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Chemical Engineering and Processing 48 (2009) 1341–1345

Contents lists available at ScienceDirect

Chemical Engineering and Processing:Process Intensification

journa l homepage: www.e lsev ier .com/ locate /cep

ree convective mass transfer at corrugated surfaces in relationo catalytic and electrochemical reactor design

brahim Hassan a, Inderjit Nirdosh b,∗, Gomaa Sedahmed c

Faculty of Engineering, Arab Academy of Science and Technology, Alexandria, EgyptDepartment of Chemical Engineering, Lakehead University, Thunder Bay, ON, Canada P7B 5E1Chemical Engineering Department, Alexandria University, Alexandria, Egypt

r t i c l e i n f o

rticle history:eceived 28 January 2009eceived in revised form 11 June 2009ccepted 18 June 2009vailable online 26 June 2009

eywords:ass transfer

ree convectionorrugated surfaces

a b s t r a c t

The free convective mass transfer behavior of V-corrugated horizontal and vertical surfaces was studiedby measuring the limiting current of the cathodic deposition of copper from acidified copper sulphatesolution. Variables studied were peak-to-valley height and angle of the V-grooves, physical properties ofthe solution and vertical electrode height. For vertical corrugated surfaces, the data were correlated bythe equation:

Sh = 0.78(Sc · Gr)0.26

while the data for the horizontal corrugated surfaces were found to fit the equation:

Sh = 1.64(Sc · Gr)0.23

A comparison with the free convection mass transfer behavior of flat plates shows that the mass transfercoefficient at vertical corrugated surface is higher than that at vertical flat plates. For horizontal surfacesthe reverse is true.

The importance of the present results to the design and operation of electrochemical reactors, mem-brane processes and catalytic reactors which employ corrugated surfaces to conduct diffusion-controlled

processes is highlighted.

. Introduction

In view of their turbulence promoting ability, corrugated sur-aces have been used widely to improve the rate of forcedonvection heat and mass transfer in equipments such a heatxchangers [1], solar collectors [2], electrochemical [3] and catalytic4] reactors and membrane processes [5]. To increase the degree ofonversion and the residence time per pass in the continuous oper-tion of equipments conducting diffusion-controlled processes, loweed rates should be used. Under such conditions free convectionecomes pronounced and contributes significantly to the rate ofass transfer along with forced convection [6] according to the

quation:

overall =[K3

forced + K3free

]1/3(1)

Accordingly, knowledge of the natural convection mass trans-er coefficient at corrugated surfaces is essential for the design and

∗ Corresponding author. Tel.: +1 807 343 8343; fax: +1 807 343 8928.E-mail address: inirdosh@lakeheadu.ca (I. Nirdosh).

255-2701/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2009.06.006

© 2009 Elsevier B.V. All rights reserved.

operation of equipments which use such surfaces. Besides, knowl-edge of the natural convection mass transfer behavior of corrugatedsurfaces is essential for predicting the rate of diffusion-controlledprocesses which might be used to produce metallic corrugated sur-faces such as etching, electropolishing, electroplating, electrolessplating, electroforming and electrochemical machining.

Although some work has been carried out on the forced con-vection heat and mass transfer behavior of corrugated surfaces[7–10], little has been done on their natural convection behav-ior. Abdurrachim et al. [11] studied the natural convection masstransfer behavior of a vertical and slightly inclined surface withsinusoidal corrugations by measuring the limiting current of thecathodic reduction of ferricyanide ions in a large excess of NaCl.The authors found that the rate of mass transfer at the corrugatedsurface is close to that of vertical flat plate. In the area of heat trans-fer, El-Sherbiny et al. [12] performed experiments in an enclosurewith one V-corrugated and one flat surface using air and found

that the heat transfer coefficient increased by up to 50% comparedto an enclosure with two smooth surfaces. Al-Arabi and El-Rafaee[13] studied the rate of natural convection heat transfer from a V-corrugated plate to air and found that corrugations provided higherrates of heat transfer than that provided by the flat plate.

