AXISYMMETRIC MHD VISCOUS FLOW ABOUT A HIGHLY-SLIPPING SPHERE TRANSLATING PARALLEL WITH A UNIFORM AMBIENT MAGNETIC FIELD

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 [1, 2] 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 (formula presented) 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.