Slip Flow Conditions Research Articles

Nonlinear Mixed Convective Analysis of Thomson and Troian Slip Flow Conditions for Ag–Cu–TiO2/H2O Hybrid Nanofluid Over a Riga Plate

The use of nanofluids to improve thermal performance is a significant area of research. In this study, a ternary nanofluid (composed of water suspending silver, copper, and titanium dioxide nanoparticles) was used to investigate flow characteristics over a Riga plate. The analysis included Thomson and Troian slip conditions, variable viscosity, and nonlinear mixed convection. After establishing the dynamics of the flow accurately, the partial differential equations representing these formulations were transformed into dimensionless nonlinear coupled ordinary differential equations. A solution methodology using the Chebyshev collocation method was developed to assess the impact of key physical parameters. The results obtain demonstrated consistency with existing literature under limiting flow conditions. The Hartmann number ( Υ ∈ [ 0.0 , 1.5 ] ) was found to increase the velocity of the ternary nanofluid by approximately 3.24 % , while slightly reducing both temperature by about 0.58 % and nanoparticle concentration by about 1.38 % in the flow distribution. In contrast, varying the mass Grashof parameter ( Λ 3 ∈ [ 0.0 , 0.3 ] ) decreased fluid velocity but promoted higher temperature and concentration distributions. The decrease in nanoparticle concentration of the ternary nanofluid due to increasing ϕ 3 * ∈ [ 0.01 , 0.09 ] led to sedimentation of ϕ 1 * and ϕ 2 * .

Analysing entropy generation of MHD (50:50) slip flow over an inclined needle

The primary objective of this study is to quantify the rate of entropy generation within the magnetohydrodynamic (MHD) slip flow system over the inclined needle. Entropy generation is a measure of the irreversibility and inefficiency in the flow process. The slip flow condition at the fluid interface can significantly impact the flow characteristics and heat transfer rates. In the hybrid nanofluid flow, which consists of non-magnetic and magnetic (Al2O3 and Fe3O4) nanoparticles, H2O+C2H6O2 (50:50) are considered as the base fluid. Furthermore, the effects of inclined magnetic fields are taken into interpretation. The PDE’s governing equations are converted into ODE’s using similarity transformations and solved by a numerical technique based on BVP4C. The results illustrate that crucial parameters such as the magnetic parameter, mixed convection parameter, nanoparticles of solid volume fractions, and Prandtl numbers are pointedly impacted by momentum and thermal profiles. The entropy and Bejan number also consider being various relationship-combined parameters. These analyses protest that raising the magnetic parameter estates an increase in the hybrid nanofluid thermal profile under slip circumstances. Examined magnetic field impact on flow and entropy generation in MHD flows, revealing significant changes in entropy generation due to interaction between magnetic field and nanoparticles. This analysis understands the impact of MHD and slip effects on entropy generation, particularly in the context of the newly emerging 50:50 fluid mixture. Hybrid nanofluids have been shown to have improved thermal conductivity compared to traditional fluids, which can enhance the cooling or heating capabilities of the inclined needle.

Hybrid nanofluid flow with quadratic velocity and thermal slip over a permeable stretching/shrinking surface

The current paper investigates the viscous flow and characteristics of heat transfer comprising water-based Fe3O4/Al2O3 hybrid nanofluid past a continuously porous stretching/shrinking sheet using quadratic thermal and velocity slip effects. The goal is to obtain analytical or exact solutions for flow and heat transfer under various physical situations. The influences of second-order slip flow conditions in the presence of hybrid nanofluid are given special consideration. The current results in the absence of the hybrid nanoparticles are in good correlation with those reported in the literature. The unique outcome is obtained for the case of the stretching sheet, while the two outcomes are observed for the phenomenon of the shrinking sheet. The temperature distribution uplifts owing to the nanoparticle volume fraction, while the velocity upsurges and declines in the upper and lower branch solutions, respectively.

