumed tobe uniform, qk(x) denoted the local conduction heat losses from the plate, and qr(x) isthe local radiative heat flux from the plate. For each run, the terms qk(x) were calcu-lated by a three-dimensional finite difference numerical procedure, which evaluated thetemperature distribution in the polystyrene from the measured temperatures at the rearface of the plates. The predicted temperatures in significant configurations of the systemhad been previously compared with those measured by thermocouples embedded in thepolystyrene insulation and the agreement was very good, the maximum deviation being±0.3 K. The qr(x) terms were calculated for each temperature distribution in the wall,ambient temperature and channel spacing, according to the procedure described by Webband Hill [17]. A two-dimensional temperature distribution at the surfaces of the wallswas assumed, according to the aforementioned indications from preliminary tests. Themaximum local radiative and conductive heat fluxes were evaluated for q� = 250 W/m2

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60 O. MANCA ET AL.

Table 1. Percentage uncertainty values (UXi/Xi 100)

Variable ui To Tw − To qc qr qc + qr q� qk H D

Uncertainty 5.0 0.068 4.0 5.7 5.0 2.5 2.0 4.2 4.0 0.01

and the corresponding percentage error for the average radiative and conductive heatfluxes were estimated to be about 2.5% and 2%.

The uncertainty of the values of Re, Gr, and Nu was evaluated following theprocedure suggested in [18,19]. Accordingly, the uncertainty of the dependent variableR as a function of the uncertainties of the independent variables Xi was given by therelation

U2R =

(∂R

∂X1UX1

)2

+(∂R

∂X2UX2

)2

+ · · · +(∂R

∂XjUXj

)2

. (7)

Therefore, on the basis of Eqs. (1) and (4) and of the not negligible uncertaintiesof the values of the independent variables reported in Table 1, the maximum uncertaintyof Re was 6%. The maximum uncertainties of Gr and Nu turned out to be 6 and 7%,respectively.

RESULTS

The experiments were performed with working fluid air. The analysis was accom-plished for two channel spacing H = 50 mm and 100 mm, length of the cavity L = 50,100, 150, and 200 mm, height of the heater equal to 100 mm and an ohmic heat flux inthe range from 50 to 250 W/m2. The corresponding dimensionless parameters were theaspect ratio H/D which held the values: 0.5 and 1.0, the aspect ratio L/D which heldthe values: 0.5, 1.0, 1.5, and 2.0. The Reynolds number (Re = uiH/ν) investigated were100 and 1000, these being in the laminar regime. The Richardson number Ri = Gr/Re2

was in the range of 30 to 110, for Re = 1000, and 2800 to 8700, for Re = 100.The wall temperature rise above the ambient temperature as a function of the

coordinate along the heated wall is presented in Figure 3 for Re = 1000, H/D = 1.0,and several values of q� and L/D. The coordinate along the heated wall is taken asdatum. The corresponding values of the Richardson number are 30, 50, 70, 90, and 110.The temperature profiles show a nearly parabolic shape due to the heat transfer above withthe forced flow and below with the cavity bottom wall. The maximum wall temperaturesare reached in the higher part of the wall. For the lower heat flux value, Figure 3a,q� = 50 W/m2 (Ri = 30), the maximum values are reached closer to the middle ofthe wall because the effect of natural convection is weaker than the forced flow overthe cavity. However, the maximum wall temperature is in the middle part of the heatedwall due to the effect of the recirculation in the cavity. This demonstrates the stagnationon the heated side wall at about one-third of the plate height from the cavity bottomand the forced convection on the upper part of the wall. The two effects enhance heattransfer in the lower and upper zones. Hence the wall temperatures in these zones arelower than the central part. As expected, the location for the maximum wall temperaturemoves up the wall when the heat flux is increased. When the L/D ratio increases the

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MIXED CONVECTION IN A CHANNEL WITH AN OPEN CAVITY 61

Figure 3. Wall temperature rise vs. the x coordinate for Re = 1000 and H = 100 mm: (a) q� = 50 W/m2K;(b) q� = 100 W/m2K; (c) q� = 200 W/m2K; (d) q� = 250 W/m2K.

wall temperature decreases. This effect is stronger for this heat flux value. It is worthnoticing that the influence of the unheated wall should decrease when the L/D ratioincreases and therefore the temperature profile should reach that of the heated wall withL/D → ∞ related to the case of a step, that is a sharp expansion with a heated verticalwall of the step. For q� = 100 W/m2 (Ri = 50), Figure 3b, the temperature values arehigher and the increase is greater for the higher L/D values. As observed previously, themaximum values are reached at a greater value of the height y. For higher heat fluxes thegreater the heat flux the smaller the percentage rise of the temperature, Figures 3c and3d. Furthermore, for these q� values, the greater the L/D ratio the lower the temperaturedecrease. For every case the maximum values of the wall temperature is reached between55 and 65 mm.

