Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous Fluid

[摘要] The problem of concentric pervious spheres carrying a fluid source at their centre and rotating slowly with different uniform angular velocitiesΩ1,Ω2about a diameter has been studied. The analysis reveals that only azimuthal component of velocity exists, and the couple, rate of dissipated energy is found analytically in the present situation. The expression of couple on inner sphere rotating slowly with uniform angular velocityΩ1, while outer sphere also rotates slowly with uniform angular velocityΩ2, is evaluated. The special cases, like (i) inner sphere is fixed (i.e.,Ω1=0), while outer sphere rotates with uniform angular velocityΩ2, (ii) outer sphere is fixed (i.e.,Ω2=0), while inner sphere rotates with uniform angular velocityΩ1, and (iii) inner sphere rotates with uniform angular velocityΩ1, while outer sphere rotates at infinity with angular velocityΩ2, have beendeduced.

[学科分类] 应用数学