Flow Of Newtonian Liquid Research Articles

Non-Darcy Newtonian Liquid Flow with Internal Heat Generation using Boundary Conditions of the Third Kind of Fully Developed Mixed Convection in a Vertical Channel

An analysis of the impact of internal heat generation and other heat parameters on the temperature, velocity and rate of heat transfer of the liquid moving upward in a channel is studied. A fully developed non-Darcy flow using boundary conditions of the third kind with internal heat generation in a vertical channel is selected as the mathematical model. By utilising the similarity transformation, the governing equations are reduced to non-linear ordinary differential equations (ODEs). The converted ODEs are numerically solved and analysed using the fourth-order Runge-Kutta (RK4) method, incorporating a shooting technique with Newton’s method. The generated numerical algorithms are programmed in MATLAB for velocity, temperature and the local Nusselt number analysis. The numerical results of the flow and temperature variables are presented graphically. The impact of the parameters on the Nusselt number is also graphed to determine which of the three types of boundary conditions is the best for allowing heat transmission. The severity of flow reversal is increased under the Robin and Dirichlet conditions by enhancing the Darcy and Forchheimer numbers while decreasing the Brinkman and internal heat generation values. The temperature profiles improved with the increase in Brinkman numbers. Both Nusselt numbers remained constant for the Neumann boundary condition for all parameters except internal heat generation and local heat exponent. The Robin boundary condition is found to be the best facilitates heat transmission, since it delivers more pleasing and realistic results than the Dirichlet and Neumann conditions

Effects of Large Particles in Pipe Flow at Low and Moderate Reynolds Numbers

AbstractThe presence of solid particles in a Newtonian liquid flow will affect the properties of the flow. For small particles these effects are fairly well understood and models, for example for the pressure drop in particle laden pipe flows have been present for a long time. However, the behavior of liquids laden with large particles are less well understood. In the present study, large particles of spherical shape are considered. By large is here meant particles that are of the same size as the large scale length scales of the flow and larger. The effect of particles volume fraction on parameters such as pressure drop and velocity distribution in the pipe flow is investigated. The sizes of the particles are 17 % and 40 % of the pipe diameter and the volume fraction is varied between 5 % and 20 %.

Local non-similar solution of radiative and magnetized flow of non-Newtonian liquid over a gravitationally affected porous surface with Newtonian heating effect

A non-similar solution of the generalized Newtonian liquid flow over a vertical non-rigid surface is presented to explore the significance of nonlinear radiation, Newtonian heating, magnetic and gravitational fields. The non-similar dynamical nature with rapid change in size and position is studied by incorporating the ordinate and stream-wise coordinates. The newly formulated mathematical results are presented in the form of partial differential equations (PDEs) which are converted to ordinary differential equations (ODEs) by utilizing the non-similar variables. The governing ODEs are then approximated by one of the collocation methods to explore the characteristic of different physical parameters while using MATLAB. The significant increasing behavior of the velocity profile is determined by the variation in Wessenberg number, bouncy ratio parameter, and suction parameters. On the other hand, the temperature profile is enhanced by uplifting the radiation, Newtonian heating, and heat generation parameters, respectively. The rate of heat transfer and resistive forces are escalating functions of stream-wise coordinate. All the new analysis and applied method are verified by giving a comparison with previous work.

Impact of Radiation and Slip on Newtonian Liquid Flow Past a Porous Stretching/Shrinking Sheet in the Presence of Carbon Nanotubes

The impacts of radiation, mass transpiration, and volume fraction of carbon nanotubes on the flow of a Newtonian fluid past a porous stretching/shrinking sheet are investigated. For this purpose, three types of base liquids are considered, namely, water, ethylene glycol and engine oil. Moreover, single and multi-wall carbon nanotubes are examined in the analysis. The overall physical problem is modeled using a system of highly nonlinear partial differential equations, which are then converted into highly nonlinear third order ordinary differential equations via a suitable similarity transformation. These equations are solved analytically along with the corresponding boundary conditions. It is found that the carbon nanotubes can significantly improve the heat transfer process. Their potential application in cutting-edge areas is also discussed to a certain extent.