1 ing and Processing 48 (2009) 1341–1345

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342 I. Hassan et al. / Chemical Engineer

The aim of the present study was to investigate the natu-al convective mass transfer behavior of horizontal and vertical-corrugated surfaces by measuring the limiting current of theathodic deposition of copper from acidified copper sulphate solu-ion. According to Selman and Tobias [14] the Cu–CuSO4 systems superior to the ferricyanide system in measuring rates of naturalonvection mass transfer by the limiting current technique. The celleactions are:

t cathode : Cu2+ + 2e− → Cu (2)

t anode : Cu → Cu2+ + 2e− (3)

Thus the amount of Cu2+ dissolved from the anode is equal tohat deposited on the cathode. As a consequence the copper iononcentration remains constant at the initial value during experi-ents.

. Experimental technique

Fig. 1 shows the cell and the electrical circuit used in the presentork. The circuit consisted of a 12 V d.c. Power supply with a volt-

ge regulator connected in series with a mutirange ammeter andhe cell. For vertical corrugated surfaces a plastic rectangular cell ofhe dimensions 6.4 cm × 7.5 cm for the base and 25 cm height wassed. A corrugated copper plate of 6.3 cm width and 25 cm heightas used as a cathode and a flat copper plate of similar dimen-

ions was used as anode. Each electrode was fitted snugly in theell at the opposite cell walls. The active height of the cathode wasontrolled by isolating the undesired part by a Teflon tape. Active

athode heights of 2.5, 5, 7.5, 10 and 15 cm were used. For horizon-al corrugated surfaces a plastic rectangular cell of the dimensions6 cm × 6.5 cm for the base and 20 cm height was used. A corru-ated copper plate of the dimensions 6.3 cm × 15 cm was rested onhe wall bottom in such a way that its corrugated side was fac-

ig. 1. (a) The cell and the electrical circuit: (1) 12 V d.c. power supply, (2) multirangemmeter, (3) cathode, (4) anode, (5) reference electrode, (6) Luggin tube, (7) highmpedance voltmeter, (8) electrolyte level. (b) Geometry of the corrugated surface.

Fig. 2. Typical polarization curves at a vertical corrugated surface. [CuSO4],M = 0.027; peak-to-valley height = 1 cm. V-angle (�): (×) 75◦; (�) 60◦; (�) 45◦; (©)30◦ .

ing upward while its insulated flat side was facing downward. Aflat horizontal copper anode of the same dimensions was placedat a distance 6 cm from the cathode, according to Wragg [15] thisdistance is sufficient to eliminate interference between cathodicnatural convection and anodic natural convection.

The anode was brazed to 0.5 cm diameter insulated copper rodwhich acted as anode support and a current feeder. The horizontalanode contained a 0.5 cm hole through which a Luggin tube waspassed to the cathode. Electrodes were corrugated in a V-Formby means of a programmable milling machine. V-grooves of fourdifferent angles (�), viz., 30◦, 45◦, 60◦ and 70◦, and four differentpeak-to-valley heights (P), viz., 0.5, 0.75, 1 and 1.5 cm, were used.

Before each run the cell was filled with a fresh solution of acid-ified copper sulphate solution; the cathode and the anode werepickled for 10 min in 10% HCl to remove any adhering oxides, thecathode was treated with fine emery paper and then both elec-trodes were rinsed and dried. The limiting current was determinedby increasing the current stepwise and measuring the steady statecathode potential against a reference electrode by means of highimpedance voltmeter. The reference electrode consisted of a cop-per wire placed in the cup of a Luggin tube filled with a solutionidentical with the cell solution, the tip of the Luggin tube beingplaced at about 0.5 mm from the corrugated surface. Four differentcopper sulphate solutions were used namely, 0.027, 0.05, 0.131 and0.25 M, and in all cases 1.5 M H2SO4 was used as a supporting elec-trolyte. All chemicals were of analytical grade. Temperature was22 ± 1 ◦C. The physical properties of the solutions (�, �, D) neededfor data correlation were obtained from the literature [14,16]. Theconcentration of CuSO4 in the solution was analysed via InductivelyCouples Plasma Spectrometry (ICP) and occasionally checked withiodometry [17].

