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Chemical Engineering and Processing 50 (2011) 1152– 1159

Contents lists available at SciVerse ScienceDirect

Chemical Engineering and Processing:Process Intensification

j ourna l h o me pa ge: www.elsev ier .com/ locate /cep

ocal heat-transfer coefficient of immersed cylindrical surface in fluidized andibrated fluidized beds

.S. Bacelosa,∗, C.F.S. Camargob, A.M. Silveirab, J.T. Freireb

Universidade Federal do Espírito Santo, Departamento de Engenharias e Computac ão, Programa de Pós-graduac ão em Energia, Rodovia BR 101 Norte, Km. 60, CEP 29.932-540, Sãoateus, ES, BrazilUniversidade Federal de São Carlos, Departamento de Engenharia Química, Programa de Pós-graduac ão em Engenharia Química, Rod. Washington luiz, Km. 235, C. P. 676, CEP3.565-905, São Carlos, SP, Brazil

r t i c l e i n f o

rticle history:eceived 31 March 2011eceived in revised form 2 September 2011ccepted 8 September 2011vailable online 16 September 2011

a b s t r a c t

Due to the good air–particle mixing couple with the high heat and mass transfer rates, fluidized andvibrated fluidized beds of particles have been widely used for many chemical engineering processesinvolving particulate systems. On the other hand, in practice, for using such beds in the treatment ofheat-sensitive materials (i.e., polymer, food products) the installation of heat-exchange surface withinthe bed are needed to provide indirect heat as well as prevent thermal degradation. Therefore, this

eywords:luidizationeat transferibrating-fluidized bedsluidized beds

paper presents an investigation to determine the local heat-transfer coefficient in fluidized and vibratedfluidized beds (by expressing Nu� vs. Re) operated with glass ballotini particles ranging from 500 to1100 �m, in diameter. The data show that, at a given air velocity, the local heat-transfer coefficientobtained in the vibrated fluidized beds is significantly higher as compared to those of fluidized beds.In addition, vibrated fluidized beds can achieve higher local heat-transfer coefficients as the particlediameter is reduced from 1100 to 500 �m and the vibration dimensionless (� ) is increased from 1 to 3.

. Introduction

Fluidized bed dryers have been commonly used for the dryingf wet particulate and granular material as well as slurries, pastesnd suspensions in beds of inert particles (size ranging from 50o 2000 �m) which fluidization regimes can be achieved. In addi-ion to drying, fluidized bed has found wide ranges of industrialpplications in various industries for mixing, granulation, coating,hemical reactions and combustion [1].

Vibrated fluidized beds (VFBs) have become increasingly impor-ant in practical applications as they cover a different range ofperational conditions, when compared to the conventional flu-dized beds. In regard to cost effectiveness, the choice of vibrateduidized bed as a contactors is competitive in large-scale produc-ion with conventional fluidized bed [2–5], spouted bed [6–10],otary [11–16], tunnel [17] and continuous tray [18], as VFBs cane operated in the presence of uniform (size ranging from 10 �mo 10 mm) or particle size distribution (reference, binary, flat andaussian mixtures) [19,20]. As well, for good solids mixing cou-

led with satisfactory gas–particle contact, VFBs can promote ratesf heat and mass transfer to the system comparable to the otherontactors.

∗ Corresponding author. Tel.: +55 27 3312 1568; fax: +55 27 3312 1618.E-mail address: marcelobacelos@ceunes.ufes.br (M.S. Bacelos).

255-2701/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2011.09.003

© 2011 Elsevier B.V. All rights reserved.

Among the advantages of introducing mechanical vibration in aconventional fluidized bed is the possibility of the decrease in theminimum fluidization velocity, bed pressure drop, volume of deadregions, channeling, and bubble formations. In addition, fluidiza-tion of cohesive, adhesive, and pasty material becomes feasible insuch beds [21–24].

The great challenge of increasing the thermal efficiency in thedryers is to reduce the loss of sensible heat with the exhaustair stream. In fluidized bed dryers, by adding internal heaters orimmersed tubes in the bed, the heat is indirectly transferred to thedrying material and the fluidizing air stream fluidizes the materialand carries over the evaporated moisture. Therefore, this minimizesthe quantity of air and its sensible heat required for the drying.

