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Mass transfer in a parallel plate electrochemical cell—the effect of change of flow area and flow cross-section at the cell inlet
MASS TRANSFER IN A PARALLEL PLATE ELECTROCHEMICAL CELL-THE EFFECT OF CHANGE OF FLOW AREA AND FLOW CROSS-SECTION AT THE CELL INLET D. J. PICKET-~ and C. J. WILSON Department
of Chemical
Engineering,
The University of Manchester Manchester M60 1QD. U.K.
(Received
infinal
form
Institute of Science and Technology,
22 September 1981)
Abstract-Experimental measurements have been made of mass transfer in a parallel plate cell which has a circular in-line flow inlet. It hasbeenfound that the mass transfer coefficient has a maximum value at a point slightly greater than six equivalent diameters downstream from the inlet. For cell Reynolds numbers between 1630 and 2960 this maximum mass transfercoefficient is directly proportional to the Bow rate but the location of the maximum is independent of flow rate. By assuming that the position of the maximum corresponds to the flow reattachment point and considering the mass transfer downstream from that point it has been shown that the local (or average) mass transfer coefficient is proportional to (L.*)-” where L* is the distance downstream from the reattachment point. For turbulent flow n = 0.37 and for laminar/transition motion n is in the range OSCH.60. A preliminary explanation of these results is proposed.
NOMENCLATURE
A Ii: F’ 1, JL K L’
L L* u ke
area of anode segment bulk concentration of ferrocyanide ion equivalent diameter Faraday limiting current average mass transfer coefficient over anode segment average mass transfer coefficient over a length of electrode L* distance from the cell inlet length of electrode measured downstream from the reattachment point average velocity kinematic viscosity Reynolds number UdJv INTRODUCTION
With a simple in-line flow connection of a circular pipe to a parallel plate electrochemical reactor, the entering solution is subjected to botha sudden enlargement and a change in shape of the flow cross-section. The combined effects of the enlargement and change of shape on the downstream flow and mass transfer have not been reported, although considerable work has been done on closely related axi-symmetric pipe enlargement systems which provide a good qualitative description of the processes[ 141. Downstream from an enlargement the decrease in velocity is accompanied by an increase in pressure, with fluid elements close to the walls losing additional kinetic energy due to friction so that they come to rest. However, as the wall fluid is still subjected to the bulk pressure gradient, it moves backwards upstream in opposition to the main flow. This flow separation has been observed downstream of a two-dimensional step by Abbot and KleinElI and occurs downstream of a more complex three-dimensional separation zone. Downstream from the separated regions the fluid
becomes reattached to the walls with subsequent redevelopment of the flow further downstream. The point of reattachment has been found to be substantially independent of flow rate. The most definitive studies of heat and mass transfer downstream of axi-symmetric pipe enlargements have been made for heat transfer by Krall and Sparrow[2] and for mass transfer using an electrochemical system by Tagg er a[.[ 31. These investigations show very good agreement with one another. For turbulent Bow the local heat (or mass) transfer coefficient has a maximum value at a point between 1.25 and 2.5 pipe diameters downstream from the enlargement and the values of this maximum are proportional to Reynolds number based on the upstream flow to a 0.67 power. The position of the maximum is substantially independent of flow rate according to the evidence of Tagg er al. Although the location of the maximum would suggest that it coincides with the point of flow reattachment, using a movable electrode, Tagg et al. have shown that flow reattachment occurs slightly further downstream. In general correlations of turbulent mass transfer in pipes and rectangular ducts show a good measure of agreement (see for example[5] ), however Reynolds numbers in parallel plate cells tend to be much lower than those employed in the pipe enlargement systems described above. This fact, together with the change in shape of flow cross-section suggests the need for further data. Accordingly this paper reports mass transfer data obtained in a parallel plate electrochemical ceil unit having a circular inlet and employing the anodic oxidation of ferrocyanide ions in excess alkali as the test reaction.
