Skip to main content
SpringerLink
Log in

Viscous lifting and drainage of a conducting fluid in the presence of a transverse magnetic field

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

A theoretical investigation of the effects of a transverse magnetic field on the combined problem of viscous lifting and drainage of a conducting fluid on a plate is presented. The effects of inertia and transverse magnetic field on the liquid film thickness is studied for two cases namely a plate withdrawn with a constant velocity and one withdrawn with a constant acceleration. The expressions for the flow rate and the free surface profiles are obtained for the above two cases. It is found that the free surface profiles are convex in nature as in the non-magnetic case thus showing that the inertia does not effect the general pattern of flow, and the effect of the magnetic field is to retard both the lifting and drainage of the fluid.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

a :

acceleration of the plate

A :

dimensionless acceleration,=a/g

B 0 :

transverse magnetic field

g :

acceleration due to gravity

h :

film thickness

H :

dimensionless film thickness,=h(g/ν 2)1/3

M :

Hartmann number,\( = \sqrt {{\sigma \mathord{\left/ {\vphantom {\sigma \mu }} \right. \kern-\nulldelimiterspace} \mu }} B_0 ({{v^2 } \mathord{\left/ {\vphantom {{v^2 } g}} \right. \kern-\nulldelimiterspace} g})^{\tfrac{1}{3}} \)

q :

mass flow rate

Q :

dimensionless mass flow rate,=q/ν

T :

dimensionless time,=t(g 2/ν)1/3

v 0 :

velocity of the plate

V 0 :

dimensionless velocity of the plate,=v 0/(νg)1/3

v :

fluid velocity

(x, y, z):

cartesian coordinates

Y :

dimensionlessy-coordinate,=y(g/ν 2)1/3

μ :

viscosity

σ :

conductivity

ρ :

density

ν :

kinematic viscosity,=μ/ρ

References

  1. Jeffreys, H., Proc. Cambridge Phil. Soc.26 (1930) 204.

    Google Scholar 

  2. Green, G., Phil. Mag. Series 622 (1936) 730.

    Google Scholar 

  3. Wyllie, G., Phil. Mag.36 (1945) 581.

    Google Scholar 

  4. Gutfinger, C. andJ. A. Tallmadge, A.I.Ch.E. J.10 (1964) 774.

    Google Scholar 

  5. Bradshaw, M. D., F. G. Young andJ. F. Osterle, Appl. Sci. Res.B 12 (1965) 266.

    Google Scholar 

  6. Van Rossum, J. J., Appl. Sci. Res.A 7 (1958) 141.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Appl. Math., Indian Inst. of Techn., Kharagpur, India

    N. Annapurna & G. Ramanaiah

Authors
  1. N. Annapurna
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Ramanaiah
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Annapurna, N., Ramanaiah, G. Viscous lifting and drainage of a conducting fluid in the presence of a transverse magnetic field. Appl. Sci. Res. 31, 139–152 (1975). https://doi.org/10.1007/BF01795832

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01795832

Keywords

Search

Navigation