Moreover, for operating conditions not suitable for fluidizedbeds (drying of particle size less than 50 �m), where vibratingfluidized bed regimes is achieved, immersed tubes or internallyheated column surface can be used, as the heat transfer coeffi-cient increases with the decrease in the particle size. This is dueto large interfacial surface heating area available in the bed whensmall particle size particles are used [23–27].

Mickley et al. [28] were the first researchers to deal with thedetermination of local heat-transfer in fluidized beds by using a

thin platinum foil on a vertical tube and monitoring its tempera-ture changes. In sequence, Tuot and Clift [29], Fitzgerald et al. [30],Baskakov et al. [31], Gloski et al. [32] and Wu et al. [33] have usedsuch technology, which differs from that of Mickley et al. [28] in the

M.S. Bacelos et al. / Chemical Engineering and Processing 50 (2011) 1152– 1159 1153

Table 1Operating conditions used.

Parameter Value

dp (�m) 500, 700, 1100h (cm) 9A (m) 8 × 10−3

� (–) 0, 1.0, 1.77, 3.0F (Hz) 5.57, 7.41, 9.65u (m/s) 0.2a, 0.3b, 0.45c

Re (–) 239, 354, 358� (◦) 0, 45, 90, 135, 180◦

a Packed bed regime.

mtBflcto

hetahpibtgteth

secpsipl

wiadstc

2

2

abvloc

Fig. 1. Schematic representation of experimental equipment: 1, blower; 2, bypass

b Loosen packed bed at the vicinity to attain minimum fluidization regime.c Minimum fluidization regime.

aterial and geometry of sensor and electric circuit used for main-aining the platinum resistance heaters at a constant temperature.y analyzing these pioneering researches on local heat-transfer inuidized beds, it can be stated that local heat-transfer is signifi-antly affected by the fluid dynamics characteristics of the bed andhe platinum resistance heaters are the most efficient sensor tobtain local heat-transfer coefficients.

As noted, heat transfer in fluidized beds with horizontal tubesas been experimentally investigated by many researchers. How-ver, with respect to the heat transfer in vibrated-fluidized beds,here is only little information about local heat transfer in the liter-ture, considering the overall heat transfer coefficient for such bedsave been examined. For vibrated fluidized beds with coarse inertarticles, Xuejun et al. [34] proposed a dimensionless mathemat-

cal model to predict the local heat-transfer coefficients betweeneds and immersed horizontal tubes, and results were comparedo the data obtained in a two-dimensional vibrated fluidized bed oflass beads with 1.83 mm average diameter. The results show thathe values of theoretical prediction are in good agreement withxperimental data, thus the model is able to predict the local heat-ransfer coefficients between vibrated fluidized beds and immersedorizontal tubes reasonably well, and the error is in range of ±15%.

In the late of 2000s, Camargo [35] has developed a platinumensor which is maintained at a constant temperature by anlectronic control circuit. Then, instantaneous local heat-transferoefficients are obtained by measuring bed temperature and theower required to hold the platinum sensor temperature con-tant. This sensor was used for measuring the local heat transfern fluidized beds with particles and the experimental data obtainedresented a consistent results as compared to those reported in the

iterature by Kurosaki et al. [27].Based on the promising data of local heat transfer obtained

ith fluidized beds, the experimental investigation was extendedts operation into the vibrated-fluidized beds of particles suit-ble for attaining fluidization regime. Therefore, this paper aims atetermining the local heat-transfer coefficient of immersed heatedurface in fluidized and vibrated fluidized beds and investigatinghe effect of operating conditions of beds on the local heat-transferoefficient.

. Materials and methods

.1. Material

The local heat-transfer coefficient was obtained using the oper-ting conditions presented in Table 1. Such conditions were chosenecause they were similar in particle size, Reynolds number, and

ibration dimensionless to that of other researches mentioned initerature reviewed on the subject, permitting to compare the databtained here to those reported in the literature. In addition, thehoice of such particles diameters, ranging from 500 to 1100 �m,

valve; 3, globe valve; 4, orifice flow meter; 5, pressure transducer; 6, motor; 7,air entrance; 8, spring, 9, immersed heater; 10, signal conditioning module; 11,temperature controller; 12, computer.

is due to both fluidized and vibrated fluidized beds regimes can beachieved.