EXPERIMENTAL The electrochemical reactor consisted of thirty-one electrodes arranged in a plane parallel bipolar as-
592
D. J.
PU333-r
AND C.
sembiy with series flow of solution between adjacent cell units, The electrodes were contained within a perspex frame 163 x 17i x 2in. sandwiched between two $ in. thick mild steel plates and two gin. thick sheets of neoprene rubber. The steel plates were bolted together and the neoprene sealed the cell body and each individual cell unit. The test section consisted of the first cell unit, located at one end, two views of which are given as Fig. 1. The sectioned anode, A, consisted of eight $ in. thick polished stainless steel plates, 49.5 mm longand each withanelectrodearea of0.25 dm’.These plates were cemented to the perspex frame, C, with epoxy resin and insulated from each other by a thin layer of epoxy approx 0.5 mm thick. Electrical connections to the plates were made with gin. steel rods, B, passing through the perspex frame and screwed and soldered into the backs of the plates. The counterelectrode, E, was made from a strip of $in. thick stainless steel 50mm wide which slotted into the perspex body and formed the other side of the 4dm long channel.‘The separation between the anode and cathode was 9.5 mm giving a flow cross-section of 50 x 9.5 mm (equivalent diameter 160mm). The narrower sides of the cell unit were formed by the neoprene sheets, F, contained by the mild steel plates, G. The flOW inlet, D, was a 4mm internal diameter perspex tube positioned with its axis equi-distant From both sets of parallel walls. The cell was positioned to give a horizontal flow with the electrode surfaces horizontal to minimise natural convection and eliminate air pockets. A conventional flow system with a pump, rotameters, constant head tanks and nitrogen purge was employed. The electrical circuit enabled individual currents to be measured on each anode segment without altering the total current. Currents were measured on a Sangamo Weston S82 multirange ammeter and power supplied by a Farnell TSV 30/5/CL stabilised dc source. The overall voltage was measured using a multirange Advance DMM 2 digital voltmeter. The electrolyte solution contained equimolar concentrations of potassium ferricyanide and potassium ferrocyanide of approx. 0.01 moldm- 3
J.
WILSON
in 1 moldme potassium hydroxide, the exact concentrations being determined volumetrically. Full details of the experimental methods have been given by Wiison[6], but the essential procedure consisted of measuring individual segment currents at a given flow rate for progressively increased applied voltage until the limiting current had been reached on every segment. The procedure was repeated for a range of flow rates corresponding to cell Reynolds numbers between 275 and 2960. RESULTS
AND DlSCUSSlON
Figure 2 shows typical current/voltage curves for seven of the anode segments numbered progressively downstream from the inlet. The current profile on the eighth segment has not been included since this demonstrated an exit effect due to both the flow and current leakage into the adjacent cell unit with a current 2&50% larger than that on the seventh segment. The limiting currents for all segmentsare also shown on Fig. 2 and, whilst the downstream segments reach a limiting current at lower applied voltages than those further upstrewn, ultimately each segment is at its limiting current simultaneously. Thus the bulk and surface concentrations of ferrocyanide ion do not vary along the cell and enable a meaningful mass transfer coeficient to be defined. The average mass transfer coefficient was calculated from the relationship K,, = IJFAC.
(1)
Values of K,, for each of the seven segments are presented for two flow rates corresponding to Reynolds numbers of 1630 and 2500 in Fig. 3. The variation of K,, for Re = 2010 is also presented in Fig. 5 where the abscissa, I., is the distance downstream from the cell entrance, ie: c-5 represents the first segment, 5-10 the second segment, etc. For the above flow rates the maximum average mass transfer cocfficient is on the third downstream segment and the feature was observed at five of the seven flow rates employed. The two exceptions were at the lowest flow rate (Re = 275) which has been presented in Fig. 2 and at Re= 1330. In both of these cases K,, was approximately constant over the first three segments.
