In this paper analytical expressions for time-dependent velocity profiles and pressure gradient are obtained for fully-developed laminar flows with given volume flow-rate conditions in circular pipe flows with Slip boundary conditions. The governing equations are solved analytically using the traditional Laplace transform method together with Mellin’ s inversion formula. The evolution of velocity profiles and pressure gradient for starting and pulsatile flow with Slip boundary conditions are analyzed. New simplified expressions and perspectives on velocity and pressure gradient for no-Slip and Slip flows are obtained from the analytical results. New scalings in starting and pulsatile flows are proposed for pipe flows with no-Slip and Slip boundary conditions using nondimensional numbers. Special attention is paid to the effect of Slip factor and pulsatile flow frequency on the time-dependent skin-friction factor. Finally, by using the starting and pulsating flow results, analytical expressions of velocity and pressure for arbitrary inflow are obtained by approximating the arbitrary volume flow-rate by a Fourier series.

The no-Slip condition is an accepted condition in common fluid dynamics applications. In some cases, when high speed and pressure occur in a flow region near the surface, such as the lubrication of non-conformal surfaces, this assumption becomes controversial and the observation shows that the fluid can slide on the surfaces. This study has numerically investigated the effect of fluid Slippage on the textured surface in transient elastohydrodynamic lubrication. The finite difference method extracted and discretized a numerical transient model based on the Newtonian lubricant fluid flow equations. The flow is assumed isothermal for a geometry including an upper cylinder and a lower flat dimple textured surface. A newly developed precise transient model is used for lubricated contact of a dimpled flat surface and a cylinder. This model considers passing the cylinder over a dimple in several time steps. In this paper, the model is comprehended by the critical shear stress model to consider boundary sliding. The results showed that with Slippage, the lubrication friction decreases compared to the no-Slip condition estimations. The occurrence of Slip causes an average 15.42% decrease in the friction coefficient for flat surfaces. For dimpled surfaces, the occurrence of sliding for different depths of dimples is on average 15% decrease in the amount of friction coefficient while it decreases about 12% for different radii of the dimple.

Simultaneous effects of Slip and heat transfer on peristaltic transport of an incompressible electrically conducting viscous fluid in an asymmetric channel is studied under the assumptions of long wavelength and low Reynolds number. The asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phases. Exact solutions for stream function, velocity field, temperature profile and pressure gradient are obtained. The effects of different parameters entering into the problem on pressure rise are discussed numerically and explained graphically. Also, pumping and trapping phenomena are discussed by numerical integration.

In this paper a laminar flow of water on an ice layer subjected to a Slip condition is considered numerically. The paper describes a parametric mathematical model to simulate the coupled heat and mass transfer events occurring in moving boundary problems associated with a quasi steady state steady flow process. The discretization technique of the elliptic governing differential equations of mass, momentum and energy is based on the control volume finite difference approach and enthalpy method. The results illustrate, the distribution of heat transfer coefficient, ice melting thickness, Slip velocity at solid moving boundary and boundary layer thickness for some values of Slip velocity coefficient cu.

We examine the velocity field of an incompressible Oldroyd-B fluid over a horizontal plate of continual length in a permeable medium with magnetohydrodynamics effect. Firstly, the results for the dimensionless classical model (governing equation) have been studied analytically then the study is extended for different fractional operators. The relations to determine the velocity fields of this problem are found by Laplace transformation and different numerical inversion algorithms. The impact of physical parameters on velocity profiles is analyzed graphically for integer and non-integer models. Non-integer operators are used to analyzing the impact of fractional parameters on the fluid curves of the fluid.

The various industrial, biological and engineering applications of squeezing flow have been the impetus for the renewed interests in the studies of fluid flow between parallel plates or disks. As a part of the renewed interests, this paper presents the study of axisymmetric magnetohydrodynamic squeezing flow of nanofluid in porous media under the influence of Slip boundary condition using differential transformation method. Good agreements are established when the results of the differential transformation method are compared with the results of numerical method Runge-Kutta coupled with shooting method. Also, the analytical solution is used to investigate the effects of porous medium, magnetic field and Slip boundary on the steady two-dimensional axisymmetric flow of the nanofluid. It is shown from the results that the velocity of the fluid increases as the magnetic field and porous parameters increase under Slip condition while the velocity of the fluid decreases with increase in the magnetic field and porous parameter under no Slip condition. By increasing the Slip parameter, the velocity of the fluid increases while the velocity of the fluid decreases as the Reynolds number increases. Studies on nanofluidics such as energy conservation, friction reduction and micro mixing biological samples can be enhanced and better understood by the insights given in this present study.

In this study, the results of a direct numerical simulation of turbulent drag reduction ina channel flow by hydrophobic coating at a nominal shear Reynolds number of Re t=180 are reported. Slip condition is imposed on the lower wall whereas the upper wallhas no-Slip condition. For this purpose, the use is made of a numerical simulation of three-dimensional, time-dependent Navier-Stokes equations for the incompressibleflow of a Newtonian fluid. Finally, statistical quantities of turbulent flow (specificallythe mean velocity profile, the root-mean-square of velocity fluctuations in differentdirections and the Reynolds shear stress are shown and discussed. The results confirmthat by increasing the amount of Slip on the lower wall, the bulk velocity passingthrough the channel increases. Also, the variation of root-mean-square of velocityfluctuations shows a similar behavior in the vicinity of the upper wall. But, theirgeneral trend is different in the proximity of the lower wall. Moreover, a change in theshape of the Reynolds shear stress profile from a minimum close to the lower walltowards a maximum close to the upper wall is observed.