A new expression for inertial particle collection efficiency by nanofibers with slip effect

The inertial particle filtration process of nanofibers in slip/transitional flow regime is studied by numerical methods. Effects of fiber Knudson number (Knf), fiber packing density (C), interception parameter (R), and particle Stokes number (St) on particle filtration performance are investigated. Results indicate that particle trajectories for slip flow are much closer to the fiber surface when compared to those with non-slip flow condition, which leads to a higher particle collection efficiency under slip flow condition than the case of no-slip flow. Particle collection efficiency improves as slip effect increases, especially for small and weak inertial particles, whereas, it is weakly related to slip effect for particles with large size and high-inertia. Particle deposition distribution on fiber surface is found to be negligibly influenced by slip effect. Based on the simulation results, a reliable prediction expression for particle collection efficiency of nanofibers due to the combination effects of inertial impaction and interception is developed in the range of 0.05 ≤ Knf ≤ 2, 0.01 ≤ C ≤ 0.1, 0.01 ≤ R ≤ 0.5, 0.1 ≤ St ≤ 10.

On the Modeling of Gas and Liquid Leaks Through Packed Glands

Abstract The prediction of gas and liquid leak rates through packed glands is overlooked and the very few studies available in the literature focus on the packing axial stress distribution. For better prediction of leakage, the change of porosity with length due to this nonuniform axial stress must be accounted for. Our previous theoretical model on leakage predictions are based on uniform capillaries. In this paper, a new model that accounts for the change of the capillary diameter with the axial stress for gaseous leak and a straight capillary model for liquid leaks are developed. The first slip flow condition is used to predict gas and liquid flow considering straight capillary model and a nonuniform capillary model the area of which dependents on the axial stress in the packing rings. An approach that uses an analytical-computational methodology based on the number and the size of pores obtained experimentally is adopted to predict gas and liquid leak rates in both the uniform and nonuniform compressed packed gland models. The Navier–Stokes equations associated with slip boundary condition at the wall are used to predict leakage. Experimental tests with helium, argon, nitrogen, and air for gazes and water and kerosene for liquids are used to validate the models. The porosity parameters characterization is conducted experimentally with a reference gas, namely, helium at different gland stresses and pressures.

Evaluation of Nusselt Number for a Flow in a Parallel Plates Using Magnetohydrodynamics Second-Order Slip Model

Abstract This study is the examination of magnetohydrodinamics (MHD) flow and heat transfer between microparallel plates with constant wall heat flux using two different boundary condition coefficients, widely known in the literature, in a second-order slip flow and temperature jump boundary condition model. The stream of incompressible viscous liquid between rigid microtwin plates with electrical conductivity was assumed to be steady, laminar, hydrodynamically and thermally fully improved. The effects of dilution, viscous dissipation, and axial transmission, which are significant at the microscale, are also contained in the analysis. Momentum and energy equations are solved analytically under second-order slip velocity and temperature jump boundary conditions. Closed type answers for the temperature field and the fully developed Nusselt number are derived as a function of the magnetic parameter (MHD), Knudsen number and modified Brinkman number. Particular attention has been paid to the effects of the magnetic field on the second-order slip flow conditions. The use of the second-order boundary condition coefficients proposed in the study varies according to the proposed boundary conditions and tends to increase and decrease the heat transfer. Otherwise, MHD increases the heat transfer for both boundary conditions.

Entropy generation analysis of three dimensional mixed convection flow of couple stress nanofluid with non-Fourier’s heat and non-Fick’s mass flux model

The current study concentrated on the analysis of entropy generation in three dimensional mixed convection flow of couple stress nanofluid under the effect of high order velocity slip flow, passive and active control conditions. The problem advances more significance with the effect of non-Fourier’s heat, and non-Fick’s mass flux model to scrutinize the heat and mass transport rate. The high-order partial differential equations obtained from the designed problem are transmuted into higher order ordinary differential equations using similarity conversion and lastly solved by using bvp4c. Through this investigation how governing parameters have affected the flow problem were examined and offered in graphical and tabular form. It is discovered that the occurrence of couple stress inflow problem upsurges the velocity of the fluid and on the other hand it causes a reduction in the entropy production. Likewise, it is detected that temperature improves by snowballing the Hartman parameter. Moreover, the temperature and concentration disseminations are greater all for the situation of an active control while correlated with a case of passive control. Also, the same is true for numerical results of Nusselt number and Sherwood number that is due to an active control is greater than all for the case of passive control. Furthermore, this theoretical and numerical deliberation bears the potential to beneficial in the field of bio-fluid dynamics.

