Skip to main content
SpringerLink
Log in

Combined influence of Hall effect, ion slip and temperature boundary condition of third kind on MHD channel flow heat transfer

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

To investigate the combined influence of Hall effect, ion slip and the temperature boundary condition of the third kind on the magnetohydrodynamic heat transfer in the thermal entrance region of a flat channel, the energy equation is solved by employing the Galerkin-Kantorowich method of variational calculus. The heat generation within the fluid is neglected. It is concluded that there can be a significant influence of Biot number and Hall parameter on the local Nusselt number. Representative results are depicted in tables.

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 :

channel cross section

B :

magnetic induction

Bi :

Biot number, Eq. (5)

D :

a matrix, Eq. (10)

E :

electric field

F :

a vector, Eq. (7)

Ha :

Hartmann number, Eq. (5)

Nu :

Nusselt number, Eq. (17)

Pe :

Peclet number, Eq. (5)

R :

a vector, Eq. (13)

Re :

Reynolds number, Eq. (5)

T :

temperature

W :

a matrix, Eq. (10)

a :

mass fraction of unionized particles

c :

half channel height, Fig. 1

c p :

specific heat at constant pressure

f :

a function, Eq. (7)

k :

overall heat transfer coefficient, Eq. (4)

p :

pressure

s :

characteristic value, Eq. (7)

v :

velocity

x, y, z :

cartesian coordinate

β e :

Hall parameter

β 1 :

ion slip parameter

η :

dynamic viscosity

λ :

thermal conductivity

ν :

kinematic viscosity

ρ :

mass density

σ :

electrical conductivity

a:

ambient

i, j :

running index

m:

mean value

w:

wall

x, y, z :

cartesian coordinate direction

0:

prescribed value

-:

dimensionless quantity, Eq. (5)

′:

reduced quantity, Eq. (5)

References

  1. Nigam, S. D. and S. N. Singh, Q. J. Mech. Appl. Math. 13 Part I (1960) 85.

    Google Scholar 

  2. Erickson, L. E., C. S. Wang, C. L. Hwang and L. T. Fan, Z. Angew. Math. Phys. 15 (1964) 408.

    Google Scholar 

  3. Jain, M. K. and J. Srinivasen, AIAA J. 2 (1964) 1886.

    Google Scholar 

  4. Back, L. H., Int. J. Heat Mass Transfer 11 (1968) 1621.

    Article  Google Scholar 

  5. Perlmutter, M. and R. Siegel, NASA Tech. Note D-875, 1961.

  6. Michiyoshi, I. and R. Matsumoto, Int. J. Heat Mass Transfer 7 (1964) 101.

    Article  Google Scholar 

  7. Hwang, C. L., P. J. Knieper and L. T. Fan, Int. J. Heat Mass Transfer 9 (1966) 773.

    Article  Google Scholar 

  8. Fan, L. T., C. L. Hwang, P. J. Knieper and H. P. Hwang, Z. Angew. Math. Phys. 18 (1967) 826.

    Google Scholar 

  9. Hsu, C. J. and G. C. Lindauer, Nucl. Sci. and Eng. 32 (1968) 16.

    Google Scholar 

  10. LeCroy, R. C. and A. H. Eraslan, ASME Paper No. 68-WA/HT 10, 1968.

  11. Javeri, V., Bestimmung der laminaren Geschwindigkeits- und Temperaturfelder im thermischen Einlaufgebiet eines MHD-Kanals mit dem Kantorowitsch-Verfahren, Diss. TU Berlin 1972.

    Google Scholar 

  12. Eraslan, A. H., AIAA J. 7 (1969) 186.

    Google Scholar 

  13. Javeri, V., Wärme- und Stoffübertragung 7 (1974) 226.

    Google Scholar 

  14. Javeri, V. Wärme- und Stoffübertragung 8 (1975) 193.

    Google Scholar 

  15. Javeri, V., Int. J. Heat Mass Transfer 20 (1977) 543.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Reaktorsicherheit, Köln 1, Germany

    V. Javeri

Authors
  1. V. Javeri
    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

Javeri, V. Combined influence of Hall effect, ion slip and temperature boundary condition of third kind on MHD channel flow heat transfer. Appl. Sci. Res. 33, 11–22 (1977). https://doi.org/10.1007/BF00383190

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00383190

Keywords

Search

Navigation