Effects Of Partial Slip Research Articles

Boundary Layer Flow of Dusty Nanofluid over Stretching Sheet with Partial Slip Effects

In this work, the effect of dust particles and slips towards boundary layer flow of dusty nanofluid was investigated over the stretching horizontal sheet. Three type of nanoparticles; copper (Cu), aluminium oxide ( ) and titania ( ) were studied. The governing equations of flow and heat transfer were transformed into non-linear ordinary differential equations by using similarity transformation. Next, these equations were solved numerically by using the boundary value problem solver, bvp4c program of Matlab software. The effects of non-governing parameters including volume fraction of dust particles, volume fraction of nanoparticles, velocity slip parameter, and thermal slip parameter were computed, analysed, and discussed. Lastly, a comparison of present study with existing literature was performed and achieved excellent agreement. It is found that nanoparticles act as good thermal conductivity. Besides that, and show significant effect on velocity of fluid and dust phase.

Magnetic Field Effect on Sisko Fluid Flow Containing Gold Nanoparticles through a Porous Curved Surface in the Presence of Radiation and Partial Slip

The radiation and magnetic field effects of nanofluids play a significant role in biomedical engineering and medical treatment. This study investigated the performance of gold particles in blood flow (Sisko fluid flow) over a porous, slippery, curved surface. The partial slip effect was considered to examine the characteristics of nanofluid flow in depth. The foremost partial differential equations of the Sisko model were reduced to ordinary differential equations by using suitable variables, and the boundary value problem of the fourth-order (bvp4c) procedure was applied to plot the results. In addition, the effects of the parameters involved on temperature and velocity were presented in light of the parametric investigation. A comparison with published results showed excellent agreement. The velocity distribution was enhanced due to the magnetic field, while the temperature increased due to the effects of a magnetic field and radiation, which are effective in therapeutic hyperthermia. In addition, the nanoparticle suspension showed increased temperature and decelerated velocity.

Bioconvection analysis for flow of Oldroyd-B nanofluid configured by a convectively heated surface with partial slip effects

The improved thermal mechanism of nano-scale particles has attended a special focus of scientists in current time. Owing to the multiple dynamic applications of such nanoparticles in various era of engineering and thermal sciences like cooling/heating materials, heat production, energy resources and bio-medical sciences like cancer treatment, destroying of damage cells, brain tumors etc. Further, bio-convective phenomenon of nanoparticles is also referred to many applications in bio-sciences like enzymes, bio-sensors, bio-fuels etc. Keeping such motivating applications in mind, present communication addresses the bioconvection assessment in Oldroyd-B nanofluid conducted over a convectively heated configuration. Further, the partial slip mechanism is followed for to examine the flow pattern. The novel zero mass flux aspects have been taken into account at the solid surface of plate such that the nano-materials fraction is attended itself on higher retardation. After altering the equations in dimensionless form, shooting numerical algorithm is employed for the solution procedure. It is observed that variation in relaxation time constant increase the velocity profile which is more progressive in presence of slip effects. The presence of slip factor improves the heat and mass transportation more effectively. Moreover, the concentration profile decline with retardation time constant and Schmidt number.

Numerical solutions of the partial differential equations for investigating the significance of partial slip due to lateral velocity and viscous dissipation: The case of blood‐gold Carreau nanofluid and dusty fluid

AbstractThe dynamics of blood conveying gold nanoparticles (GNPs) are helpful to the health workers while air conveying dust particles over rockets is helpful to space scientists during the testing phase. However, little is known on the significance of thermal diffusivity in these aforementioned cases. In this report, the partial differential equation suitable to unravel the implication of increasing partial slip and viscous dissipation on the dynamics of the mixture of (i) blood and nano size of GNPs (ii) air and dust particles on an object with an increasing diameter (uhspr) is investigated. The density, zero shear rate viscosity, heat capacity, and thermal conductivity treated in this study vary with volume fraction nanoparticles. In the second case, the interaction between the solid particles and air is incorporated into the momentum equation using the Stokes drag. Transformation and parametrization of the two‐dimensional nonlinear partial differential equations were obtained with the aid of suitable similarity variables. Thereafter, the numerical solutions of the corresponding boundary valued problems were obtained using the classical Runge–Kutta integration scheme together with shooting techniques and Matlab bvp5c package. Enhancement in the rate of viscous dissipation is a major factor suitable to increase the velocities of both fluids, boost temperature distribution across both fluids, and local skin friction coefficients. There exist a significant difference between the effect of partial slip on the dynamics of blood‐gold nanofluid and dusty fluid.

