Slow Flow of Second-Order Fluid past a non-Newtonian Liquid Sphere under Stokes' Approximations

Abstract

The  uniform steady slow  viscous flow of an incompressible non-Newtonian second order fluid past a fixed sphere of Reiner-Rivlin fluid with constant coefficient of Newtonian-viscositiesand , elastico-viscosity, and cross-viscositiesand  at  very small Reynolds  number has been delineated and   discussed under the  Stokes' approximation.   In the present model, no-slip(slide) is assumed on the boundary of the fluid  sphere's surface  so as to satisfy continuity of shear  across the surface. The unequivocal articulations for the stream functions are obtained to the second  order in the small cross-viscous parameters and  characterizing, respectively, the cross-viscosities  of  external and internal fluids, and special cases of flow past a solid and different fluid  spheres are deduced then. The effects of forces exerted by external fluid in the flow on the streamlines and the drag on the fluid sphere have been investigated and also represented graphically.  The effects of elastico-viscous parameter on drag and different fluid parameters have also been studied.