3or
Fig. 1. Sketch of electrochemical cell unit.
Fig. 2. Typical current/voltage curves For the anode segments.
Mass transferin a parallel plate electrochemicalcell
593
We-2500
1
2
3 d SECTION
1
5
I
6
7
Fig. 3. Typical variation of K,, along the anode.
z4
slope-1
E3 u rl
0
y2 ,b 0 1I----250
1
O\
Y
/ 500
1003 Re
2ocxl
OL----J_ 0 5
c
Moo
Fig. 4. Variation of themaximumvalueof K, with Reynolds
number.
Maximum values of &are plotted against Re in Fig. 4 and exhibit some scatter although for Re 3 1630 a linear relationship is seen. This is contrary to the findings of Krall ancl Sparrow and Tagg er al. but the range of cell Reynolds numbers correspond to the lower Reynolds numbers employed in the latter work and where deviation from the 0.67 power is most pronounced. The location of the maximum local mass transfer coefficient would appear to occur at a downstream position not less than 6d, from the inlet. This is rather longer than for the pipe flow and although the large electrode sections in the cell prevent accurate location of the maximum, it is almost certain that the change in shape of the flow section would give rise to a greater separation length than for pipe expansions. That the flow in the cell unit is indeed turbulent for Re = 1630can be inferred from the work of Ong[7] on a cell of similar cross-section. For Re = 550 and 1330,K,, is greater than it is for Re = 1630 and this will be considered below. At all flow rates employed, turbulent flow would occur in theentrance pipe and for the highest flow rates the flow in the cell will be turbulent both before and after the point of flow reattachment. As turbulent velocity profiles exhibit general similarity, the flow at the reattachment point should have a velocity profile that is not substantially different from the velocity profile further downstream. Thus, as a rough approximation the flow can be regarded as fully developed at the reattachment point and downstream from this. With regard to the concentration distribution, this will be confined to a narrow region close to
15 L km)
25
35
Fig. 5. Variation of K,v and calculated distribution of KL+ along the anode for Re = 2010. the anode, the distribution changing from a complex one upstream of the reattachment to a more usual form downstream. Thus a discontinuity in the concentration profile will occur at the reattachment point and it may be possible for Re 2 1630 to analyse the downstream process as full developed flow with developing mass transfer. This procedure implies the coincidence of the point of maximum mass transfer with the reattachment point in contradiction to the evidence of Tagg er al. However, for a preliminary analysis the implicit assumption is acceptable. For a test of the above hypothesis the reattachment point was assumed to be at the junction of the second and third anode segments downstream from the inlet and represented by I.* = 0 in Fig. 5. Evidently the data do not preclude other choices for the reattachment point, but the one adopted is convenient. Referring to Fig. 5, from the values of K, for each segment downstream from L* = 0, it is easy to calculate values of KL.,the average mass transfer coefficient over an electrode of length L*. The five values of K,. calculated for L* = 5, 10, 15,20 and 25cm at Re 2010 are plotted in Fig. 5 and joined by the broken curve. Calculated values of K Le as a function of L* for the four turbulent flows are presented as log-log plots in Fig. 6. The four sets of data are well represented by
II
I
5
Fig.
I
10 L* (cm)
15
I
20
6. Plot of K,a ns I.* for turbulent flow.
I
25
D.J.
594
PICKEITAND
four straight lines having the same slope of -0.37, indicating that both the local and average mass transfer coefficients are proportional to electrode length to a - 0.37 power. This differs from the value of -0.25 observed previously in parallel plate cells[5] but is in reasonable accord with the semi-theoretical analysis and data of Van Shaw er af.[S] and Shutz[9] for the mass transfer entrance region in turbulent pipe flow where a - l/3 length power was obtained. Although two of the other sets of data do not show the same location of maximum coefficient as those above, the data for the three lower flows have been treated in the same way as previously and are presented as a log-log plot of K,. as L* in Fig. 7. For Re = 275 and Re = 550 a proportionality between K,. and L* to a - 0.60 power is indicated whilst for Re = 1330 a value of -0.50 is shown. These values can be compared with the -0.50 predicted for a developing laminar flow[S]. This suggests that at lower flow rates
C.