EFFECT OF PARTIAL SLIP AND RADIATION ON LIQUID FILM FLUID FLOW OVER AN UNSTEADY POROUS STRETCHING SHEET WITH VISCOUS DISSIPATION AND HEAT SOURCE/SINK

EFFECT OF PARTIAL SLIP AND RADIATION ON LIQUID FILM FLUID FLOW OVER AN UNSTEADY POROUS STRETCHING SHEET WITH VISCOUS DISSIPATION AND HEAT SOURCE/SINK

Thermodynamic entropy of a magnetized Ree‐Eyring particle‐fluid motion with irreversibility process: A mathematical paradigm

AbstractThis article deals with the entropy generation and irreversibility process under the effects of partial slip on magnetic dusty liquid induced by peristaltic wave through a porous channel. The Ree‐Eyring fluid model has been used for a governing flow. Mathematical modelling is based on Ohm's law, continuity equation, Darcy law and momentum equation. Analytical solutions are presented for fluid and particle phase. The effects of different pertinent parameters are considered for Newtonian and non‐Newtonian cases. Numerical integration has been carried out using a computational software to analyse the pumping characteristics. The behaviour of velocity profile, trapping mechanism, entropy generation, Bejan number, temperature distribution, and pressure rise are investigated. From the obtained results, it is noticed that entropy generation and Bejan number enhanced due to the presence of Brinkman number as well as with the strong influence of non‐Newtonian effects. The presence of particles in the fluid decelerates the flow. The magnetic and fluid parameter perform in a similar manner on peristaltic pumping. The temperature profile shows increasing behaviour against higher values of Brinkman number and magnetic field. The present analysis presents different interesting results that help examine dusty fluid with other rheological working fluid models. This work is also applicable in smart fluid pumping systems in aerospace and nuclear industry as well as peristaltic electromagnetic micro‐pumps in bio‐medical engineering.

Significance of magnetic Reynolds number in a three-dimensional squeezing Darcy\u2013Forchheimer hydromagnetic nanofluid thin-film flow between two rotating disks

The remarkable aspects of carbon nanotubes like featherweight, durability, exceptional electrical and thermal conduction capabilities, and physicochemical stability make them desirous materials for electrochemical devices. Having such astonishing characteristics of nanotubes in mind our aspiration is to examine the squeezing three dimensional Darcy–Forchheimer hydromagnetic nanofluid thin-film flow amid two rotating disks with suspended multiwalled carbon nanotubes (MWCNTs) submerged into the base fluid water. The analysis is done by invoking partial slip effect at the boundary in attendance of autocatalytic reactions. The mathematical model consists of axial and azimuthal momentum and magnetic fields respectively. The tangential and axial velocity profiles and components of the magnetic field are examined numerically by employing the bvp4c method for varying magnetic, rotational, and squeezing Reynolds number. The torque effect near the upper and lower disks are studied critically using their graphical depiction. The values of the torque at the upper and lower disks are obtained for rotational and squeezed Reynolds numbers and are found in an excellent concurrence when compared with the existing literature. Numerically it is computed that the torque at the lower disk is higher in comparison to the upper disk for mounting estimates of the squeezed Reynolds number and the dimensionless parameter for magnetic force in an axial direction. From the graphical illustrations, it is learned that thermal profile declines for increasing values of the squeezed Reynolds number.

Radiation and Partial Slip Effects on Magnetohydrodynamic Jeffrey Nanofluid Containing Gyrotactic Microorganisms Over a Stretching Surface

Abstract In this study, the impact of thermal radiation and partial slip on magnetohydrodynamic flow of the Jeffrey nanofluid comprising motile gyrotactic microorganisms via vertical stretching surface is analyzed. The governing partial differential equations are reformed to a system of coupled ordinary differential equations by utilizing the similarity transformations. The transformed equations are of order four, which are complex to solve analytically and hence, the coupled system is solved computationally by using the shooting technique along the Runge–Kutta integrated scheme. The ramifications of different thermophysical parameters on the density of gyrotactic microorganisms, Jeffrey nanofluid velocity, nanoparticles concentration, temperature, Sherwood number, and Nusselt number are illustrated graphically. Comparing this study with the results already published favors the validity of this study. It is established that the Nusselt number is boosted on enhancing the thermal radiation parameter, and the reverse trend has been observed on increasing the Richardson number, whereas the gyrotactic microorganisms density is more in case of viscous nanofluid compared to the Jeffrey nanofluid.