An analytical solution for aerosol penetration in the slip flow regime

The classical theory for the diffusional loss of aerosol particles in a fully developed laminar flow through a circular tube derived by Gormley and Kennedy (1949) did not consider the slip-flow condition. However, the non-slip condition for the gas velocity boundary condition may not be appropriate for the gas flow in microgeometries such as microchannels and microtubes. This paper extends the work of Gormley and Kennedy (GK) to include the effect of slip-flow, which often occurs in the gas flow at low pressure or with a small characteristic length scale. In the present solution, the separation of variables was applied to solve the convection-diffusion equation, then confluent hypergeometric function was used to solve for the number concentration as a function of radial distance analytically. Eigenvalues were evaluated for Knudsen numbers ranging from 0.001 to 0.1. Finally, a simple power series correlation was developed to describe aerosol penetration in the slip flow regime as a function of the dimensionless deposition factor and Knudsen number (Kn). In the slip flow regime, the penetration decreases with increasing Kn. The correlation is reduced to GK’s solution when Kn = 0. The present solution of aerosol penetration calculated at Kn = 0 shows good agreement with GK’s solution and validates the applicable range of the approximate solution by Alonso et al. (2016).

Modeling and simulation for estimating thin film lubrication effects on flow of Jeffrey liquid by a spiraling disk

Advancements in mechanical expertise and rigorous need for gyratory components of machines expedite scientists towards essentiality of the eternal evolution of modified lubricants to corroborate the reliability, innocuous procedure and stability of sundry bearings. To enhance the performances at heftily ponderous load and high velocity, the high molecular polymers are utilized in mechanical bearings as lubricant. These lubricants are non-Newtonian in characteristics and comply with different constitutive relationships. One of them is the power law lubricant which complies with Ostwald model and is broadly utilized for the engineering lubrication. The derivation of the slip-flow conditions at the interface of bulk Jeffrey fluid and the thin layer non-Newtonian lubricant is performed over a disk spiraling with simultaneous radial stretching and rotation. To obtain a homogeneous solution, the power-law index is suggested 1/3 and no-slip boundary condition is converted into an incipient slip boundary condition. A single dimensionless slip parameter is introduced to regulate the velocity slip. Flow equations are obtained, and the similarity conversion is performed to obtain ordinary differential equations. Numerical results are computed to visually perceive the effects of lubrication on the flow field by incorporating the interfacial slip conditions. The presence of the lubrication enhances the fluid velocity and plays major role in the reduction of the skin friction at disk surface.

AFM Slip Length Measurements for Water at Selected Phyllosilicate Surfaces

Most reported slip length measurements have been made at the surfaces of synthetic materials and modified synthetic materials. In contrast, few slip length measurements at the surface of unmodified natural mineral surfaces have been reported. In this regard, flow at the silica face surfaces of the phyllosilicate minerals, talc and mica, was considered. A slip boundary condition was expected at the nonpolar hydrophobic silica surface of talc leading to enhanced flow, and a no-slip boundary condition was expected at the hydrophilic silica surface of mica. Atomic force microscopy (AFM) slip length measurements were made at the talc and mica surfaces. The slip length results for the hydrophobic silica surface of talc were contrasted to the results for the hydrophilic silica surface of mica (no-slip flow). The results are discussed based on molecular dynamics simulations (MDS), as reported in the literature, and AFM images of surface nanobubbles. For nonpolar hydrophobic surfaces (such as talc), it is doubtful that the MDS interfacial water structure and the water exclusion zone (3.2 Å) account for the AFM slip flow with slip lengths as great as 95 nm. Rather, a better explanation for the AFM slip flow condition is based on reduced interfacial viscosity due to the presence of dissolved gas and the accommodation of pancake nanobubbles at the talc surface having a height dimension of magnitude similar to the slip length.