2.2. Equipment

Fig. 1 shows the experimental equipment used, which comprisea fluidized and vibrated fluidized beds with a 0.12 m diameter and0.5 m high acrylic cylindrical column, an air compressor to blow airinto the beds, a flow rate orifice meter to measure the air inlet flowrate, test cylinder to measure the local heat-transfer coefficient andmanometers to measure the total bed pressure drop. In addition,pressure transducers were used to capture analogical pressure sig-nals of both the bed and the flow-rate orifice meter. Pressure andthermal data were logged in a computer. The data of pressure wereprocessed by a supervisory system, which consists of a condition-ing module, an acquisition board, and software for calculating thelocal heat-transfer coefficient. Data of thermocouples and of electri-cal resistance from test cylinder were processed by Delphi programlanguage. Such apparatus was used for determining the local heat-transfer coefficient of test cylinder immersed in the bed of specificsize of spherical particles, as can be seen in Table 1. For differentflow regimes achieved, the transparent-acrylic column permits thevisual tracking of air bubbles and particles in the bed. The bed col-umn was vibrated in the vertical direction by means of an eccentricmechanism. This mechanism adjusts the amplitude of vibration anda mechanical controller located on the axle of the electric motorallows for adjustment of frequency of vibration. The acceleration,velocity and amplitude of vibration of the system generated by theimposed vibration are monitored by a piezoelectric accelerometerand frequency of vibration is measured with an optical tachometer.

2.3. Test cylinder

Fig. 2 shows the test cylinder with 0.025 m diameter and 0.05 mlength used to obtain local heat-transfer coefficient in fluidizedand vibrated fluidized beds. The cylinder is built of brass due to itsgood thermal conductivity (111 W/m K) and is equipped on its sur-face with the platinum sensor and internally with a 3.3 � electricalresistance connected to 0.001 A accuracy Ammeter for measuringthe electrical current.

This test cylinder is composed of a small quartz piece, as

schematically shown in Fig. 3. Such quartz piece is covered on itssurface by thin platinum film connected to an electrical circuit. Suchplatinum sensor is one of the most important components of instru-ments used in this research paper. According to Wu et al. [33], this

1154 M.S. Bacelos et al. / Chemical Engineering and Processing 50 (2011) 1152– 1159

Fig. 2. Test cylinder (dimensions in mm). (a) View of cylinder; (b) side view of testcylinder.

Fig. 3. Sketch of quartz surface supporting platinum film heater element (dimen-sions in mm).

Voltage Source

Sensor

Aquisision board

Computer

RFRF

V1 V2

Fig. 4. Sketch of electrical circuit used to adjust suitable sensor temperature.

sensor must be able to attain the following conditions: good accu-racy in determining of platinum sensor temperature and heat flux,low mass and platinum film surface area to obtain fast and accu-rate monitoring of values of local heat-transfer coefficient; sensorsurface need be tangential to the brass-cylinder one in order to beseen as a perfect continuum of cylinder surface, as shown in Fig. 3. Inaddition, as recommended by Wu et al. [33], for covering platinumon quartz surface, a thin film of platinum solution from EngelhardIndustries Liquid Bright Platinum is used. Details on preparation ofplatinum film supported on quartz surface can be found in Camargo[35].

To prepare the platinum film on quartz surface, copper wireswere connected to the opposite borders of the film using conductivegum. One wire was connected to a voltage source and the other to areference electrical resistance (known resistance) as schematicallyrepresented by sketch shown in Fig. 4.

The voltage source drives electrical current through the circuit,consisting of platinum sensor and the reference electrical resis-tance, in direction of ground wire causing heating in the sensor.The voltages on sensor (V1 and V2) can be logged in computer bymeans of an acquisition board and a computer. Based on referenceelectrical resistance, RF, the current, I, flowing through circuit, canbe calculated as well as the sensor resistance (RS) by the followingequations:

I = V2

RF(1)

RS = V1 − V2

I= RF · (V1 − V2)

V2(2)

Preliminary tests showed that platinum sensor resistance (RS)presented a linear relationship to the temperature to which sen-sor was being subjected. Therefore, by changing voltage source onelectrical circuit sensor, sensor temperature was adjusted to 70 ◦C.