Impacts of slip and mass transpiration on Newtonian liquid flow over a porous stretching sheet

AbstractThis article focuses on analytic solutions for Newtonian fluid flow with slip and mass transpiration on a porous stretching sheet using the differential transform method and Pade approximants of an exceptionally nonlinear differential equation. The impacts of different parameters including mass transpiration (suction/injection), Navier's slip, and Darcy number parameters on the velocity of the liquid and tangential stress are discussed. A comprehensive comparison of our results with the previous one in the literature is made, and the results showed good agreement. An investigation is conducted of a combination of magnetic liquids that are conceivably pertinent for wound medicines, skin repair, and astute coatings for natural gadgets. It is found that there is a decrease in the velocity profiles and the boundary layer thickness for the case of suction.

Mass Transfer Characteristics of Haemofiltration Modules-Experiments and Modeling.

Reliable mathematical models are important tools for design/optimization of haemo-filtration modules. For a specific module, such a model requires knowledge of fluid- mechanical and mass transfer parameters, which have to be determined through experimental data representative of the usual countercurrent operation. Attempting to determine all these parameters, through measured/external flow-rates and pressures, combined with the inherent inaccuracies of pressure measurements, creates an ill-posed problem (as recently shown). The novel systematic methodology followed herein, demonstrated for Newtonian fluids, involves specially designed experiments, allowing first the independent reliable determination of fluid-mechanical parameters. In this paper, the method is further developed, to determine the complete mass transfer module-characteristics; i.e., the mass transfer problem is modelled/solved, employing the already fully-described flow field. Furthermore, the model is validated using new/detailed experimental data on concentration profiles of a typical solute (urea) in counter-current flow. A single intrinsic-parameter value (i.e., the unknown effective solute-diffusivity in the membrane) satisfactorily fits all data. Significant insights are also obtained regarding the relative contributions of convective and diffusive mass-transfer. This study completes the method for reliable module simulation in Newtonian-liquid flow and provides the basis for extension to plasma/blood haemofiltration, where account should be also taken of oncotic-pressure and membrane-fouling effects.

Boundary Slip Flow of Newtonian Liquids: The Analogy between Fluid Friction and Heat Transfer

Boundary Slip Flow of Newtonian Liquids: The Analogy between Fluid Friction and Heat Transfer

Computational study of planar extrudate swell flows with a viscous liquid–gas interface

AbstractWe present a computational study of planar extrudate swell flows of Newtonian liquids with a viscous liquid–gas interface. The model consists of the equations of motion coupled with the Boussinesq–Scriven constitutive equation for the interfacial stress tensor. The resulting set of equations is solved with the finite element method coupled with an elliptic mesh generation strategy to capture the free surface. The results show a detailed parametric study in terms of the capillary number and the Boussinesq number, a dimensionless parameter used to measure the ratio of viscous forces at the interface to viscous forces in the bulk liquid. The predictions reveal that the extrudate swells dramatically as the interfacial viscosity grows. The interfacial viscosity slows down the flow both in the bulk liquid and at the interface, and thus the extrudate size increases to conserve mass in the slow plug flow that develops under the free surface.