Analysis of flow of visco-elastic nanofluid with third order slips flow condition, Cattaneo-Christov heat and mass diffusion model

This communication reports, the flow of viscoelastic nanofluid with third order slip flow condition, Cattaneo-Christov heat and mass diffusion model. The joined non-linear ordinary differential equations (ODEs) were acquired from the partial differential equations, which are resulting from conservation of momentum, energy and species. By means of similarity transformations these ODEs were alerted into dimensionless form and solved numerically by means of bvp4c solver. The effects of different parameters on velocity, temperature, and concentration profiles were examined and discussed in depth by means of graphs and tables. The outcomes indicate that the velocity profile along both x and y directions augment with higher values of viscoelastic parameter. The results also confirm that an increment in the values of ratio parameter tends to grow up the velocity profile alongside y-direction. However, the velocity profile along x-direction slows down with increment in the value of third order slip parameter. Also, the results illustrate that diminution in temperature is observed for higher Sc in the region of boundary layer. Besides, both temperature and concentration can be improved via higher Biot number. The upshots also portrayed that the local skin friction coefficient augmented within mounting values of viscoelastic fluid parameter. Furthermore, for finer values of Biot number both local Nusselt number and the local Sherwood number are enlarged. In addition, the most favorable agreement is observed among the results of the present study and those of the earlier studies.

Simultaneous energy storage enhancement and pressure drop reduction in flat plate solar collectors using rotary pipes with nanofluid

Flat plate solar collectors waste a massive part of the heat accumulated near the contact region, mainly due to poor thermal characteristics of working fluid. The demanding power for pumping the flow through the pipes seems a permanent concern in solar collectors. Also, active methods seem not to be applicable in such systems due to the external energy requirement and cost associated with it. An innovative and simple technique is considered here to eliminate such deficiencies all at once by equipping the flat plate collector with rotary absorber pipes and Fe3O4/water nanofluid. Results indicate that the applied method improves the convection mechanism in each pipe by mixing the accumulated heat in the whole flow regions and saves more available solar energy. It also reduces the pressure drop by preparing a slip flow condition inside the pipes, thereby reducing the consuming pumping power. Results also reveal that by dispersing 2% Fe3O4 in water and utilizing rotary pipes one can restore around 1.65% and 10.44% of the energy loss of the collector, respectively. In other words, additional energy of 120.16 W can be stored by equipping a flat plate solar collector with rotary tubes and Fe3O4/water nanofluid. Also, equipping the collector by both rotary pipes and nanofluid causes 5.83% and 3.21% enhancement in energy and exergy efficiencies, respectively. The reported results substantiate that the required power for operating the employed method can be provided by the collector itself, which makes the proposed technique more cost-effective.

A comparison of 2 micron inner diameter open tubular column liquid chromatography with pressure-driven isocratic, slip-flow, and electrochromatographic modes of operation: a theoretical study

Modifications to the flow profile used in open tube capillary liquid chromatography (OT-CLC) include using slip-flow walls and using electroosmosis as a fluid pump as practiced in electrochromatography. These modifications are implemented experimentally by changing the capillary surface and solvent conditions which results in the change of boundary conditions at the capillary wall.In this paper we employ a theory-based study and compare the zone broadening of simple solutes using parabolic flow from a liquid pump, slip-flow from a highly hydrophobic inner surface with water eluent, and electroosmosis for the conditions of pure water and dilute salt utilizing 2 µm inner diameter OT capillaries. In general, the two types of flow other than parabolic exhibit thin zones in the early part of the chromatogram, consistent with previous studies of slip-flow and electroosmotic flow used in electrochromatography. Electrochromatography is shown to yield higher efficiency and less zone broadening than parabolic and slip-flow conditions used in this study. Nonetheless, it is found that the zone standard deviations are shown to be similar for these flow profiles as is the number of plates for these different flow profiles under the conditions utilized here. It is revealed that these modifications do not warrant the effort to maintain the special solvent conditions when compared to gradient elution OT-CLC, which gives a nearly constant peak width throughout the chromatogram, is easiest to implement, and is the method of choice for complex analysis.

Determination of the transmissivity of a heterogeneous anisotropic fracture in slip flow conditions.