3. Results and discussion

Fig. 2 shows typical polarization curves with a well-defined lim-iting current plateau, the mass transfer coefficient was obtainedfrom the limiting current using the equation:

K = ILZ FAC

(4)

Since each groove in the V-corrugated surface is bounded by

two rectangular surfaces, each having a slant height h (=P/cos �/2)and a width w, the area (A) of the corrugated surface was thereforecalculated from the equation:

A = 2nhw (5)

I. Hassan et al. / Chemical Engineering and Processing 48 (2009) 1341–1345 1343

Fg0

ws

paiTtt[avrviflsmgiadiasa

h

Fv(

was adopted to obtain a simple mass transfer equation, Lc beinggiven by:

ig. 3. Effect of groove angle (�◦) on the mass transfer coefficient at vertical corru-ated surface. Peak-to-valley height (P) = 1 cm; H = 15 cm. [CuSO4], M: (�) 0.027; (©).05; (�) 0.131; (×) 0.25.

here n is the number of grooves in the corrugatedurface.

Figs. 3 and 4 show the effect of the V-groove angle, �, andeak-to-valley height respectively on the mass transfer coefficientt the vertically oriented surface. The mass transfer coefficientncreases with increasing the angle � and the peak-to-valley height.his result could be explained in terms of the orientation of thewo planes forming the V-groove, the natural convection flow athe upper downward-facing surface is an attached laminar flow18,19] while the flow at the lower upward-facing surface may beccompanied with boundary layer separation depending on thealue of Sc·Gr. Within the present range of conditions where Sc·Granges from 5.8 × 106 to 1.36 × 109 (based on using the peak-to-alley height as a characteristic length) boundary layer separations likely to take place with eddy formation at the lower upward-acing surface of the groove [18,19]. The flow arising from theower upward-facing surface strikes the upper downward-facingurface of the groove with a consequent increase in the rate ofass transfer. For a given peak-to-valley height, as the angle of the

roove, �, increases, the amount of solution contained in the groovencreases with a subsequent increase in the tendency of the flowrising from the lower upward-facing surface towards the upperownward-facing surface of the groove to be enriched with copper

ons. Besides, the diffusional area between the mouth of the groovend the bulk solution increases with increasing the angle �, diffu-

ion of copper ions from the solution bulk to the groove solutioncross this area makes up for the deposited copper ions.

Figs. 5 and 6 show the effect of groove angle �, and peak-to-valleyeight respectively on the mass transfer coefficient at corrugated

ig. 4. Effect of groove peak-to-valley height on the mass transfer coefficient atertical corrugated surface. Groove angle (�) = 450; H = 15 cm. [CuSO4], M: (©) 0.027;�) 0.05; (�) 0.131; (×) 0.25.

Fig. 5. Effect of groove angle (�) on the mass transfer coefficient at horizontal cor-rugated surface. Peak-to-valley height (P) = 1 cm. [CuSO4], M: (©) 0.027; (�) 0.05;(�) 0.131; (×) 0.25.

horizontal surface, the mass transfer coefficient decreases withincreasing peak-to-valley height but increases with increasing thegroove angle �. For a given angle �, the decrease in the mass transfercoefficient with increasing peak-to-valley height may be ascribed tothe increase in the thickness of the attached portion of the hydrody-namic boundary layer as the free convection flow progresses alongthe two surfaces bounding the groove. For a given peak-to-valleyheight the increase in the mass transfer coefficient with increasingthe groove angle � may be attributed to the increased possibility ofboundary layer separation from the two upward-facing surfaces ofthe groove as the angle � increases [18,19].

Fig. 7 shows the effect of height of the vertical corrugated sur-face on the mass transfer coefficient, the mass transfer coefficientdecreases with increasing electrode height. This may be explainedas follow: the depleted solution emerging from different groovesflows vertically parallel to the vertical corrugated surface in theform of a curtain whose thickness increases with increasing elec-trode height, i.e., the distance across which diffusion of Cu2+ fromthe solution bulk to the depleted groove solution increases withincreasing electrode height in a manner similar to an attachedhydrodynamic boundary layer.

To obtain an overall mass transfer correlation, the characteristiclength, Lc, suggested by Weber et al. [20] for complex geometries

Lc = active surface areaperimeter of the corruaged surface projected onto a horizonal plane

(6)

Fig. 6. Effect of peak-to-valley height on the mass transfer coefficient at horizontalcorrugated surface. Groove angle (�) = 45◦ . [CuSO4], M: (©) 0.027; (�) 0.05; (�) 0.131;(×) 0.25.

