Velocity Slip Boundary Condition Research Articles

Influence of Lorentz Force and Thermal Radiation on Heat Transfer of Nanofluids Over a Stretching Sheet with Velocity–Thermal Slip

This article is concerned with the study of two-dimensional hydromagnetic flow of nanofluids over a stretching sheet with thermal radiation effects under the influence of velocity and thermal slip boundary condition. Three types of of nanofluids, namely the copper–water, the Alumina–water and the Titanium-dioxide water are considered. The resulting coupled nonlinear differential equations are solved numerically by a fifth-order Runge–Kutta–Fehlberg (RKF45) integration scheme with a shooting technique. Good agreement are observed between the present numerical results and the available results in the literature review for some special cases. The effects of magnetic field, thermal radiation, velocity slip and thermal slip at the boundary are considered here. The influence of different parameters on the dimensionless velocity, temperature, skin friction coefficient, and local Nusselt numbers is explored and presented in the form of graphs and interpreted physically. The results obtained reveal that the effects of velocity slip to decrease velocity and increase the temperature profiles whereas the effects of increase in the thermal slip condition is to decrease the temperature profiles.

Flow and heat transfer to Sisko fluid with partial slip

In this paper we study the partial slip effects on the flow and heat transfer of an incompressible non-Newtonian fluid over a nonlinear stretching sheet. The velocity slip boundary condition based on the Sisko constitutive fluid model is introduced. Suitable dimensionless variables are used to convert the governing partial differential equations into ordinary differential equations. Numerical solutions of these equations are obtained by the Runge–Kutta Fehlberg method. Additionally, the exact analytical solutions are presented in some special cases. The computational results for the velocity, temperature, skin-friction coefficient, and Nusselt number are presented in graphical and tabular forms. To validate the numerical results obtained, a comparison is made with the exact analytical solutions. The analysis of the results obtained shows that enhancement in the velocity slip parameter reduces the velocity as well as the momentum boundary layer thickness. However, quite the opposite is true with the temperature and corresponding thermal boundary layer thickness.

The effects of porosity and permeability on fluid flow and heat transfer of multi walled carbon nano-tubes suspended in oil (MWCNT/Oil nano-fluid) in a microchannel filled with a porous medium

The forced convection heat transfer and laminar flow in a two-dimensional microchannel filled with a porous medium is numerically investigated. The nano-particles which have been used are multi walled carbon nano-tubes (MWCNT) suspended in oil as the based fluid. The assumption of no-slip condition between the base fluid and nano-particles as well as the thermal equilibrium between them allows us to study the nanofluid in a single phase. The nanofluid flow through the microchannel has been modeled using the Darcy–Forchheimer equation. It is also assumed that there is a thermal equilibrium between the solid phase and the nanofluid for energy transfer. The walls of the microchannel are under the influence of a fluctuating heat flux. Also, the slip velocity boundary condition has been assumed along the walls. The effects of Darcy number, porosity and slip coefficients and Reynolds number on the velocity and temperature profiles and Nusselt number will be studied in this research.

The variations of heat transfer and slip velocity of FMWNT-water nano-fluid along the micro-channel in the lack and presence of a magnetic field

Simulation of forced convection of FMWNT-water (functionalized multi-walled carbon nano-tubes) nano-fluid in a micro-channel under a magnetic field in slip flow regime is performed. The micro-channel wall is divided into two portions. The micro-channel entrance is insulated while the rest of length of the micro-channel has constant temperature (TC). Moreover, the micro-channel domain is exposed to a magnetic field with constant strength of B0. High temperature nano-fluid (TH) enters the micro-channel and exposed to its cold walls. Slip velocity boundary condition along the walls of the micro-channel is considered. Governing equations are numerically solved using FORTRAN computer code based on the SIMPLE algorithm. Results are presented as the velocity, temperature, and Nusselt number profiles. Greater Reynolds number, Hartmann number, and volume fraction related to more heat transfer rate; however, the effects of Ha and ϕ are more noteworthy at higher Re.