Rough fractures often exhibit a broad spectrum of defect length scales ranging from the microscopic (roughness) scale to a macroscopic one (waviness) and further to the megascopic scale corresponding to the entire fracture. The influence of these multiple scales and their reciprocal interactions are expected to play a significant role on the transport properties at the megascale. Focusing on the pressure-driven slightly compressible gas slip flow, a two-scale method is presented allowing the determination of the global transmissivity of a fracture on the basis of an upscaled Reynolds model. This model is applied on a tessellation of the fracture, each tile being affected by a macroscopic transmissivity tensor which encompasses the microscale transport information as a result of the first upscaling process. Then, the megascale flow problem in this structure, made of a set of tiles characterized by a heterogeneous and anisotropic transmissivity tensor field, is solved using a boundary element method. Numerical results obtained with this two-scale method are compared to the transmissivity computed with direct simulations carried out at the microscale on the whole fracture. This is performed on two model rough fractures, namely, a spiral groove and a fractal fracture, while varying their mean apertures to investigate a wide range of the average Knudsen number characteristic of the flow at the megascale. A good agreement is obtained between the two approaches showing the robustness of the two-scale method to determine the global transmissivity of the fracture while significantly reducing the overall computational time.

Magnetohydrodynamic flow of a nanofluid due to a non‐linearly curved stretching surface with high order slip flow

AbstractThis article numerically scrutinizes magnetohydrodynamic flow of a nanofluid due to a nonlinearly curved stretching surface with third order slip flow conditions. The third order slip flow condition has not yet been discussed in fluid dynamics research. The mathematical modeling of the flow problem is given in partial differential equation form. The governing partial differential equations are transformed to high order ordinary differential equations using the similarity transformation and then solved numerically using a boundary value problem solver, bvp4c from Matlab software. The effect of the governing parameters on the flow of the velocity profile, concentration, and heat transfer characteristics are studied. Also graphs of the skin friction coefficient, local Nusselt number, and Sherwood number are drawn and their numerical values are tabulated. The numerical results of the study are compared with previously published articles in the limiting condition. The velocity of the flow field is reduced as the third order slip parameter and the first order slip parameter rises, but the velocity grows as the values of the second order slip flow parameter are elevated. The findings also indicate that the local Nusselt number is depreciated but local Sherwood numbers are elevated when the Soret and Dufour numbers are larger.

Numerical investigation of the effect of second order slip flow conditions on interfacial heat transfer in micro pipes

Heat transfer that occurs in micro scale devices has a very important place among the engineering applications that cooling or heating. This heat transfer mechanism in devices having dimensions at micron level is a completely different problem in the macro level analysis. Therefore, in the calculations made, the flow events and heat transfer in micron scale pipes are calculated by using more realistic expressions. For this reason, in this study heat transfer in a circular micro pipe with wall and fluid conjugation for laminar rarefied gas flow in transient regime is investigated under the second order slip boundary conditions at the interface. Patankar’s control volume method is used here to solve the problem numerically. This analysis includes of axial conduction, viscous dissipation and rarefaction effects which are indispensable in micro-flow structure. From the results, it is seen that the values that are indicating heat transfer are excessively affected by wall thickness, viscous heating and gas rarefaction especially in transient regime.

MHD mixed convection in an inclined cavity containing adiabatic obstacle and filled with Cu–water nanofluid in the presence of the heat generation and partial slip

A steady laminar two-dimensional magneto-hydrodynamics mixed convection flow in a square inclined cavity filled with Cu–water nanofluid is investigated numerically by using the finite difference method. The left and right vertical sidewalls of the cavity are considered adiabatic and move upward, while a partial slip flow condition is imposed on these walls. The horizontal top wall is considered cold and stationary, while a part of the stationary bottom wall is subjected to a uniform heat source and the remaining parts of it are considered adiabatic. An adiabatic obstacle is located in the center of the cavity and an external magnetic field is applied parallel to the horizontal x-axis. Parametric studies of the influence of various parameters such as Hartmann number, inclination angle of the cavity, dimensionless heat generation/absorption coefficient, obstacle aspect ratio, dimensionless length and location of the heat source, and solid volume fraction on the fluid flow and heat transfer have been performed. Comparisons with previously published numerical work are performed, and good agreements between the results are observed. It is found that the nanofluid was better than water to enhance the heat transfer when the effect of the magnetic field is weak, while the water is better than the nanofluid when its effect is strong. Moreover, the results indicated that the partial slip has a significant effect on the above-mentioned parameters.

