Ind. Eng. Chem. Res. 1995,34,2133-2137
2133
Natural Convection Mass Transfer at a Vertical Array of Closely-Spaced Horizontal Cylinders with Special Reference to Electrochemical Reactor Design G. H. Sedahmedt and I. Nirdosh* Department of Chemical Engineering, School of Engineering, Lakehead University, Thunder Bay, Ontario, Canada P7B 5El
Natural convection mass transfer at a vertical array of closely-spaced horizontal cylinders was studied by an electrochemical technique involving the measurement of the limiting current of the cathodic deposition of copper from acidified copper sulfate solution. Various combinations of solution concentration, cylinder diameter, and number of cylinders per array were used including experiments on single cylinders. Results for single cylinders are correlated in the . ~ ~mass ~ . transfer range 1.5 x lo7 < Sc-Gr < 1.3 x 1O1Oby the equation Sh = 0 . 2 3 1 ( S ~ . G r ) ~The coefficient at the array was found to decrease with increasing number of cylinders, pass through a minimum, and then increase with further increase in the number of cylinders per array; the mass transfer coefficient increased with increasing cylinder diameter in the array. Mass transfer data for different arrays were correlated for the range 6.3 x lo9 < ScGr < 3.63 x 1O1O by the equation Sh = 0.455(S~.Gr)O.~~ and for the range 6.3 x 1O1O < Sc*Gr 3.63 x 10l2by the equation Sh = 0 . 0 0 6 4 ( S ~ * G r ) ~The . ~ ~characteristic . length used in the above correlations was obtained by dividing the array area by the perimeter projected onto a horizontal plane. Practical implications of the present results in designing electrochemical reactors with heat transfer facilities are highlighted.
Introduction Many industrial electrochemical processes such as electrowinning of metals, electrochemical pollution control, and electroorganic and electroinorganic syntheses are diffusion-controlled processes whose rates depend on the geometry of the working electrode as well as the prevailing hydrodynamic conditions. Recently much work has been done t o develop new electrochemical reactors which are more efficient than the traditional parallel plate electrochemical r e a ~ t o r l -used ~ in conducting such processes. In line with this, the object of the present work was to study the natural convection mass transfer behavior of a new electrode geometry, namely an array of closely-spaced horizontal tubes. The potential importance of such a geometry is that it can be used as an electrode in electrochemical reactors used to conduct diffusion-controlled heat-sensitive electrochemical reactions which may be adversely affected by the heat generated during electrolysis. In this case the electrochemical reaction would take place at the outer surface of the array tubes while the inner surface of the tubes would serve as a heat exchanger where cold water circulates t o control the reactor temperature. This would lead to simplification of the electrochemical reactor design and reduce the capital costs owing to the elimination of external heat exchangers and internal cooling coils. The study of natural convection mass transfer behavior of the array would assist in predicting the rate of production of the diffusion-controlled electrochemical processes conducted under natural convection or under weak forced convection where natural convection contributes significantly to the rate of mass t r a n ~ f e r .By ~ virtue of the analogy between heat and mass transfer, the present study would also make it possible to predict the hot side heat transfer coefficient
' Permanent address: Chemical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria, Egypt.
where the reaction takes place. Previous heat6,7and mass transfer s t ~ d i e son ~ vertical >~ arrays of horizontal cylinders have dealt with arrays made of spaced (separated) horizontal cylinders. Arrays of closely-spaced horizontal cylinders have the advantage over spaced arrays in that the aredunit volume is higher, i.e., the productivity of the reactor using closely-spaced array would be higher. The present work may be also of a value to building catalytic and biochemical reactors where a diffusion-controlled heat sensitive reaction takes place. The present study was carried out by measuring the limiting current of the cathodic deposition of copper from acidified copper sulfate solutions.