When sensor is subjected to a suitable electrical current (e.g.,reaching the temperature of 70 ◦C) the power lost by platinumsensor can be expressed by:

Q = V2 · (V1 − V2)RF

(3)

where, V1 is the electrical voltage before sensor on the circuit inFig. 4, V; V2 is the electrical voltage after sensor on the circuit inFig. 4, V; RF is the reference electrical resistance, �.

However, by using the Newton’s law of cooling, the local heat-transfer coefficient can be expressed by the following equation:

Q

h� =

a · (TS − TL)(4)

where h� is the local heat-transfer coefficient, (W m−2 K−1); Q isthe power lost by platinum sensor, (W); a is the local area of the

M.S. Bacelos et al. / Chemical Engineering and Processing 50 (2011) 1152– 1159 1155

pa

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3

3

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2001801601401201008060402000

50

100

150

200

250

300

Nu θ

θ ( 0 )

Re=239 Re=358 Re=534

Fig. 5. Angular positions for which h� was obtained.

latinum sensor, m2. TS and TL are the temperatures of the sensornd the bed, respectively, (◦C).

.4. Experimental procedure

Initially, the bed is filled with one size of the glass bed (i.e., Ballo-ini) shown in Table 1 and then, the valve is opened to allow the airo enter into contact with the bed until the fluidized bed regimesre attained. The procedure of slowly decreasing the inlet air veloc-ty is adopted to determine the minimum fluidization conditions.his velocity varies from one that characterizes the fully fluidiza-ion velocity to zero. This procedure assures a good data replicationf the bed pressure by generating data at the same degree of particleacking. The minimum fluidization velocity (Vmf) is defined as the

owest air velocity at which the fluidization regime is attained andhe pressure drop connected to this velocity is assumed to be the

inimum fluidization pressure drop (�Pmf). Thus, by adjusting theperating conditions of bed for attaining the vibrated fluidized bedegimes, as specified in Table 1, the local heat-transfer coefficienth�) can be obtained as described by Eq. (4).

Moreover, Fig. 5 shows the angular positions of the platinumensor placed inside the particle bed with respect to the directionf air flow. The air flow direction is represented by an arrow shownn Fig. 5. This test cylinder was immersed in the bed of particlesnd fixed on a distributor of circular cross section, consisting of a.002 m thick plate with a 30% open area made up of 0.003 m diame-er slots. A screen with 400 �m diameter (e.g., smaller than particlessed) was placed just above this plate to gain more homogeneousistribution of air flow.

. Analysis and discussion

.1. Local heat-transfer coefficient in fluidized beds

Fig. 6 shows the local Nusselt number (Nu�) for a fluidized bedith particles of 500 �m diameter as a function of angular coordi-ate (�) and of Reynolds number (Re). In general, it can be observed

Fig. 6. Nu� as a function of � and Re for fluidized bed with dp = 500 �m.

in Fig. 6 that the value of Nu� significantly changes with the angu-lar position of the cylinder immersed in the fluidized bed, thusrevealing significant differences in local heat exchange. This is dueto the behavior of air–particle fluid dynamics in �-degree direc-tion around a heated cylinder permitting better or poor contacteither between immersed heated surface and particle or betweenthe immersed heated surface and particle air-free gaps, [36]. Forthis bed of inert particles, the higher values of Nu� as a function ofRe were found to occur at different angular positions. For Re = 239,the maximum value of Nu� was obtained for � = 0◦. By increas-ing the Reynolds number to 358, this maximum was observed tooccur at � = 90◦, while for Re = 534, the value of Nu� had its maxi-mum at � = 135◦. Such values of the Reynolds number refer to thevelocities at the packed bed, loosen packed bed (in the vicinity toattain minimum fluidization), and minimum fluidization regimespreviously identified in the fluidized bed characteristic curve (seeTable 1).