MHD dissipative flow and heat transfer of Casson fluids due to metachronal wave propulsion of beating cilia with thermal and velocity slip effects under an oblique magnetic field

A theoretical investigation of magnetohydrodynamic (MHD) flow and heat transfer of electrically-conducting viscoplastic fluids through a channel is conducted. The robust Casson model is implemented to simulate viscoplastic behavior of fluids. The external magnetic field is oblique to the fluid flow direction. Viscous dissipation effects are included. The flow is controlled by the metachronal wave propagation generated by cilia beating on the inner walls of the channel. The mathematical formulation is based on deformation in longitudinal and transverse velocity components induced by the ciliary beating phenomenon with cilia assumed to follow elliptic trajectories. The model also features velocity and thermal slip boundary conditions. Closed-form solutions to the non-dimensional boundary value problem are obtained under physiological limitations of low Reynolds number and large wavelength. The influence of key hydrodynamic and thermo-physical parameters i.e. Hartmann (magnetic) number, Casson (viscoplastic) fluid parameter, thermal slip parameter and velocity slip parameter on flow characteristics are investigated. A comparative study is also made with Newtonian fluids (corresponding to massive values of plastic viscosity). Stream lines are plotted to visualize trapping phenomenon. The computations reveal that velocity increases with increasing the magnitude of Hartmann number near the channel walls whereas in the core flow region (center of the channel) significant deceleration is observed. Temperature is elevated with greater Casson parameter, Hartmann number, velocity slip, eccentricity parameter, thermal slip and also Brinkmann (dissipation) number. Furthermore greater Casson parameter is found to elevate the quantity and size of the trapped bolus. In the pumping region, the pressure rise is reduced with greater Hartmann number, velocity slip, and wave number whereas it is enhanced with greater cilia length.

Size-dependent Vibration and Instability of Magneto-electro-elastic Nano-scale Pipes Containing an Internal Flow with Slip Boundary Condition

Size-dependent vibrational and instability behavior of fluid-conveying magneto-electro-elastic (MEE) tubular nano-beam subjected to magneto-electric potential and thermal field has been analyzed in this study. Considering the fluid-conveying nanotube as an Euler-Bernoulli beam, fluid-structure interaction (FSI) equations are derived by using non-classical constitutive relations for MEE materials, Maxwell’s equation, and Hamilton’s principle. Thereafter, with consideration of the non-uniformity of the flow velocity profile and slip boundary conditions, modified FSI equation is obtained. By utilizing Galerkin weighted-residual solution method, the obtained FSI equation is approximately solved to investigate eigen-frequencies and consequently instability (critical fluid velocity) of the system. In numerical results, a detailed investigation is conducted to elucidate the influences of nano-flow and nano-structure small scale effect, non-uniformity, temperature change, and external magneto-electric potential on the vibrational characteristics and stability of the system. This work and the obtained results may be useful to smart control of nano structures and improve their efficiency.

Influence of Cross-Diffusion on Slip Flow and Heat Transfer of Chemically Reacting UCM Fluid between Porous Parallel Plates with Hall and Ion Slip Currents

The present paper deals with the Hall and ion slip currents on an incompressible unsteady free convection flow and heat transfer of an upper convected Maxwell fluid between porous parallel plates with Soret and Dufour effects by considering the velocity slip and convective boundary conditions. Assume that there are periodic injection and suction at the lower and upper plates, respectively. The temperature and concentration at the lower and upper plates change periodically with time. The flow field equations are reduced to nonlinear ordinary differential equations by using similarity transformations and a semi-analytical-numerical solution has been obtained by the differential transform method. The velocity components, temperature distribution, and concentration with respect to different fluid and geometric parameters are discussed in detail and presented in the form of graphs. It is observed that the Biot number increases the temperature and concentration of the fluid. Further, the concentration of the fluid is enhanced whereas the temperature decreases with increasing slip. The present results are compared with the existing literature and are found to be in good agreement.

