Axisymmetric MHD viscous flow about a highly-slipping sphere translating parallel with a uniform ambient magnetic field

A. Sellier¹ - S. H. Aydin²

¹ LadHyX. Ecole polytechnique, 91128 Palaiseau Cédex, France
² Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Turquey

Abstract
The slow translation of a highly-slipping sphere with radius a in an unbounded viscous conducting Newtonian liquid with constant viscosity μ and conductivity σ is investigated. The liquid is subject to a steady uniform magnetic field B parallel to the sphere velocity, flows about the sphere and exerts on its a drag force. The resulting axisymmetric MHD flow is expanded as a serie of fundamental flows earlier gained elsewhere  for a different Oseen flow problem. The coefficients entering in the serie are determined by enforcing the impermeability and zero tangent stress conditions on the sphere surface, As a result, the highly-slipping sphere drag coefficient C_d is numerically obtained and its sensitivity to the problem Hartmann number Ha=a|B|/(μ/σ)^1/2 is examined. Moreover, a polynomial handy formula for C_d is proposed for Ha ≤ O(1) and the computed velocity patterns are presented and discussed for Ha=1,10. Tables 2, Figs 4, Refs 12.