1344 I. Hassan et al. / Chemical Engineering and Processing 48 (2009) 1341–1345

Fig. 7. Effect of vertical corrugated surface height on the mass transfer coefficient.Peak-to-valley height (P) = 1 cm; groove angle (�) = 60◦ . [CuSO4], M: (×) 0.027; (�)0.131; (©) 0.25.

F(

c2

S

w

t2

S

FM

Table 1Comparison between the natural convection mass transfer behavior at corrugatedsurfaces and flat surfaces.

CuSO4 conc. (M) Mass transfer coefficient (×103 cm/s)

Vertical surface Horizontal surface

Corrugated Flat Corrugated Flat

0.027 0.328 0.187 0.332 0.3390.05 0.355 0.213 0.372 0.489

ig. 8. Overall mass transfer correlation at vertical corrugated surface. [CuSO4], M:�) 0.027; (©) 0.05; (�) 0.131; (×) 0.25

Fig. 8 shows that the mass transfer data at verticalorrugated surface for the conditions 1767 < Sc < 2038 and.6 × 108 < Sc·Gr < 6.25 × 1012 fit the equation:

h = 0.78(Sc · Gr)0.26 (7)

ith an average deviation of ±11.9%.Fig. 9 indicates that the mass transfer data at horizon-

al corrugated surfaces for the conditions 1767 < Sc < 2038 and.3 × 109 < Sc·Gr < 2.5 × 1011 fit the equation:

h = 1.64(Sc · Gr)0.23 (8)

ig. 9. Overall mass transfer correlation at horizontal corrugated surface. [CuSO4],: (�) 0.027; (�) 0.05; (×) 0.131; (©) 0.25.

0.131 0.414 0.265 0.432 0.550.25 0.496 0.297 0.508 0.64

Electrode height = 15 cm; � = 45◦ , peak-to-valley height = 1.5 cm.

with an average deviation of ±5.9%. The exponents 0.26 and 0.23 ofEqs. (7) and (8) show that the flow is almost laminar at horizontaland vertical corrugated surfaces.

It would be of interest to compare the mass transfer behavior ofcorrugated surfaces with flat surfaces. Table 1 shows that the masstransfer coefficient at vertical corrugated surface is higher than thatat a vertical flat surface of the same height, the mass transfer coef-ficient of the vertical flat surface was calculated from the equation[16]

Sh = 0.67(Sc · Gr)0.25 (9)

For horizontal surfaces, Table 1 shows that the mass transfercoefficient at horizontal corrugated surfaces is less than that at a flathorizontal surface having the same projected dimensions, the masstransfer coefficient of the upward-facing flat surface was calculatedfrom the equation [21]

Sh = 0.16(Sc · Gr)0.33 (10)

It is noteworthy that Table 1 shows that for a given set of condi-tions the mass transfer coefficient at horizontal corrugated surfaceis slightly higher than that at vertical corrugated surface.

4. Conclusions

V-corrugations were found to enhance the rate of natural con-vection mass transfer at vertical surfaces over the flat plate value byan amount ranging from 56 to 75% depending on the groove angle,the peak-to-valley height and the Schmidt number. For horizontalcorrugated surfaces the mass transfer coefficient was found to beless than the corresponding flat plate value by an amount rangingfrom 2 to 24% depending on the operating conditions. However,the use of corrugated surfaces either in the vertical or the horizon-tal position in designing mass transfer equipments would offer theadvantage of high volumetric mass transfer coefficient (Ka) besidepromoting turbulence when laminar forced convection is used inoperating such equipments.

Acknowledgements

This research was funded by the Natural Sciences and Engi-neering Research Council of Canada. Sincere thanks are due to Mr.Kailash Bhatia, the Mechanical Engineering Technologist, for helpin constructing the apparatus.

