Velocity Slip Effects Research Articles

Simultaneous effects of heterogeneous-homogeneous reactions in peristaltic flow comprising thermal radiation: Rabinowitsch fluid model

This exploration addresses the comportments of homogeneous-heterogeneous reactions on peristalsis transportation mechanism of Rabinowitsch fluid model inside a flexible channel. Mathematical modelling and analysis are performed for temperature, velocity and concentration distributions to explore the bearing of influential parameters for Rabinowitsch fluid model (lubricant blended with viscosity index improver) with the dynamic damping and stiffness characteristics. The scope of the current article is valuable in explaining the blood flow dynamics in vessels while considering the essential wall characteristics and chemical reaction. The effects of magnetic field, chemical reaction and velocity slip in blood vessels wall can be described by the presented model. The partial differential equations are formulated by the use of lubrication approach. The expressions for Nusselt number and coefficient of skin friction at the flexible wall are found and evaluated. The effects of homogeneous and heterogeneous reaction parameters shows reverse comportment on concentration field. Moreover, augmentation in skin friction is notice by escalating the parametric values of rigidity and damping.

A Σ-ϒ two-fluid model with dynamic local topology detection: Application to high-speed droplet impact

A numerical methodology resolving flow complexities arising from the coexistence of both multiscale processes and flow regimes is presented. The methodology employs the compressible Navier-Stokes equations of two interpenetrating fluid media using the two-fluid formulation; this allows for compressibility and slip velocity effects to be considered. On-the-fly criteria switching between a sharp and a diffuse interface within the Eulerian-Eulerian framework along with dynamic interface sharpening is developed, based on an advanced local flow topology detection algorithm. The sharp interface regimes with dimensions larger than the grid size are resolved using the VOF method. For the dispersed flow regime, the methodology incorporates an additional transport equation for the surface-mass fraction (Σ-ϒ) for estimating the interface surface area between the two phases. To depict the advantages of the proposed multiscale two-fluid approach, a high-speed water droplet impact case has been examined and evaluated against new experimental data; these refer to a millimetre size droplet impacting a solid dry smooth surface at a velocity as high as 150 m/s, which corresponds to a Weber number of 7.6×105. Droplet splashing is followed by the formation of highly dispersed secondary cloud of droplets, with sizes ranging from 10 μm close to the wall to less than 1 μm forming at the later stages of droplet fragmentation. Additionally, under the investigated impact conditions, compressibility effects dominate the early stages of droplet splashing. A strong shock wave forms and propagates inside the droplet, where transonic Mach numbers occur; local Mach numbers up to 2.5 are observed for the expelled surrounding gas outside the droplet. Relative velocities between the two fluids are also significant; local values on the tip of the injected water film up to 5 times higher than the initial impact velocity are observed. The proposed numerical approach is found to capture relatively accurately the flow phenomena and provide additional information regarding the produced flow structure dimensions, which is not available from the experiment.

Mixed Convection Flow Behaviour in Existence of Lorentz Forces in a Vertical Micro Circular Duct having Time Periodic Boundary Conditions: Steady Periodic Regime

The purpose of this research is to study mixed convection flow behaviour in existence of Lorentz forces in a vertical micro circular subjected to a periodic sinusoidal temperature change at the surface. Effects of velocity slip and temperature jump are also taken into consideration. The research analysis is carried out by considering fully developed parallel flow and steady periodic regime. The governing equations, together with the constraint equations with arise from the definition of mean velocity and temperature, are written in a dimensionless form and mapped into equations in the complex domain. One obtains two independent boundary value problems, which provide the mean value and the oscillating term of the velocity and temperature distributions. These boundary value problems are solved analytically. Numerical procedures are examined for various active parameters namely; fluid wall interaction, rarefaction, Hartmann number, Prandtl number, the dimensionless frequency. The results of the research revealed that, magnetic field plays a damping impact in flow and results in decreases in fluid velocity for both air and water. Further, increases the rarefaction parameter and fluid-wall interaction parameter reduces the oscillation amplitude of the dimensionless velocity.

