The objective of this study is to determine the characteristics of hydromagnetic FLOW over a slendering stretching sheet in SLIP FLOW regime. Steady, two dimensional, nonlinear, hydromagnetic laminar FLOW of an incompressible, viscous and electrically conducting fluid over a stretching sheet with variable thickness in the presence of variable magnetic field and SLIP FLOW regime is considered. Govern-ing equations of the problem are converted into ordinary differential equations utilizing similarity transformations. The resulting non-linear differential equations are solved numerically by utilizing Nachtsheim-swigert shooting iterative scheme for satisfaction of asymptotic boundary conditions along with fourth order Runge-Kutta integration method. Numerical computations are carried out for various values of the physical parameters and their effects over the velocity and temperature are analyzed. Numerical values of dimensionless skin friction coefficient and non-dimensional rate of heat transfer are also obtained.

In the present research work, we introduce a new method for estimating the SLIP length on superhydrophobic surfaces. Hence, a dynamic force is added to momentum equations and velocity boundary condition is rewritten in a new form. Laminar and turbulent channel FLOWs are considered and two force functions are used with different profiles to investigate their effects on results. The turbulent channel FLOW is considered at Ret= 180 and the Large Eddy Simulation (LES) method has been applied to analyze this FLOW. All results indicate that this method can predict the streamwise SLIP length with a good accuracy, which is comparable with the Navier’s method. So, using this numerical solution and also measuring pressure drop and mass FLOW rate in the channel, SLIP length can be calculated. Consequently, the errors and difficulties of SLIP length measurements in typical methods such as AFM and μPIV would be eliminated.

In this paper, the problem of Poiseuille FLOW with couple stresses effect in a fluid layer using the linear instability and nonlinear stability theories is analyzed. Also, the nonlinear stability eigenvalue problems for x, z and y, z disturbances are derived. The Chebyshev collocation method is adopted to arrive at the eigenvalue equation, which is then solved numerically, where the equivalent of the Orr-Sommerfeld eigenvalue problem is solved using the Chebyshev collocation method. The difficulties which arise in computing the spectrum of the Orr-Sommerfeld equation are discussed. The critical Reynolds number Rc, the critical wave number ac, and the critical wave speed cc are computed for wide ranges of the couple stresses coefficient M. It is found that the couple stresses coefficient M has great stabilizing effects on the fluid FLOW where the fluid FLOW becomes more unstable as M increases.

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.

The steady-state fully-developed laminar FLOW of non-Newtonian power-law fluids is examined in a circular microchannel with SLIP boundary condition and under an imposed constant wall heat flux. Effects of SLIP as well as the hydrodynamic and thermal key parameters on heat transfer and entropy generation are investigated. The results reveal that increasing the Brinkman number and the FLOW behavior index both lead to increasing the entropy generation and decreasing the Nusselt number. In heating process, the temperature difference between the fluid and the wall decreases as the SLIP coefficient increases; similar trend may or may not be observed for cooling process, determined by the range of the SLIP coefficient as well as the Brinkman number. An increase in the SLIP coefficient leads to an increase in both the Nusselt number and the Bejan number, whereas it gives rise to a decrease in entropy generation. For each particular value of the SLIP coefficient, the Nusselt number approaches a specific value as the Brinkman number and/or the FLOW behavior index increases. An increase in the FLOW behavior index or a decrease in the SLIP coefficient results in incrementing the average entropy generation.

A control-volume numerical approach has been used to study rarefaction effects in simultaneously hydrodynamically and thermally developing FLOW in rectangular microchannels with a prescribed uniform wall heat flux in the SLIP-FLOW regime (10-3 £ Kn £ 10-1). The effects of velocity SLIP and thermal creep on the key FLOW parameters are examined in detail. Low Reynolds number FLOWs (Re≤ 1) for different channel aspect ratios (0 £ a* £ 1) are considered. The effects of rarefaction on the global features of the FLOW and thermal development in the entrance region are examined.Dramatic reductions in the friction coefficient are observed in the entrance region due to rarefaction effects, which are enhanced by thermal creep. For the fluid heating cases considered here, thermal creep increases SLIP at the wall and thereby further reduces the friction coefficient and slightly enhances heat transfer at a given Reynolds number.For an identical heat flux applied to the microchannel walls, thermal creep effects become much more pronounced at lower Reynolds numbers since it results in higher axial temperature gradients.

In this work, SLIP FLOW of helium gas has been studied in a three dimensional rectangular microchannel heat sink with 11 microchannel and 10 rectangular fins. Helium gas FLOW is considered ideal and incompressible. The finite volume method with using coupled algorithm is employed to carry out the computation. To validate the present work, comparison with numerical and experimental studies is done and it is seen that the computed results have good agreement. To investigate the effect of fins and walls material on heat sink performance, all simulations are carried out and compared with each other for three materials consisting of aluminum, silicon and copper. The results show that along the microchannel, local Knudsen number decreases. Also thermal resistance increases continuously with increasing Knudsen number from 0. 006 to 0. 048. The results indicate that for various inlet Knudsen numbers, copper heat sink has the lowest thermal resistance. Furthermore, copper heat sink has the highest average Nusselt number for Knudsen number higher than 0. 024 but for Knudsen number lower than 0. 024, silicon heat sink has higher average Nusselt number than copper heat sink.

The problem of unsteady Stokes FLOW of certain Newtonian fluids in a circular pipe of uniform cross section is discussed. The pipe is uniformly porous. The unsteady Navier-Stokes equations for the system in cylindrical polar coordinates have been solved analytically to obtain a complete description of the FLOW. The solution of the FLOW equations subject to the SLIP boundary conditions leads to the detailed expressions for axial and radial components of velocity and the pressure distribution depending on position coordinates and time. As a special case we have presented the situation when no-SLIP boundary conditions are implemented. The velocity profile is analyzed for different values of the FLOW parameters like Womersley number, SLIP length and time.