Impact of Partial Slip and Heat Source on MHD Mixed Convection Flow of Nanofluid in a Double Lid-Driven Cavity Containing Insulated Obstacle

The current investigation analyzes the effects of partial slip and heat generation on the mixed convection flow with heat transfer in an inclined double lid-driven square cavity containing centered square adiabatic obstacle in the presence of magnetic field. The used cavity is subjected to constant heat flux and filled with Cu-water nanofluid. The top and bottom horizontal walls are thermally insulated and move with uniform velocity while the right vertical wall is maintained at a constant low temperature. A uniform heat flux is located in a part of th left wall of the cavity while the remaining part of this wall is thermally insulated. Finite volume technique is utilized to solve dimensionless governing equations of the problem. The proposed method is validated with the previous published numerical studies which distinctly offer a good agreement. The obtained results show that changing in the heat source length affects much the flow and thermal fields than the position of heat source. The averag Nusselt number decreases when the aspect ratio of the obstacle and heat source length increases. The heat transfer rate behaves nonlinearly with inclination of the cavity.

Effects of partial slip on the local-global linear stability of the infinite rotating disk boundary layer

A numerical investigation is undertaken on the effect of small-scale surface roughness on the local absolute and global stability of the flow due to a rotating disk. Surface roughness is modeled via the imposition of the partial-slip wall boundary condition, with radial and concentric anisotropic roughnesses and isotropic roughness considered. The effect of the partial-slip parameters on the neutral characteristics for absolute instability is presented, while the azimuthal mode numbers required for global linear instability to occur are determined for the genuine inhomogeneous base flow. Predictions for the threshold values for the azimuthal mode numbers needed for globally unstable behavior are also computed by coupling solutions of the Ginzburg–Landau equation with the local linear stability properties obtained using the homogeneous flow approximation. These are found to be in excellent agreement with the exact values realized from the numerical simulations. In general, surface roughness is demonstrated to stabilize the absolute instability and the global linear instabilities.

A Novel Formulation for MHD Slip Flow of Elastico-Viscous Fluid Induced by Peristaltic Waves with Heat/Mass Transfer Effects

Prime motive of this research is to formulate and analyze the elastico-viscous fluid flow triggered by sinusoidal waves progressing across the walls of symmetric channel. The research is based on the Walters-B model that depicts normal stress effects attributed to the fluid elasticity. Here, we endeavor to derive correct form of equations representing peristalsis of Walters-B liquid. The said model is investigated by employing generic Robin-type boundary conditions signifying partial slip effects. The case of hydrodynamic flow has been separately analyzed. Series expansions are considered about a parameter $$\delta$$ , measuring the ratio of wavelength of peristaltic wave to the channel width. Emphasis is paid to the influence of new attributes of the problem, namely viscoelasticity and wall slip on the pressure rise, axial flow, temperature and concentration of species. Heat transfer coefficient is computed graphically across the channel wall for a variety of controlling flow parameters. Even at small Reynolds number, a marked axial velocity is predicted, provided that elastico-viscous fluid parameter is sufficiently large. Moreover, heat transfer rate at channel walls is lowered due to the inclusion of viscoelasticity.

Analysis of oblique stagnation point flow over a rough surface

The present study explores the partial slip effects on the oblique stagnation point flow of viscous fluid. The governing equations are formulated as a similarity solution of the Navier-Stokes equations, and the no-slip boundary conditions are replaced by the Navier's partial slip boundary conditions. The resulting system of nonlinear equations are governed by the dimensionless shear parameter γ, slip parameter λ and a free parameter β. The oblique stagnation point flow consists of classical orthogonal stagnation point flow along with a shear flow on the surface. Previous works of the oblique stagnation point were studied numerically, and several speculations regarding the behaviour of the solutions are made. Current work is to confirm the speculations. We prove the existence and the uniqueness results for the classical boundary layer flow near an orthogonal stagnation point flow for a rough surface. Moreover, a general solution is also given for shear flow which confirms the existence of negative shear flow for a large value of free parameter β and describes the effects of partial slip on reverse flow. Further, the detailed effects of physical parameters on the flow domain are shown through tables and graphs. It is observed that the streamlines are skewed towards left of orthogonal stagnation point for positive values of shear parameter γ and towards right for negative values.