Mathematical Modelling and Exact Solution of Fully Developed Natural Convection Flow in a Vertical Permeable Micro-Channel in the Existence of Thermal Radiation

Analytical solution to the steady natural convection flow in a vertical permeable micro-channel in the existence of thermal radiation is presented. Specifically, the effects of velocity slip and temperature jump is considered. Due to the presence of thermal radiation, the momentum and energy equations are coupled system of ordinary differential equations. The effect of various parameters controlling the physical situation such as thermal radiation, temperature difference, Knudsen number, and fluid wall interaction are discussed with the aid of line graphs and tables. The results of the analyses indicated that the rate of heat transfer on the permeable micro-channel walls can be enhanced with the increase in the temperature difference parameter. Furthermore, the skin friction on the cold wall could be reduced with the increase in suction/injection parameter. For both asymmetric heating situations, increase in suction velocity (negative value of S) results to increase volume flow rate.

Effects of Slip Velocity and Hall Currents on Peristaltic Transport of Bingham-Papanastasiou Fluid with Heat Transfer

Effects of Slip Velocity and Hall Currents on Peristaltic Transport of Bingham-Papanastasiou Fluid with Heat Transfer

Effect of Brownian Diffusion on Squeezing Elastico-Viscous Nanofluid Flow with Cattaneo-Christov Heat Flux Model in a Channel with Double Slip Effect

The present study deals with the analysis of heat transfer of the unsteady Maxwell nanofluid flow in a squeezed rotating channel of a porous extensile surface subject to the velocity and thermal slip effects incorporating the theory of heat flow intensity of Cattaneo-Christov model for the expression of the energy distribution in preference to the classical Fourier’s law. A set of transformations is occupied to renovate the current model in a system of nonlinear ordinary differential equations that are numerically decoded with the help of MATLAB integrated function bvp4c. The effects of various flow control parameters are investigated for the momentum, temperature and diffusion profiles, as well as for the wall shearing stress and the heat and mass transfer. The results are finally described from the material point of view. A comparison of heat flux models of Cattaneo-Christov and Fourier is also performed. An important result from the present work is that the squeezing parameter is strong enough in the middle of the channel to retard the fluid flow.

Surface temperature and free-stream velocity oscillation effects on mixed convention slip flow from surface of a horizontal circular cylinder

The present phenomena address the slip velocity effects on mixed convection flow of electrically conducting fluid with surface temperature and free stream velocity oscillation over a non-conducting horizontal cylinder. To remove the difficulties in illustrating the coupled PDE, the primitive variable formulation for finite dif?ference technique is proposed to transform dimensionless equations into primitive form. The numerical simulations of coupled non-dimensional equations are exam?ined in terms of fluid slip velocity, temperature, and magnetic velocity which are used to calculate the oscillating components of skin friction, heat transfer, and cur?rent density for various emerging parameters magnetic force parameter, ?, mixed convection parameter, ?, magnetic Prandtl number, ?, Prandtl number, and slip factor, SL. It is observed that the effect of slip flow on the non-conducting cylinder is reduced the fluid motion. A minimum oscillating behavior is noted in skin friction at each position but maximum amplitude of oscillation in heat transfer is observed at each position ? = ?/4 and 2?/3. It is further noticed that a fluid velocity increas?es sharply with the impact of slip factor on the fluid-flow mechanism. Moreover, due to frictional forces with lower magnitude between viscous layers, the rise in Prandtl number leads to decrease in skin fiction and heat transfer which is physi?cally in good agreement.

