IJPAM: Volume 73, No. 2 (2011)

THREE-DIMENSIONAL MHD STAGNATION POINT-FLOW
OF A NEWTONIAN AND A MICROPOLAR FLUID

Alessandra Borrelli$^1$, Giulia Giantesio$^2$, Maria Cristina Patria$^3$
$^{1,2,3}$Department of Mathematics
Via Machiavelli, 35, Ferrara, ITALY


Abstract. The steady three-dimensional stagnation-point flow of an electrically conducting Newtonian or micropolar fluid in the presence of a uniform external magnetic field ${\H}_0$ is analysed and some physical situations are examined.

In particular, we prove that, if we impress an external magnetic field ${\H}_{0}$, and we neglect the induced magnetic field, then the steady three-dimensional MHD stagnation-point flow is possible if, and only if, ${\H}_0$ has the direction of one of the coordinate axes.

In all cases it is shown that the governing nonlinear partial differential equations admit similarity solutions. We find that the flow has to satisfy an ordinary differential problem whose solution depends on ${\H}_{0}$ through the Hartmann number $M^2$.

Finally, the skin-friction components along the axes are computed.

Received: July 21, 2011

AMS Subject Classification: 76W05, 76D10

Key Words and Phrases: Newtonian fluids, Micropolar fluids, MHD flow, three-dimensional stagnation-point flow

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 73
Issue: 2