J.
WILSON
there is, in addition to the separation, a transition from turbulent to laminar flow in the ceil. This transition could occur either upstream or downstream of the reattachment point. In any event, the development of a laminar velocity profile would be much more gradual than that for the turbulent profile. The high value of K,, at Re = 1330 may represent a more complex process, with transition flow. Evidently the particular length dependencies of K,* as exhibited in Figs 6 and 7 are somewhat influenced by the assumed position of reattachment, however definite differences between the mass transfer in the turbulent and laminar/transition regimes exist and there is little correspondence with data reported on parallel plate celfs with long or short flow entrance lengths. Obviously there are insufficient data for a really satisfactory and general analysis of the processes described above, the information here being obtained as a part of a study having different objectives. However, further investigations of the above phenomena are in progress.
REFERENCES D. E. Abbot and S. J. Klein, J. bus. Engng 84, 317 (1962). K. M. Krall and E. M. Sparrow,.I. Heat Tran.$erl38,131 (1966). 3. D. J. Tagg, M. A. Patrick and A. A. Wragg, Trans. Inst. chern. Engrs 57, 176 (1979). 4. A. K. Run&all, Inr. J. Heat MassTraqfer 14,781 (1971). 5. D. 1.Pickett. ElectrocItetinl ReactorDesian. 2nd Edition, 1. 2
Elsevier, A&terdam (1979). Ph.D. thesis,
6. C. J. Wilson,
University
of Manchester
(1974).
+
10
75
20
25
l? b-n)
Fig. 7. Plot of K,. vs L* for kuninar/transitian Bow.
K. L. Ong, Ph.D. thesis,Universityof Manehater (1972). :: P. Van Sbaw,L. P. Reissand T. J. Hatuatty, A. I. Ch. E. II 9, 362 (1963).
9. G. Shutz, inc. 3. Hear Mass
Tmns$r
7, 1077 (1964).
of Chemical
Engineering,
The University of Manchester Manchester M60 1QD. U.K.
(Received
infinal
form
Institute of Science and Technology,
22 September 1981)
Abstract-Experimental measurements have been made of mass transfer in a parallel plate cell which has a circular in-line flow inlet. It hasbeenfound that the mass transfer coefficient has a maximum value at a point slightly greater than six equivalent diameters downstream from the inlet. For cell Reynolds numbers between 1630 and 2960 this maximum mass transfercoefficient is directly proportional to the Bow rate but the location of the maximum is independent of flow rate. By assuming that the position of the maximum corresponds to the flow reattachment point and considering the mass transfer downstream from that point it has been shown that the local (or average) mass transfer coefficient is proportional to (L.*)-” where L* is the distance downstream from the reattachment point. For turbulent flow n = 0.37 and for laminar/transition motion n is in the range OSCH.60. A preliminary explanation of these results is proposed.