On analyzing the data in Fig. 6, it can thus be stated that for thelowest air velocity (Re = 239), the maximum value obtained for thelocal heat-transfer coefficient corresponds to the stagnation pointdue to the contribution of convective heat transfer exerted mainlyby the air since under this experimental condition, there is not aconsiderable movement of inert particles around the heated cylin-der. This behavior of heat transfer achieved for Re = 239 is similar tothat of air in crossflow about a cylinder heated surface (i.e., withoutbeing in contact with particles) [36]. Hence, for Re = 239, the rate ofheat transfer decreases with the angular direction from 0 to 180◦

as the extent of air–particle layer around the cylinder increases.This probably explains such a behavior of the local Nusselt num-ber which tends to decrease as air–particle change from stagnationregion (i.e., � = 0◦) to the point of �-degree equals to 180◦. More-over, such a behavior is also similar to that described by the flow ofair past the exterior surface of a cylinder heated surface using lowRe numbers [36].

In addition, in Fig. 6, as the air velocity increases (Re > 239), thevalue of local Nusselt number is observed to increase across theentire cylinder circumference. Under these conditions, air bubblesare expected to start moving across the surface of the cylinder andthe particles begin to move significantly. It can be inferred thatthis movement of particles is what causes the shift of the position

of the maximum local heat-transfer coefficient toward the lateralsurface of the cylinder (i.e., in the range of �-degree from stagna-tion point from 0 to 90◦) with the increase in the Re from 239 to

1156 M.S. Bacelos et al. / Chemical Engineering and Processing 50 (2011) 1152– 1159

2001801601401201008060402000

50

100

150

200

250

300

Nu θ

θ ( 0 )

Re =239 Re =358 Re =534

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2001801601401201008060402000

50

100

150

200

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Nu θ

θ ( 0 )

Re =23 9 Re =35 8 Re =53 4

Fig. 7. Nu� as a function of � and Re for fluidized bed with dp = 700 �m.

58. In this case, for this range of Re, visual observations showedir–particle movement in the bed to have occurred from the bot-om upward, i.e., for � between 0 and 90◦, thus confirming the heatransfer data obtained in Fig. 6. As well, for Re > 239, at the �-degree0 and 135◦, respectively, it is assumed that the decrease in theaximum value of Nu� is due to the stagnant particles located in

hese positions. The air bubbles, eventually generated, are not suffi-ient to efficiently remove these particles as compared to the loweregion of the cylinder (� < 90).

Furthermore, for the greatest value of the air velocity achievednto the bed (Re = 534), the maximum value of local heat-transferoefficient is found to occur around angular direction equals to35◦. Under this condition, the bed attains the fluidized regime andhe particles movement is quite intense. It can be inferred that theoupled effect of both mixing and particles sliding on the surface ofhe cylinder occurs in this region making it a region of short particleesidence time, while a similar situation does not occur at the top ofhe cylinder. The local heat-transfer coefficient at the top (� = 180◦)s lower than that obtained at � equals to 135◦. This air–particleehavior are in agreement to those reported by Kurosaki et al. [37],hich schematically described the mechanisms of heat transfer

etween air–particle and heated cylinder surface.For 700 �m particle diameter, Fig. 7 shows that the higher Nu�

alues are observed to occur on the lateral surface of the cylinderi.e., � = 90◦), except for the lowest value of Re = 239 attained in theed (referring to the packed bed regime). This is due to the appear-nce of region of high particle mixing on the lateral surface (� = 90◦)hich could be visually observed in the bed.

On the other hand, in contrast to the behavior of maximum valuef Nu� for fluidized beds with 500 �m particle diameter in Fig. 6,eds of dp = 700 �m in Fig. 7 shows that, for Re = 534, the maximumalue of Nu� is found to occur at � = 90◦. This can be explained aseing due to the fact that the smaller particles (dp = 500 �m) exhibit

higher degree of circulation and agitation in bed as compared tohe larger ones (dp = 700 �m), considering the same Reynolds num-er (Re = 534). Such an air–particle fluid dynamic behavior of bedsith 500 �m particle diameter promotes a vigorous movement of

nert particles in the sliding region of the cylinder (� = 135◦) thusncreasing Nu� in this region, as can be seen in Fig. 7.

Furthermore, the comparison of the maximum Nu� attained inigs. 6 and 7, for both beds (with dp equals to 500 and 700 �m,espectively) at Re equals to 534, shows that Nu� is higher at theop of the cylinder as compared to those at the stagnation point,

Fig. 8. Nu� as a function of � and Re for vibrated fluidized bed with dp = 700 �m andat � = 1.

suggesting that the decrease in particle residence time in this regionhas a greater contribution to the local heat-transfer than an increaseof convective heat transfer exerted mainly by the air at the stagna-tion point.