Forced convective heat transfer from spheres to Newtonian fluids in steady axisymmetric flow regime with velocity slip at fluid–solid interface

The heat transfer phenomenon of spherical particles in Newtonian fluids with velocity slip and uniform thermal boundary condition at the fluid–solid interface has been numerically investigated using a computational fluid dynamics (CFD) based in-house solver. At the interface linear slip velocity boundary condition has been adopted. The dimensionless continuity, momentum and energy equations along with the appropriate non-dimensional boundary conditions are solved by a segregated approach. This numerical procedure is a finite difference method based CFD solver implemented on a staggered grid arrangement in spherical coordinates. The convective and diffusive terms are discretized using the quadratic upstream interpolation for convective kinematics and a second order central differencing scheme respectively. Prior to obtaining new results, the present numerical solver is extensively validated by comparing the present values of the average Nusselt numbers with the existing literature values for either extreme values of the slip conditions, i.e., for fully slip and no-slip conditions. Further new results are obtained over the range of conditions as the Reynolds number, Re = 0.1–200; the Prandtl number, Pr = 1–100; and dimensionless slip parameter, λ = 0.01–100. The effects of these parameters on the isotherm contours and the local and average Nusselt numbers are thoroughly discussed and finally on the basis of present numerical results (196 data points), an empirical correlation is proposed for the average Nusselt numbers of single spheres with velocity slip at the interface as function of Re, Pe, and λ.

Unsteady MHD flow over exponentially stretching sheet with slip conditions

The present paper examines the hydromagnetic three-dimensional flow induced by a stretched surface. An incompressible material saturates the porous medium. Velocity and thermal slip boundary conditions are considered. Suitable transformations are used to obtain the nonlinear ordinary differential equations. Series solutions of the resulting systems are constructed. The effects of various pertinent parameters on the axial velocity and temperature distributions are analyzed graphically. The skin friction and the Nusselt number are computed numerically and graphically.

Transport of Cu–H2O nanofluid through a channel with wavy walls under velocity slip and connective boundary conditions

Present study examines the mixed convective peristaltic transport of Cu–H2O nanofluid with velocity slip and convective boundary conditions. Analysis is performed using the two-phase model of the nanofluid. Viscous dissipation and heat generation/absorption effects are also taken into account. Problem is formulated using the long wavelength and low Reynolds number approach. Numerical solutions for the pressure rise per wavelength, pressure gradient, axial velocity, temperature and heat transfer rate at the boundary are obtained and studied through graphs. Results show that the area of peristaltic pumping decreases with an increase in the nanoparticles volume fraction. Increase in the velocity slip parameter shows an increase of the pressure gradient in the occluded part of the channel. Further, addition of copper nanoparticles reduces both the axial velocity and temperature of the base fluid. Temperature of the nanofluid also decreases sufficiently for an increase in the value of Biot number.

Finite Volume Modeling of Gas Flow in Microbearings with Rough Surface Topography

abstractThe random surface roughness effects on the performances of gas-lubricated slider microbearings are investigated using finite volume analysis. The rough surface morphologies with the atomic force microscope (AFM) data and the numerical procedures used to generate self-affine surfaces by the midpoint displacement method are proposed and compared. Three-dimensional finite volume modeling of the gas microbearing and its flow field mesh are described considering the velocity-slip boundary condition. The results indicate that surface roughness causes a deviation in the pressure distribution, load-carrying capacity, velocity profile, and local Reynolds number from conventional theory with various values depending on the degree of surface roughness used. The pressure decreases irregularly due to the fractal surface and produces a larger change. The larger the roughness exponent is, the larger the gas slip velocity at the bottom of the wall. In addition, the velocity-slip boundary condition can cause a decrease in the gas flow velocity. The surface roughness effect also leads to random variations in the local Reynolds number. This demonstrates that the random surface roughness potentially causes very complicated flow behavior in the ultra-thin-film bearing lubrication in microelectromechanical systems (MEMS) and should be adequately characterized in terms of the fractal nature of the bearing surfaces.

