Micropolarity-Ramification of Laminar/Turbulent Circular-Plane-Jet
  In the present work we formulated the boundary-value-problem, comprising partial differential equations (PDEs) of steady flow for laminar/turbulent circular jet of a micropolar fluid. A new boundary layer-similarity transformation/solution was derived which is valid not only for the Newtonian fluids but also for the micropolar fluids. Through this transformation PDEs are transformed into the ordinary differential equations (ODEs). These ODEs were solved numerically by the finite-difference method. The obtained results were compared with existing results [9] for the Newtonian fluids. The comparison was favourable. The micropolarity influences were highlighted in the present work. The axial-fluid-speed and normal stress-component decreases but radial-fluid-speed, microspin and one of the normal stress-component increase as the micropolarity effect enhances. The fluid-speed, microspin, shear stresses, normal stresses and couple stresses are dominant in the vicinity of the jet-source whereas they all vanish as far away from the jet-source analogous to the plane-jet-flow [8]. In addition, axial-speed, discharge, microspin, shear stresses and the components of couple stress intensify with z linearly but radial velocity, normal stresses and the component of couple stress are independent of z. The micropolarity-effects on discharge diminish if the diameter of jet-source reduces. Analogous to the plane-jet-flow [8], teace(stress tensor)=0, for the micropolar as well as for the Newtonian fluids. The normal stresses decreases as r goes on increasing, analogous to the shear-stresses. But all the normal components of the couple stress tensor vanish. The couple stress tensor is symmetric and skew-symmetric if analogous to the plane-jet flow [8]. Finally the fluid-speed will also intensify if turbulent-influences are enhanced. 
Abuzar Abid Siddiqui
physics.flu-dyn