In Figure 4 wall temperature profiles are reported for H/D = 0.5 and for the samevalues of the heat flux and L/D of Figure 3. For the smallest value of the ratio L/Dthe values of the temperature rise are greater than the ones in the previous case dueto a greater influence of the forced flow on the buoyancy. In fact, for Re = 1000 andH = 50 mm the average velocity is double of the average velocity for H = 100 mm.The effect is stronger for the lowest value of the ratio L/D investigated in this article.Anyway, the temperature profiles are similar to the ones for H/D = 1.0.

The effect of a decrease of the Reynolds number is presented in Figure 5 whichgives the temperature profiles for Re = 100. Maximum wall temperature is attained at a

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62 O. MANCA ET AL.

Figure 4. Wall temperature rise vs. the x coordinate for Re = 1000 and H = 50 mm: (a) q� = 50 W/m2K;(b) q� = 100 W/m2K; (c) q� = 200 W/m2K; (d) q� = 250 W/m2K.

Figure 5. Wall temperature rise vs. the x coordinate for Re = 100 and H = 50 mm; (a) q� = 50 W/m2K;(b) q� = 200 W/m2K.

greater height due to a greater effect of the buoyancy than in the case with Re = 1000.For q� = 50 W/m2, Figure 5a, wall temperature for L/D = 0.5 are lower than in thecase with Re = 1000, because the influence of the buoyancy is larger. When the L/Dratio increases, the maximum wall temperature are nearly equal in both cases (Re = 100and 1000) because in the cavity the mixing with the forced flow is more marked. Forq� = 200 W/m2 (Ri = 8700), Figure 5b, the values of the surface temperature are lower

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MIXED CONVECTION IN A CHANNEL WITH AN OPEN CAVITY 63

Figure 6. Sketch of the main flow in the system.

Figure 7. Flow visualization for Re = 1000, Ri = 90, H/D = 0.5, and: (a) L/D = 0.50; (b) L/D = 1.0;(c) L/D = 1.5; (d) L/D = 2.0.

Figure 8. Flow visualization for Re = 100, Ri = 8700, H/D = 0.5, and: (a) L/D = 0.50; (b) L/D = 1.0;(c) L/D = 1.5; (d) L/D = 2.0.

due to the effect of the buoyancy which is more significant. The warmer fluid leaves theheated wall and it does not remain in the cavity.

In Figure 6, a sketch of the main flow in the system is reported. From the heatedwall hot plume interacts with the forced flow in the channel resulting in a stagnantrecirculation in the open cavity. The hot plume and the recirculation extend further intothe channel as the wall heat flux increases.

Visualization of the fluid flow inside the system for a qualitative description isreported in Figures 7–10. In Figure 7 the photographs at Re = 1000, H/D = 0.5, andRi = 90 (q� = 200 W/m2) for L/D = 0.50, 1.0, 1.5, and 2.0 are given. For L/D =0.50, Figure 7a, it is observed that the smoke moves over the heated wall and penetratesin the channel without mixing with the forced flow. The greater part of the warm fluidenters again in the cavity close to the opposite unheated wall. Inside the cavity the fluidseems to mould a single cell. In Figure 7b, for L/D = 1.0, the cell in the cavity ismore evident. The plume coming from the heated wall penetrates less in the channel.

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64 O. MANCA ET AL.

Figure 9. Flow visualization for Re = 100, Ri = 4700, H/D = 0.5, and: (a) L/D = 0.50; (b) L/D = 1.0;(c) L/D = 1.5; (d) L/D = 2.0.

When L/D increases, Figures 7c and 7d, it is noticed that the cell stays in proximityto the unheated vertical wall and takes up along the forced flow direction a part of thecavity nearly equal to the height of the cavity. The more external particles of the cellmove toward the heated wall following a horizontal direction along the top opening ofthe cavity and after moving toward the lower part of the cavity along the zone close tothe heated wall. These patterns, for L/D = 2.0, are in a very good agreement with thestream function fields numerically carried out in [16].

In Figure 8 the photographs at Re = 100, Ri = 8700 (q� = 200 W/m2), andH/D = 0.50, for L/D = 0.50, 1.0, 1.5, and 2.0 are reported. In this case, it is observedthat the buoyancy effects are more marked. In fact, the plume rises from the heatedwall up to the horizontal upper plate of the channel. The inclination angle, respect tothe vertical direction, of the plume depends on the L/D values, the greater L/D thegreater is the inclination. The inclination is due to the forced flow in the channel. ForL/D = 0.50, Figure 8a, the warm air moves both toward the entrance and the exit of thesystem. The part of fluid going toward the entrance section determines a recirculation inthe upper zone of the channel inflow. This could be due to the velocity increase in theentrance section caused by the plume. There is also recirculation adjacent the unheatedwall. At higher L/D values, it is observed that the cell increases and takes up all cavity.

