Skip to main content
SpringerLink
Log in

Rarefied MHD laminar radial channel flow

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

The steady axisymmetrical laminar flow of slightly rarefied electrically conducting gas between two circular parallel disks in the presence of a transverse magnetic field is analytically investigated. A solution is obtained by expanding the velocity and the pressure distribution in terms of a power series of 1/r. The effect of rare-faction is taken to be manifested by slip of the velocity at the boundary. Velocity, induced magnetic field, pressure and shear stress distributions are determined and compared with the case of no rarefaction.

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

b :

outer radius of channel

C f :

skin friction coefficient, τ w /(ρQ 2/t 4)

H 0 :

impressed magnetic field

H * r :

induced magnetic field in the radial direction

H r :

induced dimensionless magnetic field in the radial direction, H * r /H 0

M :

Hartmann number, μH 0 t(σ/ρν)1/2

P :

dimensionless static pressure, P*t 4/ρQ 2

P*:

static pressure

P b :

dimensionless pressure at outer radius of channel

P 0 :

reference dimensionless pressure

Q :

source discharge

R :

gas constant

Rm :

magnetic Reynolds number, σμQ/t

Re :

Reynolds number, Q/νt

2t :

channel width

T :

absolute gas temperature

u :

dimensionless radial component of the velocity, u*t 2/Q

u*:

radial component of the velocity

w :

dimensionless axial component of the velocity, w*t 2/Q

w*:

axial component of the velocity

z, r :

dimensionless axial and radial directions, z*/t and r*/t, respectively

z*, r*:

axial and radial direction, respectively

λ :

molecular mean free path

μ :

magnetic permeability

ν :

coefficient of kinematic viscosity

ρ :

density

σ :

electrical conductivity

References

  1. Hughes, W. F. and R. A. Elco, J. of Fluid Mech. 13 (1962) 21.

    Google Scholar 

  2. Maki, E. R., D. C. Kuzma, and R. J. Donnelly, J. of Fluid Mech. 26 (1966) 537.

    Google Scholar 

  3. Ramanaiah, G., Appl. Sci. Res. 17 (1967) 296.

    Google Scholar 

  4. Khader, M. S. and J. S. Goodling, Appl. Sci. Res. 27 (1972) 93.

    Google Scholar 

  5. Khader, M. S., G. E. Tanger, and R. I. Vachon, Eighth Southeastern Seminar on Thermal Sci. Proc. (1972) 289.

  6. Schaaf, S. A. and P. L. Chambre, Flow of Rarefied Gases, Princeton Univ. Press, Princeton, N. J., 1961.

    Google Scholar 

  7. Eckert, E. R. G. and R. M. Drake, Analysis of Heat and Mass Transfer, McGraw-Hill, N. Y., 1972.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mech. Eng., Cairo Univ. Giza, Egypt

    M. S. Khader

  2. Dept. of Mech. Eng., Auburn Univ., 36830, Auburn, Alabama, USA

    J. S. Goodling & R. I. Vachon

Authors
  1. M. S. Khader
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. S. Goodling
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. I. Vachon
    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

Khader, M.S., Goodling, J.S. & Vachon, R.I. Rarefied MHD laminar radial channel flow. Appl. Sci. Res. 30, 127–143 (1974). https://doi.org/10.1007/BF00386066

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00386066

Keywords

Search

Navigation