Finite difference simulations for magnetically effected swirling flow of Newtonian liquid induced by porous disk with inclusion of thermophoretic particles diffusion

Heat and mass transfer analysis of viscous liquid flow generated by rotation of disk has generated prodigious interest due to promising utilizations in numerous processes such as thermal energy generation systems, turbine rotators, geothermal energy preservations, chemical processing, medicinal instrumentations, computing devices and so forth. In view of such extraordinary utilizations in numerous engineering procedures existent exertion is excogitated to disclose flowing phenomenon over rotating disk. To raise the importance of current analysis influential physical aspects like magnetic field, permeability, Dufour and Soret diffusion phenomenon are also incorporated. Subsequently, flow field distributions are analyzed for suction and injection cases. Modelling is structured via PDE’s by obliging constitutive conservation laws. Boundary layer approach is executed to reduce complexity of attained partial differential system. Transformations developed by Karman are implemented to convert developed differential framework into ODE’s. Implicitly finite differenced technique known as Keller Box is engaged to find solution of coupled intricate high order ordinary differential equations. Influence of flow controlling parameters on associated distributions are revealed through graphical and tabular representations. The related quantities of engineering interest like coefficients of wall drag force, along radial and tangential directions are also computed. Credibility of presently computed results is established by constructing comparison with previously published literature. It is inferred that magnetic strength parameter enhances tangential and radial components of velocity whereas contrary trend is depicted in axially directed velocity. In addition, temperature and momentum distributions show up surging attribute versus magnetic field parameter. All associated profiles have exhibited decrementing aspects against suction parameter. It is also revealed that increment in Soret tends to produce depreciation in temperature profile whereas concentration distribution is enhanced.

Dynamics of Cattaneo-Christov Double Diffusion (CCDD) and arrhenius activation law on mixed convective flow towards a stretched Riga device

Background Current paper elaborate the impact of MHD flow of Newtonian liquid over a extendable Riga sheet. Cattaneo-Christov (CC) heat and mass flux models in formulation are taken here. Fluid filling porous medium is considered. Influences of activation energy is also considered. Boundary layer approximation is used in obtaining partial differential equations (PDEs). Applying suitable transformation to reduce the given PDEs into ordinary differential (ODEs) system. Method Homotopy method is utilized to solve non-linear differential system. Results The impacts of influencing parameters like modified Hartman number, mixed convection parameter, inverse Darcy parameter, non-dimensional parameter, Biot number, non-dimensional activation energy, Eckert number, thermal relaxation and solutal concentration variables are examined through graphs. Conclusions Velocity profile enhances for larger estimation of ratio parameter and modified Hartman number. Temperature distribution is higher for Eckert and Biot number. Concentration profile is enhancing for more values of nondimensional activation energy.

Slug Regime Transitions in a Two-Phase Flow in Horizontal Round Pipe. CFD Simulations

The main objective of the study is to propose a technical solution integrated into the pipeline for the transition of the flow regime from slug to bubbly two-phase flow. The object of research is isothermal two-phase gas–Newtonian-liquid flow in a horizontal circular pipeline. There is local resistance in the pipe in the form of a streamlined transverse mesh partition. The mesh partition ensures the transition of the flow from the slug regime to the bubbly regime. The purpose of the study is to propose a technical solution integrated into the pipeline for changing the flow regime of a two-phase flow from slug to bubbly flow. The method of research is a simulation using computational fluid dynamics (CFD) numerical simulation. The Navier–Stokes equations averaged by Reynolds describes the fluid motion. The k-ε models were used to close the Reynolds-averaged Navier–Stokes (RANS) equations. The computing cluster «Polytechnic—RSK Tornado» was used to solve the tasks. The results of simulation show that pressure drop on the grid did not exceed 10% of the pressure drop along the length of the pipeline. The mesh partition transits the flow regime from slug to layered one, which will help to increase the service life and operational safety of a real pipeline at insignificant energy costs to overcome the additional resistance integrated into the pipeline.