In Figure 9 the flow visualization at Re = 100 and Ri = 4700 (q� = 100 W/m2)and H/D = 0.50, for L/D = 0.50, 1.0, 1.5, and 2.0 are reported. It is noted that alsoin this case the plume coming from the cavity is deviated by the forced flow but itdoes not reach the upper plate of the channel. For L/D = 0.50, Figure 9a, the patternsindicate that the plume stays in the lower part of the channel very close to the mouthof the cavity and it moves toward the exit section. In this case inside the cavity thereare vortexes structures. In Figure 9b, for L/D = 1.0, the patterns of the plume do notclose completely the upper opening of the cavity and there is a direct fluid flow from thechannel toward the cavity. This effect is more marked at L/D = 1.5 and 2.0, as shownin Figures 8c and 8d. For L/D = 1.5, Figure 8c, it is observed a vortex adjacent to theunheated wall.

As observed in the photographs for the lowest wall heat flux, q� = 50 W/m2, Ri =2800, the effect of buoyancy is weaker and the forced flow drags the plume further in thechannel, particularly for L/D = 0.50, Figure 10a. Inside the cavity exists a vortex cell.For L/D = 1.0, Figure 10b, the plume pattern does not arrive completely to the unheatedwall and a part of fluid enters in the cavity. Two different cells are noticed in the cavity,one adjacent to the mouth of the cavity and another close to the unheated vertical wall.

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Figure 10. Flow visualization for Re = 100, Ri = 2800, H/D = 0.5, and: (a) L/D = 0.50; (b) L/D = 1.0;(c) L/D = 1.5; (d) L/D = 2.

For the higher L/D values, 1.5 and 2.0, there is a backflow coming from the outflowsection. The backflow determines secondary flows inside the cavity, Figures 10c and 10d,which are more disordered at greater L/D.

Dimensional values of the maximum surface temperature for Re = 1000 andH/D = 0.5 and 1.0 are reported in Figure 11. When the L/D increases the maxi-mum wall temperature decreases. This is due to the cavity volume increasing with anincrease in L/D and is in agreement with the temperature profiles in Figure 5. Further-more, at a specified value of L/D the maximum wall temperature rise $Tmax is a nearly

Figure 11. Maximum surface temperature rise on the heated wall vs. longitudinal x-coordinate for several Ri:(a) Re = 1000 and H/D = 0.5; (b) Re = 1000 and H/D = 1.0; (c) Re = 100 and H/D = 0.5.

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66 O. MANCA ET AL.

Figure 12. Maximum surface temperature rise on the heated wall vs. Ri for several L/D: (a) Re = 1000 andH/D = 0.5; (b) Re = 1000 and H/D = 1.0.

linear function of the Richardson number, as shown in Figure 12. The maximum walltemperature increases with Ri due to an increase in the wall heat flux.

Dimensionless values of the maximum surface temperature defined by Eq. (5) isshown in Figure 13. The dependences are similar to those highlighted for the dimensionalvalues. All values are within a ±10% band with respect to an average behavior. In Fig-ure 14 the average Nusselt number is reported as a function of the L/D ratio. The lowerthe value of L/D the greater the dependence of Nu respect to the Richardson number.

Figure 13. Dimensionless maximum surface temperature rise on the heated wall vs. L/D for several Ri:(a) Re = 1000 and H/D = 0.5; (b) Re = 1000 and H/D = 1.0; (c) Re = 100 and H/D = 0.5.

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Figure 14. Nusselt number vs. L/D for several Ri and: (a) Re = 1000 and H/D = 0.5; (b) Re = 1000 andH/D = 1.0; (d) Re = 100 and H/D = 0.5.

CONCLUSIONS

An experimental investigation on mixed convection in a partially open cavity wascarried out for a forced flow entering in the cavity from the heated vertical wall side.The surface temperature profiles of the heated wall showed that the larger the distancebetween the vertical walls of the cavity the lower the surface temperature. At the sameReynolds number and at higher the channel gap there was a slightly increase of thesurface temperature. At lowest investigated Reynolds number (Re = 100) the surfacetemperature was lower than the corresponding surface temperature for Re = 1000, atsame Richardson number.

The flow visualization had pointed out that for Re = 1000 and for the investigatedRichardson numbers, there were two nearly distinct fluid motions: a parallel forced flowin the channel and a recirculation flow inside the cavity. These results were in a verygood agreement with the stream function fields presented in [16]. For Re = 100 theeffect of a stronger buoyancy determined a penetration of thermal plume from the heatedplate wall into the upper channel.

A linear dependence of maximum wall temperature on Richardson number forall considered L/D values was shown. The dimensionless maximum wall temperaturesin terms of L/D had values in ±5% respect to an average function. Nusselt numbersincreased when L/D increased in the investigated range of Richardson numbers, 30 ≤Ri ≤ 110, for Re = 1000, and 2800 ≤ Ri ≤ 8700, for Re = 100.

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