Appendix A. Nomenclature

A area of the corrugated surface (m2)

a specific surface area (m2/m3)C bulk concentration of CuSO4D diffusivity (m2/s)F Faraday’s constant (96500 C/equiv.)g acceleration due to gravity (m/s2)

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I. Hassan et al. / Chemical Engineer

V-groove slant height (=P/cos �/2) (m)active height of the vertical corrugated surface (m)

L limiting current (A)mass transfer coefficient (m/s)

c characteristic length defined by Eq. (6) (m)number of grooves in the corrugated surfacepeak-to-valley height (m)width of the corrugated surface (m)number of electrons involved in the reaction

imensionless numbersh Sherwood number (KLc/D)c Schmidt number (�/�D)r Grashoff number (gLc

3��/��2)

reek symbolsangle of the V-groove (◦)absolute solution viscosity (kg/m s)kinematic solution viscosity (m2/s)solution density (kg/m3)

� density difference between the bulk and the interfacialsolutions (kg/m3)

eferences

[1] F. Kreith, M.S. Bohm, Principles of Heat Transfer, West Publishing Co., N.Y.,1993.

[2] R. Anderson, F. Kreith, Natural convection in active and passive solar thermalsystems, Adv. Heat Transf. 18 (1987) 1–86.

[3] S.L. Gojkovic, Mass transfer in electrochemical oxidation of methanol at plat-inum electrocatalyst, J. Electroanal. Chem. 573 (2004) 271–276.

[

[

[

d Processing 48 (2009) 1341–1345 1345

[4] Z. Zhang, W.A. Anderson, M. Moo-Young, Experimental analysis of a corrugatedplate photocatalytic reactor, Chem. Eng. J. 99 (2004) 145–152.

[5] M.H.V. Mulder, in: R.D. Noble, S.A. Stern (Eds.), Membrane Separation Technol-ogy: Principles and Applications, Elsevier, Amsterdam, 1995.

[6] S.W. Churchill, A comprehensive correlating equation for laminar assistedforced and free convection, AIChE J. 23 (1997) 10–16.

[7] P. Naphon, Laminar convective heat transfer and pressure drop in the corrugatedchannels, Int. Commun. Heat Mass Transf. 34 (2007) 62–71.

[8] S.D. Hwang, I.H. Jang, H.H. Cho, Experimental study on flow and local heat/masstransfer characteristics inside corrugated duct, Int. J. Heat Fluid Flow 27 (2006)21–32.

[9] L.Z. Zhang, Convective mass transfer in cross corrugated membrane exchangers,J. Membr. Sci. 260 (2005) 75–93.

10] C. Zimmerer, P. Gschwind, G. Gaiser, V. Kottle, Comparison of heat and masstransfer in different heat exchanger with corrugated walls, Exp. Therm. FluidSci. 26 (2002) 269–273.

11] H. Abdurrachim, F. Karouta, M. Daguenet, Laminar natural convection aboutcorrugated surfaces—theoretical and experimental verification, J. Electroanal.Chem. 122 (1981) 53–66.

12] S.M. El-Sherbiny, K.G.T. Hollands, G.D. Raithby, Free convection across inclinedair layers with one surface V-corrugated, Trans. ASME 100 (1978) 410–415.

13] M. Al-Arabi, M.M. El-Refaee, Heat transfer by natural convection from corru-gated plates to air, Int. J. Heat Mass Transf. 21 (1978) 357–359.

14] J.R. Selman, C.W. Tobias, Mass transfer measurements by the limiting currenttechnique, Adv. Chem. Eng. 10 (1978) 211–318.

15] A.A. Wragg, Free convection mass transfer at horizontal electrodes, Electrochim.Acta 13 (1968) 2159–2165.

16] C.R. Wilke, M. Eisenberg, C.W. Tobias, Correlation of limiting currents under freeconvection conditions, J. Electrochem. Soc. 100 (1953) 513–523.

17] A.I. Vogel, Quantitative Inorganic Analysis, 4th ed., Longmans, Green and Co.,London, 1978, 372–380.

18] M.A. Patrick, A.A. Wragg, D.M. Pargeter, Mass transfer by free convection duringelectrolysis at inclined electrodes, Can. J. Chem. Eng. 55 (1977) 432–438.

19] M.G. Fouad, A.M. Ahmed, Mass transfer by free convection at inclined elec-trodes, Electrochim. Acta 14 (1969) 651–666.

20] M.E. Weber, P. Astrauskas, S. Petsalis, Natural convection mass transfer to non-spherical objects at high Rayleigh number, Can. J. Chem. Eng. 62 (1984) 68–72.

21] G.H. Sedahmed, I. Nirdosh, Natural convection mass transfer at an enclosurebetween two horizontal discs, Chem. Eng. Commun. 101 (1991) 93–102.