An existing approach for deriving analytical expressions for slip-flow properties of Stokes flow is generalised and applied to a range of micro and nanoscale applications. The technique, which exploits the reciprocal theorem, can generate first-order predictions of the impact of Navier or Maxwell slip boundary conditions on surface moments of the traction force (e.g. on drag and torque). This article brings dedicated focus to the technique, generalises it to predict first-order slip effects on arbitrary moments of the surface traction, numerically verifies the technique on a number of cases and applies the method to a range of micro and nano-scale applications. Applications include predicting: the drag on translating spheres with varying slip length; the efficiency of a micro journal bearing; the speed of a self-propelled particle (a ‘squirmer’); and the pressure drop required to drive flow through long, straight micro/nano channels. Certain general results are also obtained. For example, for low-slip Stokes flow: any surface distribution of positive slip length will reduce the drag on any translating particle; and any perimetric distribution of positive slip length will reduce the pressure loss through a straight channel flow of arbitrary cross-section.

In the present paper, we analyzed the effects of magnetic field on the three dimensional flow of a nanofluid having the suspension of ferrous nano-particles within the framework of a non-uniformly thicked sheet in a slip flow regime. The sheet of variable thickness is assumed to be stretched in horizontal and transverse directions. The effects of thermophoretic forces and Brownian motion have also been incorporated into the governing equations. The RK-Fehlberg-integration scheme with shooting technique is employed to resolve the altered governing non-linear differential equations. Velocity, temperature and concentration profiles are presented and discussed for two cases namely uniform thickness stretching sheet UTSS (n = 1) and variable thickness stretching sheet VTSS (n ≠ 1), and skin friction coefficient, reduced Nusselt number and Sherwood number are computed and analyzed through tables. The results reveal that heat and mass transfer processes over slendering sheet matches with those over a flat sheet in the presence of slip flow regime.

Impulsively started external convection at microscale level is studied numerically in both planar and axisymmetric geometries. Using similarity transformation, the resulting coupled partial and non-linear ordinary differential equations are simultaneously solved by finite differences together with a well established ordinary differential equation solver, over a range of problem parameters. Rarefaction effects within the slip flow regime on the thermal boundary layer response, heat transfer rate and transition time when system experiences sudden changes in surface temperature are analyzed, and a comparison between sudden surface cooling and heating is presented. The results show that the thermal boundary layer thickness, heat transfer rate and the transition time is considerably influenced by the degree of rarefaction. The transition time tends to be less sensitive with increasing rarefaction. The velocity slip and temperature jump factors are found to have opposite effects on the transition time and the heat transfer rate, with the velocity slip factor having the most profound influence on these parameters.