Experimental Technique Figure 1 shows the cell and electrical circuit used. The cell consisted of a 2 L glass container of 12 cm inside diameter and 19 cm height. Two types of cathodes were used, namely horizontal single cylinders and vertical arrays of closely-spaced horizontal cylinders. Five copper cylinders of diameters 0.64,1.27,1.59,2.22, and 2.54 cm were used, all having a length of 7 cm. Arrays of closely-spaced horizontal cylinders were built by fixing the closely-spaced horizontal cylinders at their ends t o two vertical rectangular strips of insulated copper having a width equal t o the cylinder diameter. Each cylinder was fixed to the two vertical supports by a screw thread. To study the effect of number of cylinders per array on the rate of mass transfer, six arrays were built having number of cylinders two, three, four, five, six, and seven; cylinder diameter and length were 1.59 and 7 cm, respectively. To study the effect of cylinder diameter on the array mass transfer coefficient, six different arrays were built of cylinders of diameters 0.64, 1.27, 1.59,2.22, or 2.54 cm, each array containing seven cylinders with array width being 7 cm in all cases. The cell anode was a cylindrical sheet of copper having 11.8 cm diameter and 19 cm height. The cathode was
0888-5885/95/2634-2133$09.Q0100 1995 American Chemical Society
2134 Ind. Eng. Chem. Res., Vol. 34,No. 6, 1995 No. of cylindmper arrayz7 Cylinder diamcter=2.5cm [CuSO,I,M
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Figure 2. Typical polarization curves obtained for a seven cylinder array at different CuSO4 concentrations.
Figure 1. The apparatus.
held in position by a 2 mm insulated copper wire threaded to the single cylinder cathode or to the upper cylinder of the array. Besides acting as a cathode holder the insulated wire acted also as a current feeder to the cathode. The circuit used consisted of a dc power supply with an internal voltage regulator and a multirange ammeter connected in series with the cell. Before each run the cell was filled with the solution. Cathodes were treated as described by Wilke et al.1° and positioned in the center of the cell. Polarization curves from which the limiting current was obtained were constructed by increasing the current stepwise and measuring the steady state cathode potential against CdCuS04 reference electrode placed in the cup of a Luggin tube filled with the cell solution by means of a potentiometer. The tip of the Luggin tube was placed 0.5-1 mm from the cathode surface. In case of array cathodes, the tip of the Luggin tube was placed a t the middle of the array. Preliminary experiments showed that location of the Luggin tip has no effect on the limiting current. Four CuSO4 concentrations were used, namely, 0.0498,0.0966, 0.188, and 0.247 mom. Higher CuSO4 concentrations were avoided because they gave an ill-defined limiting current plateau probably because of copper powder formation and H2 evolution at the array cathode a t high CuSO4 concentrations. In all cases 1.5 m o m H2S04 was used as supporting electrolyte to eliminate the transfer of copper ions to the cathode surface by electrical migration. All solutions were prepared from AR grade chemicals and demineralized water. Each run was carried out twice. The temperature was 23 f 0.5 "C.
Results and Discussion Figure 2 shows typical polarization curves with a welldefined limiting current plateau obtained for different CuSO4 concentrations. From these polarization curves the limiting current was obtained and used to calculate the mass transfer coefficient according to the equation
The mass transfer coefficient for a single horizontal
cylinder was correlated to other variables by the dimensionless groups Sh, Sc, and Gr. Physical properties of the solution (e,,LA, D ) used to calculate these dimensionless groups are listed in Table 1and were obtained from the literature. Figure 3 shows that the data for single horizontal cylinders for the conditions 2.4 x lo7 < Sc-Gr < 6.9 x lo9 fit the equation
Sh = 0 . 2 3 ( S ~ . G r ) ' . ~ ~ ~
(2)
with an average deviation of f8.8%. The correlation coefficient was found to be 0.9666. The exponent 0.283 indicates mass transfer by unstable natural convection flow. This is consistent with the finding of Schutz12that deviation from laminar flow natural convection a t horizontal cylinders takes place a t Sc-Gr =- lo9 owing to the onset of turbulence. Figure 3 also shows that the present data are in fair agreement with the results of previous studies on natural convection mass transfer a t horizontal cylinders. Sedahmed and Shemilt13correlated their data for the range 1.5 x lo7 -= Sc-Gr < 1.3 x 1O1O by the equation
Sh = 0.264(S~.Gr)'.~~
(3)
Smith and Wrage correlated their data in the range 6.58 x lo6 < Sc*Gr < lo9 by the equation