Moreover the data of local heat transfer of immersed surface influidized beds with glass beads (ballotini) particles were comparedto the data obtained by Kurosaki et al. [27]. These authors obtainedlocal values of Nu� for a 4 cm diameter cylinder immersed horizon-tally in a rectangular fluidized bed (25 × 9 × 100 cm) with a 16 cmstatic bed height.

Comparing the data obtained by Kurosaki et al. [27] with thoseof this present research, it can be noted that there is similar ten-dencies for the dependence of Nu� on the angular coordinate andthe Reynolds number, even considering the differences among thesystems. Data from Kurosaki et al. [27] were obtained with bed par-ticles of dp = 400 �m and Reynolds number equal to 213 and 393.It was verified that, data from these authors, obtained for Re = 213,present a similar behavior to that of this research using dp = 500 �mand Re = 239. In addition, data from Kurosaki et al. [27] obtainedfor Re = 393 are also comparable to those of this research usingdp = 500 �m and Re = 358. Thus, the comparison proves that thedata of this research are consistent with those reported by theseauthors.

3.2. Local heat-transfer coefficient in vibrated fluidized beds

Fig. 8 shows the results of Nu� as a function of angular coor-dinate for vibrated fluidized bed with 700 �m particle diameter at� = 1. It can be seen in Fig. 8 that, under this operating condition, anapproximately similar trend of Nu� vs. � is also observed in Fig. 7 forthe conventional fluidized bed with the same particle diameter. Byanalyzing data in Figs. 7 and 8, for fluidized and vibrated fluidizedbeds operating at the lowest air velocity (Re = 239), respectively, itcan be seen that the value of Nu� for � = 0◦ is larger than for � = 180◦,conversely to what happens to the highest air velocity (Re = 534).Therefore, the differences between the values of Nu� at the cylin-der top and the stagnation point depend on the air velocity andare more pronounce for the low air velocities, where packed bedregime is achieved in both beds studied. Such a behavior of heat

transfer for the bed without vibration presented in Fig. 7 must berelated to the fact that, for low velocities, there is a greater effectof convective heat transfer of the air at the stagnation point. As theair velocity increases (Re > 239), the particle movement becomes

M.S. Bacelos et al. / Chemical Engineering and Processing 50 (2011) 1152– 1159 1157

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Fig. 10. Nu� as a function of � and dp for vibrated and fluidized beds at Re = 358 and� = 180◦ .

5505004504003503002502000

50

100

150

200

250

300

350

400

Nu θ

Re (- )

Τ = 0Τ = 1Τ = 1.77Τ = 3

ig. 9. Nu� as a function of � and � for vibrated and fluidized beds with dp = 1100 �mnd at Re = 534.

he dominant process in the heat exchange since at the top of theylinder the particles tend to have a shorter residence time at highelocities.

Concerning the effect of vibration on the behavior of Nu� inuidized beds, it can be verified in Fig. 9 that, at all angular posi-ions, the vibration causes an increase in the local heat-transferoefficient, reflecting in the increase of the Nusselt number, whenompared to the bed without vibration. In addition, for both flu-dized and vibrated fluidized beds with 1100 �m particle diameter,t the highest Reynolds number (Re = 534), it can be found the sameehavior of Nu� with the air–particle in crossflow about a cylinderurface, reaching the maximum Nu� at 90◦ and minimum at 0◦ forll range of vibration dimensionless studied. This behavior can bettributed to the intense particle movement in the bed under thisperating condition, which causes the lateral of cylinder (i.e., at the-degree 90 and 135◦) to be submitted to regions more favorableo heat exchange.

Moreover, for all angular directions of the test cylinder, it can beoted in Fig. 9 that peak of the local Nusselt number is attained forhe intermediate value of vibration dimensionless (� = 1.8), thenfter a sharp decrease in Nu� values is observed. This trend ofharp decrease in Nu� for � > 1.8 can be probably explained dueo the particle free-air film established around platinum sensorurface, which blocks the contact of particles in crossflow about

cylinder heated surface, thus reducing the rate of heat transfern the entire circumference of the sensor. Furthermore, for all par-icles investigated, the higher values of Nu� is located at � = 1.8s depicted in Fig. 10. This is in agreement with data (not shownere) of the overall heat-transfer coefficient obtained by Camargo35].