Sensitivity analysis of size effect on the performance of hydrostatic bearing

For size effect on solid-liquid interface of hydrostatic bearing oil film gap flow in two-dimension, fluid dynamic method is applied to investigate the influence of size effect on bearing capacity, dynamic stiffness and other performances. With the consideration of size effect, Reynolds equation is modified by adopting velocity slip boundary condition into Reynolds equation. The sensitivity factors are used to make a quantitative and qualitative analysis. Numerical simulation results show that size effect will affect bearing performances to a certain degree and the effect curve of size effect on bearing performances are given. The four maximum oil film pressures reduce with the increase of slip length. The maximum sensitivity of bearing capacity is 81.94%.

Effect of slip on heat transfer and entropy generation characteristics of simplified Phan-Thien–Tanner fluids with viscous dissipation under uniform heat flux boundary conditions: Exponential formulation

This study concerns the heat transfer and entropy generation characteristics of viscoelastic fluid flow modeled by the exponential formulation of simplified Phan-Thien–Tanner (s-PTT) model. This is the first such study in literature of thermal behavior of viscoelastic fluids modeled by the exponential formulation of s-PTT model. The flow between two parallel plates is laminar, hydrodynamically and thermally fully developed, viscous dissipative and subject to uniform heat flux on the walls. The slip velocity boundary condition is imposed on the fluid–solid interface and the slip is captured by three slip laws, namely, Navier's non-linear slip law, Hatzikiriakos slip law, and asymptotic slip law. The governing equations have been solved analytically. Closed form solutions for the velocity distribution have been derived while the temperature distribution is presented in terms of an infinite but convergent series. The results pertaining to the three slip laws have been presented in detail. Finally, a comparison has been made between the results for exponential formulation and those for the linear formulation of the s-PTT model. The comparison shows that results for linear formulation deviate significantly from those for exponential formulation and thus the accuracy of the exponential formulation justifies the extra mathematical complexity which it entails.

Numerical analysis for peristaltic transport of Carreau-Yasuda fluid with variable thermal conductivity and convective conditions

Peristalsis of Carreau-Yasuda fluid is investigated. Analysis is carried out in the presence of velocity slip and convective boundary conditions. Thermal conductivity of the fluid is taken to be temperature dependent. Lubrication analysis is used in the formulation of the problem. Resulting nonlinear system of equations is solved numerically. Impact of embedded parameters on the quantities of interest is examined through graphs and tables. Comparison of the behavior of the Carreau-Yasuda, Carreau and Newtonian fluid models is presented. Results show that the heat transfer rate at the wall for the Carreau fluid model is large when compared with the Newtonian or the Carreau-Yasuda fluid model. Also the heat transfer rate at the wall decreases with increase in the velocity slip and variable thermal conductivity parameters. Further, an increase in the Biot number reduces the fluid temperature by a considerable amount.

Influence of inclined Lorentz forces on boundary layer flow of Casson fluid over an impermeable stretching sheet with heat transfer

The inclined magnetic field effect on the boundary layer flow of a Casson model non-Newtonian fluid over a stretching sheet in the existence of thermal radiation and velocity slip boundary condition is investigated for both prescribed surface temperature and power law of surface heat flux cases. It is assumed that the magnetic field is applied with an aligned angle which varied from 0° to 90°. Both analytical and numerical solutions are obtained for the transformed non-dimensional ODE's using confluent hypergeometric function and fourth order Runge–Kutta method with shooting technique respectively. The combined effects of inclined magnetic field with other pertinent parameters such as Casson parameter, velocity slip parameter, radiation parameter and Prandtl number on velocity profile, temperature profile, local skin friction coefficient, local Nusselt number and non-dimensional wall temperature are discussed through graphs. It is found that the aligned angle plays a vital role in controlling the magnetic field strength on the Casson fluid flow region and the increasing values of aligned angle of the magnetic field lead to decrease the skin friction coefficient and the Nusselt number and increase the non-dimensional wall temperature.