NOMENCLATURE
A Ii: F’ 1, JL K L’
L L* u ke
area of anode segment bulk concentration of ferrocyanide ion equivalent diameter Faraday limiting current average mass transfer coefficient over anode segment average mass transfer coefficient over a length of electrode L* distance from the cell inlet length of electrode measured downstream from the reattachment point average velocity kinematic viscosity Reynolds number UdJv INTRODUCTION
With a simple in-line flow connection of a circular pipe to a parallel plate electrochemical reactor, the entering solution is subjected to botha sudden enlargement and a change in shape of the flow cross-section. The combined effects of the enlargement and change of shape on the downstream flow and mass transfer have not been reported, although considerable work has been done on closely related axi-symmetric pipe enlargement systems which provide a good qualitative description of the processes[ 141. Downstream from an enlargement the decrease in velocity is accompanied by an increase in pressure, with fluid elements close to the walls losing additional kinetic energy due to friction so that they come to rest. However, as the wall fluid is still subjected to the bulk pressure gradient, it moves backwards upstream in opposition to the main flow. This flow separation has been observed downstream of a two-dimensional step by Abbot and KleinElI and occurs downstream of a more complex three-dimensional separation zone. Downstream from the separated regions the fluid
becomes reattached to the walls with subsequent redevelopment of the flow further downstream. The point of reattachment has been found to be substantially independent of flow rate. The most definitive studies of heat and mass transfer downstream of axi-symmetric pipe enlargements have been made for heat transfer by Krall and Sparrow[2] and for mass transfer using an electrochemical system by Tagg er a[.[ 31. These investigations show very good agreement with one another. For turbulent Bow the local heat (or mass) transfer coefficient has a maximum value at a point between 1.25 and 2.5 pipe diameters downstream from the enlargement and the values of this maximum are proportional to Reynolds number based on the upstream flow to a 0.67 power. The position of the maximum is substantially independent of flow rate according to the evidence of Tagg er al. Although the location of the maximum would suggest that it coincides with the point of flow reattachment, using a movable electrode, Tagg et al. have shown that flow reattachment occurs slightly further downstream. In general correlations of turbulent mass transfer in pipes and rectangular ducts show a good measure of agreement (see for example[5] ), however Reynolds numbers in parallel plate cells tend to be much lower than those employed in the pipe enlargement systems described above. This fact, together with the change in shape of flow cross-section suggests the need for further data. Accordingly this paper reports mass transfer data obtained in a parallel plate electrochemical ceil unit having a circular inlet and employing the anodic oxidation of ferrocyanide ions in excess alkali as the test reaction.
EXPERIMENTAL The electrochemical reactor consisted of thirty-one electrodes arranged in a plane parallel bipolar as-
592
D. J.
PU333-r
AND C.
sembiy with series flow of solution between adjacent cell units, The electrodes were contained within a perspex frame 163 x 17i x 2in. sandwiched between two $ in. thick mild steel plates and two gin. thick sheets of neoprene rubber. The steel plates were bolted together and the neoprene sealed the cell body and each individual cell unit. The test section consisted of the first cell unit, located at one end, two views of which are given as Fig. 1. The sectioned anode, A, consisted of eight $ in. thick polished stainless steel plates, 49.5 mm longand each withanelectrodearea of0.25 dm’.These plates were cemented to the perspex frame, C, with epoxy resin and insulated from each other by a thin layer of epoxy approx 0.5 mm thick. Electrical connections to the plates were made with gin. steel rods, B, passing through the perspex frame and screwed and soldered into the backs of the plates. The counterelectrode, E, was made from a strip of $in. thick stainless steel 50mm wide which slotted into the perspex body and formed the other side of the 4dm long channel.‘The separation between the anode and cathode was 9.5 mm giving a flow cross-section of 50 x 9.5 mm (equivalent diameter 160mm). The narrower sides of the cell unit were formed by the neoprene sheets, F, contained by the mild steel plates, G. The flOW inlet, D, was a 4mm internal diameter perspex tube positioned with its axis equi-distant From both sets of parallel walls. The cell was positioned to give a horizontal flow with the electrode surfaces horizontal to minimise natural convection and eliminate air pockets. A conventional flow system with a pump, rotameters, constant head tanks and nitrogen purge was employed. The electrical circuit enabled individual currents to be measured on each anode segment without altering the total current. Currents were measured on a Sangamo Weston S82 multirange ammeter and power supplied by a Farnell TSV 30/5/CL stabilised dc source. The overall voltage was measured using a multirange Advance DMM 2 digital voltmeter. The electrolyte solution contained equimolar concentrations of potassium ferricyanide and potassium ferrocyanide of approx. 0.01 moldm- 3
J.