Sh = 0.56(S~.Gr)'.~~ Schutz12correlated his data in the range lo9 by the equation
(4)
lo3 < ScGr
6.3 x 1O1O shows that the flow changes from laminar to turbulent at this value. A comparison between the present data and the vertical flat plate datal5 represented for the conditions lo9 ScGr 1014by the equation
Sh = 0 . 1 ( S ~ * G r ) ~ . ~ ~
(10)
shows that the rates of mass transfer at the array electrode lie below that of the vertical plate. The low mass transfer rates at the cylinder array compared to the vertical plate may be attributed in part to the diminished concentration effect which prevails in recessed parts between successive cylinders. It is noteworthy that the mass transfer behavior of cylinder array compared to the vertical plate is different from that of corrugated vertical surfaces. Abdurrachim et a1.16 studied the natural convection mass transfer behavior of a sinusoidally corrugated vertical plate using an electrochemicaltechnique which involved measuring the limited current of the cathodic reduction of ferricyanide; the corrugation height was 0.05 cm while the corrugation wavelength ranged from 0.5 t o 1.5 cm. They found that the mass transfer data at the corrugated surface coincided with the vertical plate data. It seems that the decreased concentration effect which prevails in cylinder array recessed areas is not pronounced in the case of the corrugated surface owing to the small protrusion height of the corrugated surface (0.05 cm). In view of the present results with closely-spaced cylinder array and the results obtained with arrays of separated cylinders,s the question arises as to which array type is more advantageous in building electrochemical reactors with heat transfer facilities. For a given array height, separated cylinder arrays have a lower active area per unit electrode volume but have a higher mass transfer coefficient than closely-spaced cylinder arrays.8 In designing electrochemical reactors, electrode efficiency is usually measured by the value of the volumetric mass transfer coefficient per unit electrode volume (KAN). Table 2 shows a tentative comparison between KAN for a separated cylinder array of six cylinders using the available data of Smith and Wrag2 and a closely-spaced array (present data). In
Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995 2137 Table 2. Comparison between the Volumetric Mass Transfer Coefficients per Unit Electrode Volume for Separated Cylinder Arrays* and Closely-SpacedArrays (Present Work) Using an Array of Six Cylinders cylinder diameter (cm) 2.83 2.83 2.83 2.83" 0.94 0.94 0.94" a
cylinder separation (312)d (514)d (9/8)d
Od" 2d 1.5d Od"
KAN (s.1) 1.328 x 1.329 x 1.375 x 6.89 x 4.26 x 4.50 x 5.02 x
Present data.
ei
= density of the interfacial solution constants
Appendix. Sample Calculation of the CharacteristicLength (L,) for Cylinder Array Consider a cylinder array composed of seven horizontal cylinders with insulated ends, each cylinder of 2.54 cm diameter and 7 cm length. array area = number of cylinders x cylinder area = 7 x 3.14 x 2.54 x 7 = 390.8 cm2 perimeter of the array projected onto a horizontal plane = 2[cylinder diameter cylinder length]
+
+
calculating the separated array volume, the empty space between cylinders was included in the array volume. Table 2 shows that the volumetric mass transfer coefficient per unit array volume is higher for the closelyspaced array especially for a large cylinder diameter.
= 2[2.54 71 = 19.08 cm According to equality 7, L,is given by
Conclusions 1. Natural convection mass transfer at arrays of
Literature Cited
closely-spaced horizontal cylinders was found to depend on the cylinder diameter and the number of cylinders per array. The mass transfer coefficient of the array increased with increasing cylinder diameter. With increasing the number of cylinders per array, the mass transfer coefficient initially decreased below the single cylinder value and then changed slightly with further increases in the number of cylinders. 2. Mass transfer data at arrays of closely-spaced cylinders were correlated easily owing to the absence of the irregular effect of the intercylinder spacing encountered in the case of arrays of separated cylinders. The data fit the equations
Sh = 0 . 4 5 5 ( S ~ * G r ) ~ . ~ ~ for 6.3 x lo9 < ScGr < 6.3 x
lolo, and
Sh = 0 . 0 0 6 4 ( S ~ * G r ) ~ . ~ ~ for 6.3 x 1O1O < ScGr < 3.63 x 10l2. 3. Closely-spacedcylinder arrays have a lower mass transfer coefficient than the separated cylinder arrays. However, the fact that closely-spaced cylinder arrays have higher area per unit electrode volume makes their volumetric mass transfer coefficient (Ku), which determines the electrode productivity, compete with that of separated cylinder arrays.