Surface temperature and free-stream velocity oscillation effects on mixed convention slip flow from surface of a horizontal circular cylinder

The present phenomena address the slip velocity effects on mixed convection flow of electrically conducting fluid with surface temperature and free stream velocity oscillation over a non-conducting horizontal cylinder. To remove the difficulties in illustrating the coupled PDE, the primitive variable formulation for finite dif?ference technique is proposed to transform dimensionless equations into primitive form. The numerical simulations of coupled non-dimensional equations are exam?ined in terms of fluid slip velocity, temperature, and magnetic velocity which are used to calculate the oscillating components of skin friction, heat transfer, and cur?rent density for various emerging parameters magnetic force parameter, ?, mixed convection parameter, ?, magnetic Prandtl number, ?, Prandtl number, and slip factor, SL. It is observed that the effect of slip flow on the non-conducting cylinder is reduced the fluid motion. A minimum oscillating behavior is noted in skin friction at each position but maximum amplitude of oscillation in heat transfer is observed at each position ? = ?/4 and 2?/3. It is further noticed that a fluid velocity increas?es sharply with the impact of slip factor on the fluid-flow mechanism. Moreover, due to frictional forces with lower magnitude between viscous layers, the rise in Prandtl number leads to decrease in skin fiction and heat transfer which is physi?cally in good agreement.

Comment on the paper “Thermal and velocity slip effects on MHD mixed convection flow of Williamson nanofluid along a vertical surface: Modified Legendre wavelets approach, Feroz Ahmed Soomro, Muhammad Usman, Rizwan Ul Haq, W. Wang” [Phys. E Low-dimens. Syst. Nanostruct. 104 (2018) 130–137

Comment on the paper “Thermal and velocity slip effects on MHD mixed convection flow of Williamson nanofluid along a vertical surface: Modified Legendre wavelets approach, Feroz Ahmed Soomro, Muhammad Usman, Rizwan Ul Haq, W. Wang” [Phys. E Low-dimens. Syst. Nanostruct. 104 (2018) 130–137

Heat generation/absorption and velocity slip effects on unsteady axisymmetric flow of Williamson magneto-nanofluid

Engineers and researchers in the field of heat transfer are in search of new techniques to optimize the performance of energy devices through heat transfer enhancement. For that reason, the flow analysis involving nanoparticles is assumed to be one of the most important techniques for enhancing heat transfer systems. Being a two-component system, different numerical approaches are available to model the thermo-fluids behavior of nanofluids. The current study describes the investigation of Buongiorno model for evaluation of transient flow and heat transfer of Williamson nanofluids under the impacts of velocity slip and magnetic field. In addition, the effects of heat generation/absorption and convective heat transfer have been employed in this analysis. The Boussinesq-approximations are implemented to obtain the governing conservation equations for nanofluids transport phenomenon. The leading equations of the modeled physical problem have been solved using a MATLAB code, based on Nachtsheim–Swigert shooting iteration scheme. The novelty of the current investigation is the existence of multiple solutions for the nanofluids flow past a radially shrinking surface by considering the effects of uniform suction at the wall. In this review, it is seen that the investigated physical parameters affect remarkably on the nanofluid stream function, temperature and nanoparticles concentration. The skin friction, local Nusselt number and the local Sherwood number and some samples of velocity, temperature and nanoparticle concentration profiles are discussed and presented with the help of graphs. From this study, it is observed that the existence range of dual solutions is significantly raised by the higher Weissenberg number.

Induced magnetic field and second order velocity slip effects on TiO2-water/ethylene glycol nanofluids

This paper explores stagnation-point flow mechanism and the convective heat transmission of an incompressible viscous fluid encouraged by impermeable stretching sheet. Water and the ethylene glycol driven nanofluids comprising titanium oxide nanoparticles in company of non-uniform heat source/sink accounted here. Effect of second order velocity slip and induced magnetic-field accounted in the presumed model. Primary equations of adopted model have been standardized through similarity methodology and resolved the subsequent equations numerically by expending RK-4 shooting exercise. The stimulus of encouraging flow parameters on the flow specific is made accurately through diagrams and charts. We measure the strength besides trend of the relation amongst the numerous emergent flow parameters with Skin friction coefficient, Nusselt number by using correlation co-efficient and the impression of the relation confirmed by employing Ficher’s test. Here dual characteristic of induced magnetic-field has been witnessed for magnetic Prandtl number.