WILSON
in 1 moldme potassium hydroxide, the exact concentrations being determined volumetrically. Full details of the experimental methods have been given by Wiison[6], but the essential procedure consisted of measuring individual segment currents at a given flow rate for progressively increased applied voltage until the limiting current had been reached on every segment. The procedure was repeated for a range of flow rates corresponding to cell Reynolds numbers between 275 and 2960. RESULTS
AND DlSCUSSlON
Figure 2 shows typical current/voltage curves for seven of the anode segments numbered progressively downstream from the inlet. The current profile on the eighth segment has not been included since this demonstrated an exit effect due to both the flow and current leakage into the adjacent cell unit with a current 2&50% larger than that on the seventh segment. The limiting currents for all segmentsare also shown on Fig. 2 and, whilst the downstream segments reach a limiting current at lower applied voltages than those further upstrewn, ultimately each segment is at its limiting current simultaneously. Thus the bulk and surface concentrations of ferrocyanide ion do not vary along the cell and enable a meaningful mass transfer coeficient to be defined. The average mass transfer coefficient was calculated from the relationship K,, = IJFAC.
(1)
Values of K,, for each of the seven segments are presented for two flow rates corresponding to Reynolds numbers of 1630 and 2500 in Fig. 3. The variation of K,, for Re = 2010 is also presented in Fig. 5 where the abscissa, I., is the distance downstream from the cell entrance, ie: c-5 represents the first segment, 5-10 the second segment, etc. For the above flow rates the maximum average mass transfer cocfficient is on the third downstream segment and the feature was observed at five of the seven flow rates employed. The two exceptions were at the lowest flow rate (Re = 275) which has been presented in Fig. 2 and at Re= 1330. In both of these cases K,, was approximately constant over the first three segments.
3or
Fig. 1. Sketch of electrochemical cell unit.
Fig. 2. Typical current/voltage curves For the anode segments.
Mass transferin a parallel plate electrochemicalcell
593
We-2500
1
2
3 d SECTION
1
5
I
6
7
Fig. 3. Typical variation of K,, along the anode.
z4
slope-1
E3 u rl
0
y2 ,b 0 1I----250
1
O\
Y
/ 500
1003 Re
2ocxl
OL----J_ 0 5
c
Moo
Fig. 4. Variation of themaximumvalueof K, with Reynolds
number.
Maximum values of &are plotted against Re in Fig. 4 and exhibit some scatter although for Re 3 1630 a linear relationship is seen. This is contrary to the findings of Krall ancl Sparrow and Tagg er al. but the range of cell Reynolds numbers correspond to the lower Reynolds numbers employed in the latter work and where deviation from the 0.67 power is most pronounced. The location of the maximum local mass transfer coefficient would appear to occur at a downstream position not less than 6d, from the inlet. This is rather longer than for the pipe flow and although the large electrode sections in the cell prevent accurate location of the maximum, it is almost certain that the change in shape of the flow section would give rise to a greater separation length than for pipe expansions. That the flow in the cell unit is indeed turbulent for Re = 1630can be inferred from the work of Ong[7] on a cell of similar cross-section. For Re = 550 and 1330,K,, is greater than it is for Re = 1630 and this will be considered below. At all flow rates employed, turbulent flow would occur in theentrance pipe and for the highest flow rates the flow in the cell will be turbulent both before and after the point of flow reattachment. As turbulent velocity profiles exhibit general similarity, the flow at the reattachment point should have a velocity profile that is not substantially different from the velocity profile further downstream. Thus, as a rough approximation the flow can be regarded as fully developed at the reattachment point and downstream from this. With regard to the concentration distribution, this will be confined to a narrow region close to
15 L km)
25
35
Fig. 5. Variation of K,v and calculated distribution of KL+ along the anode for Re = 2010. the anode, the distribution changing from a complex one upstream of the reattachment to a more usual form downstream. Thus a discontinuity in the concentration profile will occur at the reattachment point and it may be possible for Re 2 1630 to analyse the downstream process as full developed flow with developing mass transfer. This procedure implies the coincidence of the point of maximum mass transfer with the reattachment point in contradiction to the evidence of Tagg er al. However, for a preliminary analysis the implicit assumption is acceptable. For a test of the above hypothesis the reattachment point was assumed to be at the junction of the second and third anode segments downstream from the inlet and represented by I.* = 0 in Fig. 5. Evidently the data do not preclude other choices for the reattachment point, but the one adopted is convenient. Referring to Fig. 5, from the values of K, for each segment downstream from L* = 0, it is easy to calculate values of KL.,the average mass transfer coefficient over an electrode of length L*. The five values of K,. calculated for L* = 5, 10, 15,20 and 25cm at Re 2010 are plotted in Fig. 5 and joined by the broken curve. Calculated values of K Le as a function of L* for the four turbulent flows are presented as log-log plots in Fig. 6. The four sets of data are well represented by
II
I
5
Fig.