Nomenclature A = surface area of the cathode a = specific surface area C = bulk concentration of cupric ions d = cylinder diameter D = diffisivity F = Faraday's constant g = acceleration due to gravity ZL = limiting current K = mass transfer coefficient L, = characteristic length (for single cylinder L, = d; for arrays L, is given by eq 7) Sh = Sherwood number (ILCJD) S c = Schmidt number (v/D) Gr = Grashof number (gLC3A~lv2@i) V = array volume a, p, y = constants p = dynamic viscosity v = kinematic viscosity @/e) Ae = density difference between bulk solution and interfacial solution
L, = 390.8l19.08 = 20.48 cm (1)Pickett, D. Electrochemical Reactor Design; Elsevier: New York, 1977. (2)Heitz, E.;Kreysa, G. Principles of Electrochemical Engineering; VCH: Weinheim, 1986. (3)Walsh, F.A First Course in Electrochemical Engineering; The Electrochemical Consultancy: London, 1993. (4)Pletcher, D.; Walsh, F. W. Industrial Electrochemistry, 2nd ed.; Chapman and Hall: New York, 1990. (5) Selman, J. R.; Tobias, C. W. Mass transfer measurement by the limiting current technique. Adv. Chem. Eng. 1978,IO,211318. (6)Marsters, G. F. Arrays of heated horizontal cylinders in natural convection. Int. J. Heat Mass Transfer 1972,15,921933. (7)Ishihara, I.; Katsuta, K. Studies on natural convection heat transfer from horizontal cylinders in a vertical array. Heat Transfer Sci. Technol. [Proc. Znt. Symp. Heat Transfer], 1985; Wang, Bu Xuan, Ed.; Hemisphere: Washington, DC, 1987;pp 121-128. (8) Smith, A. F. J.; Wragg, A. A. An electrochemical study of mass transfer in free convection at vertical arrays of horizontal cylinders. J. Appl. Electrochem. 1974,4,219-228. (9)Wragg, A. A,; Patric, M. A.; Mustoe, L. H. Transient and optical studies of free convective mass transfer during electrodeposition a t single and multi-cylinder cathodes. J.Appl. Elecrochem. 1975,5,359-361. (10)Wilke, C. R.; Eisenberg, M.; Tobias, C. W. Correlation of limiting currents under free convection conditions. J.Electrochem. SOC.1953,100,513-523. (11)Eisenberg, M.; Tobias, C. W.; Wilke, C. R. Selected physical properties of ternary electrolytes employed in ionic mass transfer studies. J. Electrochem. Soc. 1956,103, 413-416. (12)Schutz, G. Natural convection mass transfer measurements on spheres and horizontal cylinders by an electrochemical method. Znt. J.Heat Mass Transfer 1963,6,873-879. (13)Sedahmed, G.H.; Shemilt, L. W. Natural convection mass transfer at cylinders in different positions. Chem. Eng. Sei. 1982, 37,159-166. (14)Webber, M. E.; Astraukas, P.; Petsalis, S. Natural convection mass transfer to nonspherical objects at high Rayleigh number. Can. J. Chem. Eng. 1984,62,68-72. (15)Incropera, F.P.; Dewitt, D. P. Fundamentals of Heat and Mass Transfer, 3rd ed.; John Wiley & Sons: New York, 1990. (16)Abdurrachim, H.; Karouta, F.; Daguenet, M.; Dumargue, P. Laminar natural convection about corrugated surfaces. J. Electroanal. Chem. 1981,122, 53. Received for review December 2, 1994 Revised manuscript received March 22, 1995 Accepted March 29, 1995@
IE930601H Abstract published in Advance ACS Abstracts, May 1, 1995. @
