Abstract
The characteristics of induced flow in a cylindrical magnetoelectrolytic cell under the influence of uniform and non-uniform magnetic fields are analysed. Experimental surface velocity values are predicted with reasonable accuracy by magnetohydrodynamic models incorporating open-channel flow concepts.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- A, D :
-
parameters in Equation 7 [Gak equation]
- B :
-
magnetic flux density vector;B r,B z its radial and axial components;B 0 its magnitude, ¯B its average magnitude
- B 1 (pr) :
-
auxiliary function in the annular Hankel transform technique (Equation 6)
- e :
-
unit vectors in the cylindrical coordinate system with componentse r,e o,e z
- F θ :
-
magnitude of the MHD force density in theθ-direction
- f c :
-
friction coefficient of energy loss due to curvature
- g :
-
acceleration due to gravity
- H :
-
height of the electrodes in electrolytic cell
- h f :
-
energy head loss due to friction
- h c :
-
energy head loss due to curvature
- I :
-
electric current flow
- J :
-
electric current density vector
- K :
-
lumped parameter;K=IB o/2πHη
- K f,K c :
-
K factors in terms of friction and curvature losses
- k :
-
geometric shape factor,R/r o
- P :
-
pressure
- p :
-
annular Hankel transform parameter
- R :
-
radius of the outer electrode
- r o :
-
radius of the inner electrode
- r :
-
radius measured from the centre of the electrolytic cell
- V gq :
-
velocity in theθ-direction
- ¯V θ :
-
its average
- α n :
-
regression coefficients in Equation 13
- η :
-
dynamic viscosity of electrolyte
- gn :
-
kinematic viscosity of electrolyte
- ρ :
-
density of electrolyte
- φ(p) :
-
function defined in Equation 8a
- ψ(r) :
-
surface profile function (Equation 29)
References
F.A. Holland,Fluid Flow for Chemical Engineers, E. Arnold, 1973, Chapter 14.
N. Curl and H.J. Davies,Modern Fluid Dynamics, Van Nostrand, 1968, Volume 1, Section 5.3.
S. Mohanta, Ph.D. Thesis, Univ. of Waterloo, 1974.
C.J. Tranter,Integral Transforms In Mathematical Physics, Methuen 1962, pp. 88–91.
E. Z. Gak,Elektrokhimiya 3 (1967) 89.
W. M. Owen,Trans. Am. Soc. Civ. Engrs. 119 (1954) 1157.
S. Mohanta, M.A.Sc. Thesis, Univ. of Waterloo, 1971; S. Mohanta and T.Z. Fahidy,Can. Journ. Chem Engrg. 50 (1972), 248.
Handbook of Applied Hydraulics, ed. by C.V. Davis and K.E. Soresmen, McGraw Hill, 1969.
H.M. Morris and J.M. Wiggert,Applied Hydraulics in Engineering, Ronald Press, 1972.
A. Shukry,Trans. Am. Soc. Civ. Eng. 115 (1950) 751.
E.H. Lewitt,Hydraulics and Fluid Mechanics, 10th edn, Pitman and Sons, 1958, p. 107.
Chemical Engineer's Handbook, ed. by J.H. Perry, McGraw Hill, 1963.
I. N. Sneddon,Phil. Mag. 7 (1946) 17.
E. Jahnke and F. Emde,Table of Functions, Dover, 1945, Chapter 8.
M. Abramowitz and I.A. Stegun,Handbook of Mathematical Functions, Dover, 1965, Chapters 9, 10,11.
H.E. Fettis and J.C. Castin, ‘An Extended Table of Zeros of Cross Products of Bessel Functions’, ARL 66-0023, Feb. 1966; Dec. 1968.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mohanta, S., Fahidy, T.Z. The hydrodynamics of a magnetoelectrolytic cell. J Appl Electrochem 6, 211–220 (1976). https://doi.org/10.1007/BF00616143
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00616143