I
10 L* (cm)
15
I
20
6. Plot of K,a ns I.* for turbulent flow.
I
25
D.J.
594
PICKEITAND
four straight lines having the same slope of -0.37, indicating that both the local and average mass transfer coefficients are proportional to electrode length to a - 0.37 power. This differs from the value of -0.25 observed previously in parallel plate cells[5] but is in reasonable accord with the semi-theoretical analysis and data of Van Shaw er af.[S] and Shutz[9] for the mass transfer entrance region in turbulent pipe flow where a - l/3 length power was obtained. Although two of the other sets of data do not show the same location of maximum coefficient as those above, the data for the three lower flows have been treated in the same way as previously and are presented as a log-log plot of K,. as L* in Fig. 7. For Re = 275 and Re = 550 a proportionality between K,. and L* to a - 0.60 power is indicated whilst for Re = 1330 a value of -0.50 is shown. These values can be compared with the -0.50 predicted for a developing laminar flow[S]. This suggests that at lower flow rates
C.
J.
WILSON
there is, in addition to the separation, a transition from turbulent to laminar flow in the ceil. This transition could occur either upstream or downstream of the reattachment point. In any event, the development of a laminar velocity profile would be much more gradual than that for the turbulent profile. The high value of K,, at Re = 1330 may represent a more complex process, with transition flow. Evidently the particular length dependencies of K,* as exhibited in Figs 6 and 7 are somewhat influenced by the assumed position of reattachment, however definite differences between the mass transfer in the turbulent and laminar/transition regimes exist and there is little correspondence with data reported on parallel plate celfs with long or short flow entrance lengths. Obviously there are insufficient data for a really satisfactory and general analysis of the processes described above, the information here being obtained as a part of a study having different objectives. However, further investigations of the above phenomena are in progress.
REFERENCES D. E. Abbot and S. J. Klein, J. bus. Engng 84, 317 (1962). K. M. Krall and E. M. Sparrow,.I. Heat Tran.$erl38,131 (1966). 3. D. J. Tagg, M. A. Patrick and A. A. Wragg, Trans. Inst. chern. Engrs 57, 176 (1979). 4. A. K. Run&all, Inr. J. Heat MassTraqfer 14,781 (1971). 5. D. 1.Pickett. ElectrocItetinl ReactorDesian. 2nd Edition, 1. 2
Elsevier, A&terdam (1979). Ph.D. thesis,
6. C. J. Wilson,
University
of Manchester
(1974).
+
10
75
20
25
l? b-n)
Fig. 7. Plot of K,. vs L* for kuninar/transitian Bow.
K. L. Ong, Ph.D. thesis,Universityof Manehater (1972). :: P. Van Sbaw,L. P. Reissand T. J. Hatuatty, A. I. Ch. E. II 9, 362 (1963).
9. G. Shutz, inc. 3. Hear Mass
Tmns$r
7, 1077 (1964).