Partial slip effects on the peristaltic motion of an upper-convected Maxwell fluid through an irregular channel

A theoretical investigation was carried out in this paper by taking the partial slip result in an irregular wavy channel for the incompressible upper-convected Maxwell fluid. Due to peristaltic motion, asymmetric waves with different amplitudes are produced. This flow is driven in an irregular channel due to the pressure gradient, where the perturbation technique applied to tackle the stream function and the pressure gradient. A numerical integration technique was used to find out the different expressions of the frictional rise per wavelength and pressure rise per wavelength and presented their graphs. The graphical results for the partial slip parameter, small wave number, phase difference, Reynolds number, Weissenberg number, wave amplitudes a and b, and channel width d are included. The pressure gradient is an increasing function of the wave number, but the slip parameter is vice versa. The velocity profile u is increased by a small increase in the wave number while it is decreased by a rise in the slip parameter. The frictional forces have the same behavior for the lower and upper wall. According to the slip effects, the bolus has improved behavior. Moreover, the relaxation parameter enhanced the strength of the bolus.

Significance of bioconvection in chemical reactive flow of magnetized Carreau–Yasuda nanofluid with thermal radiation and second-order slip

Several non-Newtonian fluids are of practical interest, and it is fascinating to examine the rheology of such fluids with various flow features. In this study, the flow of Carreau–Yasuda nanofluid has been analyzed in the presence of gyrotactic microorganisms. The impressive features of nanofluid are displayed by abiding the thermophoresis and Brownian motion aspects. The second-order velocity slip effects are decomposed in the mathematical simulations. Further, the governing flow problem governed the impact of thermal radiation, chemical reaction and convective Nield boundary conditions. Although some attempts are available in the literature which examines the rheological features of Carreau–Yasuda nanofluid, whereas the analysis for bioconvection of flow of this non-Newtonian fluid model in the presence of second-order slip features is not proposed yet. Further, it has been noticed that many investigators used first-order or partial slip effects associated with their flow problems. The flow problem becomes more realistic due to the interaction of second-order slip constrains and subsequently develops a more stable boundary layer. The governing equations for the formulated flow problem are partial differential equations. Standard dimensionless quantities are recommended to alter the flow equations in dimensionless forms. The solution of the locally similar problem has been computed numerically via shooting technique. All the computations are performed by using bvp4c with the help of MATLAB software. Following the iterative procedure, the solution is accurate up to convincing accuracy of $$ 10^{ - 4} . $$ The step size for the present simulation is taken as $$ \Delta \eta = 1 \times 10^{ - 4} . $$ The results are also verified by comparing with already reported numerical computation and found a convincible accuracy. The implication of each parameter is executed for velocity, temperature, concentration and microorganisms’ distributions. Moreover, the substantial quantities, namely skin friction coefficient, motile density number, local Nusselt number, and local Sherwood number numerically evaluated and are overviewed for various parameters. The study reveals that velocity distribution decays with the presence of first-order slip parameter and Rayleigh number, while an enhanced velocity profile has been noted for variation of Weissenberg number. An improved nanoparticle temperature and concentration distributions have been found with the utilization of the second-order slip factor and combine parameter. It is further observed that the density of motile microorganisms declined with Peclet number and bioconvection Lewis number. In recent days, a growing interest has been developed from scientists toward the significance of nanoparticles because of their diverse engineering, industrial and commercial applications. The proposed observations can be useful in extrusion systems applications, biomolecules, biomimetic systems, energy production improvement and enhancement of manufacturing processes.

Combined effects of partial slip and variable diffusion coefficient on mass and heat transfer subjected to chemical reaction

This article is a generalization of already published work and investigates the combined effects of chemical reaction, partial slip, temperature and concentration, jumps on the transport of heat energy and solute of variable mass conductance in a fluid of temperature dependent viscosity and thermal conductivity. Publish benchmark (Hayat et al 2015 Partial slip effects in flow over nonlinear stretching surface Appl. Math. Mech. 36 1513–26) is the special case of present work. It is also important to highlight that partial slip effects in the presence of variable diffusion coefficients are investigated first time. It is found that the distractive chemical reaction accelerates the rate of diffusion of solute. However, diffusion rate is decelerated by constructive chemical reaction. The concentration of solute in the liquid regime increases as the mass diffusion increases due to the rise in temperature. It is also observed that the diffusion of momentum of wall in fluid of constant viscosity is faster than the diffusion of momentum fluid of viscosity varying under rise in temperature. Further, an increase in thermal conductivity due to rise in temperature causes an enhancement in rate of heat conduction from wall into the fluid. Eventually, temperature of fluid rises.