Thermohydrodynamics of bidirectional groove dry gas seals with slip flow

Thermo-hydrodynamic behaviour of bidirectional dry gas seals with trapezoidal shaped symmetric grooves is studied. A multi-physics model, coupling compressible laminar flow and heat transfer in both the fluid and the solid bodies is used in a multi-physics modelling environment. The multi-physics model also includes slip flow conditions, corresponding to relatively high Knudsen numbers, as well as the effect of asperity interactions on the opposing seal faces. A comparison of the seal performance under isothermal and thermal flow conditions shows the importance of including the thermal effects. The difference in the predicted opening force between isothermal and thermal model can exceed 2.5%, which is equivalent to a force of around 1 kN. The importance of designing gas seals to operate at the minimum possible gap to reduce power losses as well as leakage from the contact is highlighted. However, it is shown that there exists a critical minimum gap, below which the power loss in the contact can abruptly increase due to asperity interactions, generating significantly increased operating temperatures.

Compressibility Effects in 2d Wall Heating Microchannel flow

In this article we present a numerical solution of the Navier-Stokes equations and energy equation in parallel plate microchannels with the first order slip boundary conditions on the walls, adopting control volume scheme of CFD technique. Wall heating condition was considered on the walls. Noslip boundary conditions for compressible and incompressible flows were also solved to compare the effect of slip conditions. Compressibility effects were also investigated for compressible slip and compressible noslip flow conditions. A series of simulations were performed for different heights and lengths of channels and pressure ratios. Results are presented in graphs and tables and are compared with the available analytical and experimental results. It was found that the friction constants are the highest for noslip compressible flow and lowest for the slip flow against pressure ratio and mach numbers. Friction constant decreases continuously for compressible slip flow but it approaches to an asymptotic value of 96 for compressible noslip flow for the decrease of aspect ratio.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 57-71

Laminar and turbulent flows over hydrophobic surfaces with shear-dependent slip length

Motivated by extensive discussion in the literature, by experimental evidence and by recent direct numerical simulations, we study flows over hydrophobic surfaces with shear-dependent slip lengths and we report their drag-reduction properties. The laminar channel-flow and pipe-flow solutions are derived and the effects of hydrophobicity are quantified by the decrease of the streamwise pressure gradient for constant mass flow rate and by the increase of the mass flow rate for constant streamwise pressure gradient. The nonlinear Lyapunov stability analysis, first applied to a two-dimensional channel flow by Balogh et al. [“Stability enhancement by boundary control in 2-D channel flow,” IEEE Trans. Autom. Control 46, 1696-1711 (2001)], is employed on the three-dimensional channel flow with walls featuring shear-dependent slip lengths. The feedback law extracted through the stability analysis is recognized for the first time to coincide with the slip-length model used to represent the hydrophobic surfaces, thereby providing a precise physical interpretation for the feedback law advanced by Balogh et al. The theoretical framework by Fukagata et al. [“A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces,” Phys. Fluids 18, 051703 (2006)] is employed to model the drag-reduction effect engendered by the shear-dependent slip-length surfaces and the theoretical drag-reduction values are in very good agreement with our direct numerical simulation data. The turbulent drag reduction is measured as a function of the hydrophobic-surface parameters and is found to be a function of the time- and space-averaged slip length, irrespective of the local and instantaneous slip behaviour at the wall. For slip parameters and flow conditions that could be realized in the laboratory, the maximum computed turbulent drag reduction is 50% and the drag reduction effect degrades when slip along the spanwise direction is considered. The power spent by the turbulent flow on the hydrophobic walls is computed for the first time and is found to be a non-negligible portion of the power saved through drag reduction, thereby recognizing the hydrophobic surfaces as a passive-absorbing drag-reduction method. The turbulent flow is further investigated through flow visualizations and statistics of the relevant quantities, such as vorticity and strain rates. When rescaled in drag-reduction viscous units, the streamwise vortices over the hydrophobic surface are strongly altered, while the low-speed streaks maintain their characteristic spanwise spacing. We finally show that the reduction of vortex stretching and enstrophy production is primarily caused by the eigenvectors of the strain rate tensor orienting perpendicularly to the vorticity vector.