A lattice Boltzmann modeling of viscoelastic drops’ deformation and breakup in simple shear flows

The deformation and breakup of viscoelastic drops in simple shear flows of Newtonian liquids are studied numerically. Our three-dimensional numerical scheme, extended from our previous two-dimensional algorithm, employs a diffusive-interface lattice Boltzmann method together with a lattice advection–diffusion scheme, the former to model the macroscopic hydrodynamic equations for multiphase fluids and the latter to describe the polymer dynamics modeled by the Oldroyd-B constitutive model. A block-structured adaptive mesh refinement technique is implemented to reduce the computational cost. The multiphase model is validated by a simulation of Newtonian drop deformation and breakup under an unconfined steady shear, while the coupled algorithm is validated by simulating viscoelastic drop deformation in the shear flow of a Newtonian matrix. The results agree with the available numerical and experimental results from the literature. We quantify the drop response by changing the polymer relaxation time λ and the concentration of the polymer c. The viscoelasticity in the drop phase suppresses the drop deformation, and the steady-state drop deformation parameter D exhibits a non-monotonic behavior with the increase in Deborah number De (increase in λ) at a fixed capillary number Ca. This is explained by the two distribution modes of the polymeric elastic stresses that depend on the polymer relaxation time. As the concentration of the polymer c increases, the degree of suppression of deformation becomes stronger and the transient result of D displays an overshoot. The critical capillary number for unconfined drop breakup increases due to the inhibitive effects of viscoelasticity. Different distribution modes of elastic stresses are reported for different De.

Lie group analysis of upper convected Maxwell fluid flow along stretching surface

In this article, significance of inclined magnetohydrodynamic flow of an upper-convected Maxwell (UCM) liquid along a penetrable stretched plate is explored. Heat transfer phenomenon is studied with heat generation and absorption effect. We utilize Lie group methodology for adaptation of non-linear differential equations and calculate its absolute invariants explicitly. A numerical method, namely the fourth-order Runge Kutta algorithm with shooting technique is used to solve non-linear ordinary differential equations along with boundary conditions. Velocity profiles for flow of Newtonian and UCM liquid are compared. Plots reflecting effect of inclined and non-inclined MHD for the variations of various parameters are explored and examined. It is observed that oposite behaviour occurs corresponding to heat absorption and generation parameter for both cases of inclination and non-inclination MHD.

Suspension of flexible cylinders in laminar liquid flow

AbstractA methodology for particle‐resolved simulation of dense suspensions of flexible cylindrical particles in Newtonian liquid flow is described. It is based on the Lattice–Boltzmann method for solving the liquid flow and an immersed boundary method for imposing no‐slip at the particle surfaces and providing the distribution of liquid–solid interaction forces over the particle surfaces. These forces—along with contact forces—translate, rotate as well as bend the cylindrical particles. Verification tests have been performed for a single cylinder settling and deforming under gravity at a low Reynolds number. The method has been applied to a clamped flexible cylinder in microchannel flow for which experimental data are available. It then is used to investigate the behavior of hundreds of flexible cylinders with length over diameter aspect ratios of 4 and 6 in a container agitated by an impeller at a Reynolds number of 87 which implies laminar flow. The overall solids volume fraction is 15%. We study the effect of the bending stiffness of the particles on the solids suspension process, on the extent of particle deformation as well as on the torque required to spin the impeller.

Evaluation of non-Newtonian Viscosities of Liquid Foods in Swallowing Process Using Inclined Flow Channel Instrument

Abstract To evaluate the non-Newtonian viscosities of liquid foods thickened for assistance of swallowing in nursing-care practice, an inclined flow channel instrument was investigated for development into a structurally simple and easy-to-use viscometer. Experimental analysis of the flows of Newtonian and non-Newtonian test liquids in the instrument derived a dimensionless relation expressing changes of the friction coefficient in the flow process which was indicated by the relative flow length, considering the shear rate level in the swallowing process. A methodology to evaluate uniquely the viscosities of liquid foods undergoing the swallowing process was presented using the measurements such as the flow length and velocity in the instrument.