Performance evaluation and comparative analysis of hydrostatic spindle affect by the oil film slip

To better understand the performance of a hydrostatic spindle in motion, the impact of oil film slip on the load capacity, stiffness and dynamic stiffness of the spindle is studied. Based on the velocity slip boundary conditions, the stress characteristic equation and the liquid flow equation of the hydrostatic spindle are formed into a coupled equation system that is used to numerically analyze the load capacity stiffness of the spindle system. The spindle properties and oil film characteristics are considered in the initial stage of oil film. From the simulation results, it is concluded that the occurrence of oil film slip results in the increase of the bearing capacity and stiffness, with a highest increase rate of approximately 40%. The existence of the slip phenomenon is confirmed in the oil film flow process of a spindle system, with a slip length of approximately 3μm determined by the simulation results, which are verified by the measurement of the axial stiffness of the spindle. This study explores a new method for the analysis of the static and dynamic performance and the determination of the dynamic stiffness of a hydrostatic spindle.

Ammonia Decomposition for Hydrogen Production in Catalytic Microchannels with Slip/Jump Effects

The rarefaction effects on the catalytic decomposition of NH3 in ruthenium–coated planar microchannels is numerically simulated in the Knudsen number range 0.015-0.03. A colocated finite–volume method is used to solve the governing equations. A concentration jump model derived from the kinetic theory of gases is employed to account for the concentration discontinuity at the reactive walls. A detailed surface reaction mechanism for ammonia decomposition on ruthenium along with a multi-component species diffusion model are used to study the effects of concentration jump coupled with velocity slip and temperature jump on the walls. The velocity-slip, temperature-jump and concentration-jump boundary conditions have miscellaneous effects on flow, temperature and species concentration fields. The results suggest that the velocity-slip boundary condition only slightly influences the species distribution at the edge of the Knudsen layer as well as inside the channel, while the temperature-jump boundary condition affects the heat and mass transfer characteristics the most. The concentration-jump effect, on the other hand, can counter balance the temperature-jump effects in some cases.

Heat transfer effects on carbon nanotubes suspended nanofluid flow in a channel with non-parallel walls under the effect of velocity slip boundary condition: a numerical study

The present article is dedicated to analyze the flow and heat transfer of carbon nanotube (CNT)-based nanofluids under the effects of velocity slip in a channel with non-parallel walls. Water is taken as a base fluid, and two forms of CNTs are used to perform the analysis, namely the single- and multi-walled carbon nanotubes (SWCNTs and MWCNTs, respectively). Both the cases of narrowing and widening channel are discussed. The equations governing the flow are obtained by using an appropriate similarity transform. Numerical solution is obtained by using a well-known algorithm called Runge---Kutta---Fehlberg method. The influence of involved parameters on dimensionless velocity and temperature profiles is displayed graphically coupled with comprehensive discussions. Also, to verify the numerical results, a comparative analysis is carried out that ensures the authenticity of the results. Variation of skin friction coefficient and the rate of heat transfer at the walls are also performed. Some already existing solutions of the particular cases of the same problem are also verified as the special cases of the solutions obtained here.

Effect of the Velocity Slip Boundary Condition on the Flow and Heat Transfer of Nanofluids Over a Stretching Sheet

Effect of the Velocity Slip Boundary Condition on the Flow and Heat Transfer of Nanofluids Over a Stretching Sheet

Improved modified Reynolds equation for thin-film gas lubrication from an extended slip velocity boundary condition

An extended slip velocity boundary condition is derived from the regularized 13 moment equations firstly. Different from the existing slip velocity boundary condition, the slip coefficients of the extended one are not fixed, which will change with the wall accommodation coefficient and the Knudsen number of the gas flow. Using the extended slip velocity condition, an improved modified Reynolds equation for thin-film gas lubrication is established. From solving the improved modified Reynolds equation, the pressure distribution of the slider gas bearing is obtained and has a better agreement with that from the direct simulation Monte Carlo method under different pitch angles and wall velocities. It is found that the improved modified Reynolds equation can predict a more accurate pressure distribution of the slider gas bearing than the Fukui and Kaneko's lubrication model from the linearized Boltzmann equation in the near transition regime.