A Numerical Simulation for Darcy-Forchheimer Flow of Nanofluid by a Rotating Disk With Partial Slip Effects

A numerical simulation for Darcy–Forchheimer flow of nanofluid by a rotating disk with partial slip effects

Effect of nonlinear partial slip and thermal radiation on Oldroyd 8‐constant fluid in a channel with convective boundary condition

AbstractThis investigation deals with the effects of nonlinear slip, nonlinear thermal radiation, and non‐Newtonian flow parameters on heat transfer of an incompressible magnetohydrodynamic steady flow of an Oldroyd 8‐constant fluid through two parallel infinite plates with convective cooling. The Rosseland approximation is adopted to simulate the radiation effects. Heat exchange with the surrounding at the surfaces is assumed to obey Newton's law of cooling. The system of coupled and highly nonlinear ordinary differential equations governing the model is solved numerically using the method of weighted residual. The combined effects of non‐Newtonian flow parameters, velocity slip parameter, magnetic field parameter, Biot numbers, thermal radiation on the fluid velocity, temperature distributions, skin friction, and the Nusselt number are presented graphically and discussed. It is found that the velocity slip has an increasing effect on the fluid velocity and temperature profiles. For larger values of the thermal radiation parameter, the temperature profile and the Nusselt number are noticed to be increased.

Effects of partial slip on micropolar fluid flow and heat transfer over a permeable shrinking sheet with thermal radiation and convective boundary condition

In the presence of thermal radiation, partial slip and convective boundary condition, micropolar fluid flow and heat transfer over a shrinking sheet has been studied. The problem is modeled as a mathematical formulation that involves a system of the partial differential equation. The similarity approach is adopted and self-similar ordinary differential equations are obtained and then those are solved numerically using the shooting method. The flow field is affected by the presence of physical parameters, such as micropolar parameter, wall mass transfer parameter and slip parameter whereas the temperature field is affected by thermal radiation, Biot number and Prandtl number. The skin friction, couple stress and heat transfer coefficients are tabulated and analyzed. The effects of the governing parameters on the velocity, angular and temperature profiles are illustrated graphically. Dual solutions of velocity, angular velocity and temperature are obtained for several values of the each parameter involved. Results shows that, the thickness of boundary layer decline as skin friction coefficient decreases for both solution as the velocity slip increases while for heat transfer coefficient, the physically increases of Biot number corresponding to increment of temperature distribution.

Soret and Dufour Effects on Unsteady Boundary Layer Flow and Heat Transfer in Copper-Water Nanofluid Over a Shrinking Sheet with Partial Slip and Stability Analysis

The influences of partial slip, Soret and Dufour on unsteady boundary layer flow, heat and mass transfer over shrinking sheet in Copper-water nanofluid are investigated numerically using Tiwari and Das's model. The governing equations are transformed to ordinary differential equations using similarity transformation. The system of equations is solved by boundary value problem with fourth order accuracy (bvp4c) program in Matlan and the numerical results are presented graphically to show the behaviour of the flow. The findings show that the dual solutions exist for certain range of suction effect (s > 0.58) with the presence of partial slip effect. Besides, Soret effect increases the heat transfer and declines the mass transfer at the surface while Dufour effect showed the opposite trend. Since the dual solutions are obtained, the stability analysis is performed and it is found that the first solution is a stable and physically-realizable solution.

Peristaltic transport of Jeffrey fluid in a rectangular duct through a porous medium under the effect of partial slip: An application to upgrade industrial sieves/filters

The peristaltic transport of Jeffrey fluid through the rectangular duct is investigated. The effect of porosity under the influence of partial slip is also taken into consideration. The equations describing the flow transport along with boundary conditions are first made dimensionless using appropriate transformations and are then solved to get the exact solutions. The role of pressure rise generated by the fluid is also presented. The obtained results are examined graphically through pertinent parameters affecting the flow. The streamlines have also been displayed to analyse the trapping phenomenon.