self-similar solution of unsteady axisymmetric stagnation-point flow of a nanofluid impinging on oscillating cylinder

The unsteady, viscous flow of nanofluid in the vicinity of an axisymmetric stagnation point of an oscillating cylinder is investigated. the cylinder is moving toward or away from the impinging flow. the impinging free stream is steady and with a constant strain rate𝑘̄ . self similar solution of the navier–stokes equations is derived fromthis unsteady problem. a reduction of these equations is obtained by use of appropriate transformations introduced for the first time. all the solutions above are presented for reynolds numbers 𝑅𝑒 = k̄𝑎²/2𝜐𝑓 ranging from 1 to 2000, selected values of dimensionless time, and selected values of particle fractions where a is cylinder radius and 𝜐𝑓 isthe kinematic viscosity of the base fluid. for all reynolds numbers, as the particle fraction increases, the depth of diffusion of the fluid velocity field in the radial direction, the depth of the diffusion of the fluid velocity field in -direction, and shear-stress decreases. furthermore, it has been determined that the maximum dimensionless shear stress is 370, which corresponds to a volume fraction of 0.05 and t* = 0.45. additionally, for all volume fractions, the maximum and minimum values of the hydrodynamic boundary layer thickness are associated with t* = 0.75 and t* = 0.45, respectively. the problem is particularly important in pressure-lubricated bearings.