Mathematical Model of Flow in a Doubly Constricted Permeable Channel with Effect of Slip Velocity

A mathematical model of steady laminar flow in a channel of varying cross section is studied under the effect of slip velocity at the permeable boundary. The fluid reabsorption at walls is taken care by the assumption of flow rate as a function of the axial coordinate at each cross section. An analytical solution of Navier-Stokes equations is determined by employing the perturbation technique. The graphical results are presented to illustrate the significance of slip velocity and various parameters on the velocity profiles, mean pressure drop, wall shear stress and stream function.

Dual Solutions and Stability Analysis of Micropolar Nanofluid Flow with Slip Effect on Stretching/Shrinking Surfaces

The purpose of the present paper is to investigate the micropolar nanofluid flow on permeable stretching and shrinking surfaces with the velocity, thermal and concentration slip effects. Furthermore, the thermal radiation effect has also been considered. Boundary layer momentum, angular velocity, heat and mass transfer equations are converted to non-linear ordinary differential equations (ODEs). Then, the obtained ODEs are solved by applying the shooting method and in the results, the dual solutions are obtained in the certain ranges of pertinent parameters in both cases of shrinking and stretching surfaces. Due to the presence of the dual solutions, stability analysis is done and it was found that the first solution is stable and physically feasible. The results are also compared with previously published literature and found to be in excellent agreement. Moreover, the obtained results reveal the angular velocity increases in the first solution when the value of micropolar parameter increases. The velocity of nanofluid flow decreases in the first solution as the velocity slip parameter increases, whereas the temperature profiles increase in both solutions when thermal radiation, Brownian motion and the thermophoresis parameters are increased. Concentration profile increases by increasing N t and decreases by increasing N b .

Numerical analysis of water based CNTs flow of micropolar fluid through rotating frame

BackgroundIn this article, the nanomaterial flow of micropolar fluid in rotating frame is considered. The SWCNT and MWCNT with base fluid namely pure water is also taken into account to analyze the flow behavior over stretching surface. Mathematical model have been constructed under the nanomaterial of micropolar fluid. MethodThe governing equations have been developed in the form of system of partial differential equations. The partial differential equations are transformed into ordinary differential equations using similarity transformations. The transformed system has been solved through MAPLE software. ResultsThe physical parameters like as thermal slip effects, velocity slip effects and magnetic hydrodynamics on the micropolar nanofluid are presented by tables and graphs. Surprisingly in the rotating parameter, F′′(0) and − θ′(0) increases for higher values of the rotating parameter while opposite to be noted for G′′(0). The Nusselt number and skin friction increases for higher values of micropolar parameter but MWCNT achieves higher heat transfer as associated to SWCNT.

Influence of Soret and Dufour effects on unsteady 3D MHD slip flow of Carreau nanofluid over a slendering stretchable sheet with chemical reaction

This paper presents a numerical exploration on the unsteady three-dimensional hydromagnetic flow of Carreau nanofluid over a slendering stretchable sheet in the presence of thermal radiation and chemical reaction. Furthermore, the effects of velocity slip, thermal slip, solutal slip, Soret and Dufour are taken into account. The prevailing time-dependent partial differential equations are metamorphosed into a system of coupled nonlinear ordinary differential equations by using the appropriate similarity transformations. The resultant nonlinear coupled differential equations are solved numerically by using the Runge–Kutta fourth-order method along with shooting scheme. The sway of sundry parameters on velocity, temperature, concentration, shear stress, temperature gradient and concentration gradient has been premeditated, and numerical results are presented graphically and in tabular form. Comparison amid the previously published results, and the current numerical results are made for the limiting cases, which are found to be in a virtuous agreement.

MHD non-Newtonian thin film fluid flow due to an unsteady stretching sheet under thermocapillarity phenomenon

This theoretical work explores the effect of the magnetic field on the liquid thin film flow of a non-Newtonian Powell–Eyring fluid. The thermocapillarity phenomenon in association with the effect of slip velocity is studied. In our research, we cannot ignore the important role of the numerical shooting method which employed to get the solution for our problem. This method helped us to sketch both the dimensionless velocity and the dimensionless temperature for several parameters. Furthermore, the authentication on the correctness and effectiveness for our method is checked by performing a comparison between this problem in the absence of some parameters and the previously published work, which confirms the robustness for the shooting method. Finally, an overview of the effect of the emerging parameters on the velocity and temperature profiles as well as the local skin-friction coefficient and the local Nusselt number is done.