Fig. 10 presents the behavior of Nu� at the top of the cylin-er as a function of � for the studied particle diameters. For allarticles, it can be verified in Fig. 10 that the vibration causes an

ncrease in Nu� . In addition, for 0 < � < 1, it can also be noted that thencrease in Nusselt number is higher for smaller particle diameters.s expected, the smaller particles are used, the larger interfacialurface heating area will be available to promote high rates of heatransfer between the particles and immersed heating area in theed.

With respect to the sliding cylinder region near 135◦, in general,

t can be observed in Fig. 11 that, for values of Re = 239, the contribu-ion of vibration (from � = 1.8 to 3) to the increase in Nu� becomesess pronounced; whereas, for Re > 239, the difference betweenalues of Nu� for � = 1.8 and 3 becomes larger. Furthermore, the

Fig. 11. Nu� as a function of Re and � for vibrated and fluidized beds withdp = 500 �m and � = 135◦ .

vibration achieved in the bed turns out to play a major role in theheat transfer rates as � is increased until reaching the value of1.8, as the higher values of Nu� are attained as shown in Fig. 11.This implies that, at this position of the cylinder, probably the slid-ing of the particles might increase the thermal conductance of theboundary layer formed around between cylinder and air–particleflowing through the layer for the value of � equals to 1.8. Whenthe vibration is increased to � = 3, the particles are in a state ofgreater agitation, being largely sustained by air flow causing slidingof the particles in this region of the cylinder to be less pronounced.At this operating condition (� = 3), the bed is more aerated andthe particles tend to stay in an “air cushion” and consequently, thecylinder is replaced by a larger particle free-air film on its surface,acting as a resistance to heat flow thus, decreasing the value ofNu�.

4. Conclusions

Comparing to the fluidized beds, for all range of air velocity andvibration dimensionless investigated, the vibrated fluidized beds

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resented a significant increase in the local heat-transfer coefficientor the entire cylindrical circumference. This is attributed to theoosen particle bed as well as the good air–particle mixing achievedy vibrated fluidized beds.

In general, with respect to the heat transfer in vibrated fluidizededs, as particle diameter decreases, ranging from 500 to 1100 �m

n diameter, the local heat-transfer coefficient increases with anncrease in the air velocity and vibration on the beds. In addition,he maximum Nu� attained in the vibrated fluidized beds wereocated at � equals to 1.8. For higher values of � , the contribu-ion of vibration on the increase in the Nu� is less pronounceds Re increases. On the other hand, for 0 < � < 1.8, the increasen the Nu� is greater as particle size decreases, suggesting that aeduction of particle diameter should increase the ratio of inter-acial surface heating area available per unit of bed volume andacilitate the contact between the heater and vibrated air–particleed.

Moreover, such results imply that performance of vibrated flu-dized beds on heat transfer is competitive with fluidized bedsomposed of suitable particles (i.e., dp < 1000 �m) and state thatibrated fluidized beds can be used in practical applications com-only used for fluidized beds.

cknowledgement

The authors wish to express their gratitude to Conselho Nacionale Desenvolvimento Científico e Tecnológico–CNPq for its financialupport in carrying out this research.

ppendix A. Nomenclature

amplitude of vibration [m] local area of the platinum sensor [m2]

cylinder diameter [m]p particle diameter [�m]

vibration frequency [Hz] gravity accelaration [m/s2]

� local heat-transfer coefficient in the angular direction �[W m−2 K−1]

electrical current [A] bed height [m]f air thermal conductivity [W/(m K)]u� Nusselt number in the angular direction �, defined by

h�.d/kf [–] power lost by platinum sensor [W]e Reynolds number, defined by ud/� [–]F reference electrical resistance [�]S sensor electrical resistance [�]S sensor temperature [◦C]L bed temperature

superficial air velocity, calculated using the inside columndiameter [m/s]

1 electrical voltage before sensor on the circuit in Fig. 4 [V]2 electrical voltage after sensor on the circuit in Fig. 4 [V]

reek symbols vibration dimensionless, defined by (a·2�f)2/g [–]

angular position on the heated cylinder surface [◦] kinematic viscosity air [m/s2]

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