Mass transpiration on Newtonian flow over a porous stretching/shrinking sheet with slip

The motivation behind this article is to research the Newtonian liquid flow porous stretching/shrinking sheet utilizing a Brinkman model. The leading system of non-linear partial differential equations relating the article is mapped to standard ordinary differential equations via similarity transformations. Exact result is obtained for velocity. The effects of the Brinkman number or viscosity ratio, slip parameter, Darcy number, suction/injection (mass transpiration) parameter and the mass suction parameter on the velocity dispersion are introduced graphically and talked about. The outcomes have conceivable innovative applications in extrusion process and such other unified zones and in the fluid based frameworks including stretchable materials. Examination of fluid flow past a permeable stretching/shrinking sheet embedded in a non-Darcy permeable medium has been performed for a wide scope of various parameters. Exact solution has been obtained.

Crisis of the Laminar Flow of a Non-Newtonian Liquid in a Pipe

The laminar-turbulent transition of flows of Newtonian (viscous) and non-Newtonian liquids in pipes was investigated on the basis of the combined analysis of the generalized equation of the first and second laws of thermodynamics for a simple system and the Darcy–Weisbach equation. It is shown that a reason for the crises of the laminar flows of such liquids in pipes is the disturbance of the balance between the positive entropy production and the negative entropy flow in them. An analysis of calculation and experimental data on the disturbance of the laminar flow of a non-Newtonian liquid in a pipe and the transformation of this flow into a turbulent flow has shown that the crises of a laminar flow of an elastoviscoplastic liquid in a pipe happens at a larger critical Reynolds number compared to that of a laminar flow of a viscoplastic liquid at one and the same values of the Hedstrom parameter.

Laminar flow of Newtonian liquids in ducts of rectangular cross-section a model for both physics and mathematics

In this paper, we considered the laminar fully developed flow, of a Newtonian fluid, inducts of rectangular cross-section. Poisson’s partial differential equation Saint-Venant solution was used, to calculate Poiseuille number values whatever is rectangles aspect ratio. From these results, we considered limit cases of square duct and plane Poiseuille flow (infinite parallel plates). We showed there exists a rectangle equivalent to a circular cross-section for energy dissipation through viscous friction. Finally, we gave some mathematical consequences of this approach for odd integers zeta function calculations and Catalan’s constant.

Power consumption for an agitated vessel equipped with pitched blade turbine and short baffles

Power characteristics for an agitated vessel equipped with planar short baffles of length L and pitched blade turbine of pitch β are presented in the paper. The studies were carried out in the vessel of inner diameter D = 0.6 m, where the baffles were located in the distance p from the vessel bottom (p + L = H). Torque was measured using strain gauge method within the turbulent regime of the flow of Newtonian liquid in the agitated vessel. The effects of the pitch β and geometrical parameter p/H on the power number Ne were determined mathematically. The results showed that, for the assumed value of the angle β, the function Ne = f (L/H) decreases with the decrease in the baffle length L (i.e. with the increase in the parameter p). Moreover, for the assumed value of the baffle length L, the function Ne = f (β) increases with the increase in the angle β of the inclination of the impeller blade.

Numerical investigation of magneto-nanoparticles for unsteady 3D generalized Newtonian liquid flow

The impact of Buongiorno’s model in flow of a 3D unsteady Sisko fluid is discussed in the presence of zero mass nanoparticles flux conditions. The 3D unsteady Sisko fluid equations are first simplified through classical boundary layer approximations and then non-dimensionalized by employing the suitable transformations. The numerical solutions for the resulting flow, heat and mass transfer have been computed by utilizing the two different numerical techniques, namely the bvp4c function in Matlab and the shooting technique with the Runge-Kutta Fehlberg and Newton-Raphson methods. The results of the numerical computations are described in terms of the temperature and concentration plots. The distinct behaviors of nanoliquid velocity, temperature and concentration distributions for shear-thinning and shear-thickening are reported. It is perceived from the results that the effect of Brownian motion becomes negligible for the newly suggested revised relation. To see the validity of the numerical computations, we compare the results of the numerical techniques bvp4c with an efficient numerical method, namely the shooting technique and the RK45 Fehlberg method and perceived an excellent correlation between these methods.