Non-uniqueness of solutions to a MHD stagnation-point flow over an exponentially permeable stretching/shrinking sheet with velocity slip

In this study, a magnetohydrodynamic (MHD) stagnation-point boundary layer flow over an exponentially stretching/shrinking sheet with suction/injection and velocity slip effects is presented. The governing equations were first transformed into a non-linear ordinary differential equations with the help of similarity transformations. Following from there, the equations obtained were solved numerically utilizing the bvp4c programme in MATLAB. It was determined that the non-linear ordinary differential equations possessed non-uniqueness of solutions (dual solutions). Stability analysis was performed to verify the stability of the dual solutions obtained. The results revealed that the first solution was stable while the second solution was unstable. Apart from that, it was also found that as the magnetic, suction and velocity slip parameters increased, the range of the non-uniqueness of solutions increased correspondingly. Hence, it is proposed that the existence of magnetic, suction and velocity slip effects delayed the boundary layer separation.

Stagnation-Point Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Hybrid Nanofluid with Slip Velocity Effect: Stability Analysis

The effect of slip on stagnation point flow and heat transfer over an exponentially stretching/shrinking sheet filled with Copper-Alumina/water nanofluids is investigated numerically in this paper. The governing boundary layer equations are transformed into a set of ordinary differential equations using a similarity transformation and then solved numerically using the bvp4c function in Matlab. The effects of nanoparticle volume fraction, slip parameter and stretching/shrinking parameter on the flow pattern and heat transfer have been studied. It is found that dual solutions exist for hybrid nanofluid in the case of shrinking sheet. Furthermore, slip parameter and Copper nanoparticle acts in widening the range of solution. Hybrid nanofluids have the higher heat transfer rate compared to nanofluid and viscous fluid. A stability analysis showed that the first solution is linearly stable and physically realizable.

The numerical solution for BVP of the liquid film flow over an unsteady stretching sheet with thermal radiation and magnetic field using the finite element method

The method introduced in this paper is based on the finite element method. As an application for this efficient numerical method, we employ it in solving the system of ordinary differential equations which describes the thin-film flow and heat transfer with the effect of thermal radiation, magnetic field and slip velocity. The effect of the parameters which govern the proposed problem is discussed. From this theoretical and numerical study, it is observed that the slip velocity parameter tends to decrease the fluid velocity, whereas both the magnetic parameter and the radiation parameter can enhance the temperature distribution.

Stagnation flow of hybrid nanoparticles with MHD and slip effects

AbstractThe flow of hybrid nanoparticles with significant physical parameters with different base fluids in the presence of Biot number, velocity slip, and MHD effects has not been explored so far, particularly for a circular cylinder. Therefore, the current report is presented to offer a numerical solution for hybrid nanoparticles with base fluids (water and ethylene glycerol) via a circular cylinder. The physical situation is interpreted in terms of partial differential equations and is converted into ordinary differential equations after applying the similarity transformation. The results are presented in both tabular and graphical forms. The impact of physical parameters on velocity distribution is examined through graphs. The comparative results of hybrid nanoparticles for distinct base fluids as ethylene glycol and water are proposed and the hybrid nanoparticles with base fluid water seems to be greater than that of the hybrid nanoparticles with base fluid EG. The temperature profile of hybrid nanoparticles is found to be a decreasing function with growth in velocity slip parameter but an opposite trend is noted in case of nanoparticles . The skin friction and Nusselt number augmented for the increase in magnetic field, velocity slip, and nanoparticle while it shows a decreasing trend toward thermal slip parameter. For the both cases, improvement in Biot number helps enhance the heat transfer constantly.