Solutions For Newtonian Fluids Research Articles

The impact of ultrasonic-assisted extraction on the in vitro hypoglycemic activity of peach gum polysaccharide in relation to its conformational conversion.

Peach gum (PG) is an exudate of the peach tree (Prunus persica of the Rosaceae family), which consists primarily of polysaccharides with a large molecular weight and branching structure. Consequently, PG can only swell in water and does not dissolve easily, which severely limits its application. Current conventional extraction methods for PG polysaccharide (PGPS) are time consuming and inefficient. This study investigated the impact of ultrasonic-assisted extraction (UAE) on PGPS structure and conformation, and their relationship to hypoglycemic activity in vitro. In comparison with conventional aqueous extraction, UAE enhanced PGPS yielded from 28.07-32.83% to 80.37-84.90% (w/w) in 2 h. It drastically decreased the molecular size and conformational parameters of PGPS, including weight-average molecular weight (Mw), number-average molecular weight (Mn), z-average radius of gyration (Rg), hydrodynamic radius (Rh) and instrinsic viscosity ([η]) values. Peach gum polysaccharide conformation converted extended molecules to flexible random coil chains or compact spheres with no obvious primary structure alteration. Furthermore, UAE altered the flow behavior of PGPS solution from that of a non-Newtonian fluid to that of a Newtonian fluid. As a result, PGPS treated with UAE displayed weaker inhibitory activity than untreated PGPS, mostly because UAE weakens the binding strength of PGPS to α-glucosidase. However, this negative effect of UAE on PGPS activity was compensated by the increased solubility of polysaccharide. This enabled PGPS to achieve a wider range of doses. Ultrasonic-assisted extraction is capable of degrading PGPS efficiently while preserving its primary structure, resulting in a Newtonian fluid solution. The degraded PGPS conformations displayed a consistent correlation with their inhibitory effect on α-glucosidase activity. © 2024 Society of Chemical Industry.

Closed-form solution of oscillating Maxwell nano-fluid with heat and mass transfer

The primary goal of this article is to analyze the oscillating behavior of Maxwell Nano-fluid with regard to heat and mass transfer. Due to high thermal conductivity of engine oil is taken as a base fluid and graphene Nano-particles are introduced in it. Coupled partial differential equations are used to model the governing equations. To evaluate the given differential equations, certain dimensionless factors and Laplace transformations are used. The analytical solution is obtained for temperature, concentration and velocity. The temperature and concentration gradient are also finds to analyze the rate of heat and mass transfer. As a special case, the solution for Newtonian fluid is discussed. Finally, the behaviors of various physical factors are studied graphically for both sine and cosine oscillation and give physical meanings to the parameters.

Analytical solution of tank drainage flow for electrically conducting Newtonian fluid

The electrically conducting, incompressible and isothermal Newtonian fluid-flow in unsteady tank drainage is studied. The perturbation method is employed to obtain solution and results have been compared with those of obtained by adomian decomposition method result. The results of adomian decomposition method are same as those of perturbation method. The Newtonian fluid solution is worked out with substitution ? = 0. Explicit expressions on behalf of velocity field, flow rate, relationship however will the times vary with length, average velocity and time needed for complete drainage are acquired. Impacts of different developing parameters on velocity profile, vz, flow rate and depth of the tank, H(t), are exhibited graphically.

Heat Transfer in Magnetohydrodynamic Flow of a Casson Fluid with Porous Medium and Newtonian Heating

This paper deals with exact solutions for unsteady magnetohydrodynamic (MHD) flow of a Casson fluid over an infinite vertical oscillating plate embedded in a porous medium. The analysis of heat transfer in the presence of Newtonian heating is also considered. Some suitable non-dimensional variables are introduced. The governing equations together with imposed conditions are transformed into dimensionless forms. Expressions for the velocity and temperature fields are obtained using the Laplace transform. Skin-friction and Nusselt number are also evaluated. Solution for Newtonian fluid is also reduced as a special case. The graphical results show that velocity decreases significantly with increases of magnetic effects, but it increases when either conjugate parameter or porosity parameter increases. The main outcomes of the present work is that fluid flow can be controlled by the increasing the values of Prandtl number as well as by the increasing of Casson parameter.

Exact Solution of Unsteady MHD Free Convective Chemically Reacting Visco-Elastic Fluid Flow Past a Moving Vertical Plate Through Porous Medium

The influence of radiation on the unsteady MHD free convection Viscoelastic fluid flow past an exponentially accelerated moving vertical plate through porous medium with chemical reaction is investigated theoretically. The fluid considered here is a gray, absorbing-emitting radiation but non-scattering medium, and the Boussinesq’s approximation is considered for pressure gradient in momentum equation and Taylor’s series expansion to describe the radiative heat flux in the energy equation. The dimensionless governing partial differential equations are solved using Laplace transform technique. They satisfy all imposed initial and boundary conditions and for $$S\rightarrow 0$$ can be reduce to the similar solutions for Newtonian fluids. The corresponding expressions for skin friction, Nusselt number and Sherwood number also evaluated. Numerical results for velocity, temperature and concentration are shown graphically. This study is of fundamental importance and frequently arises in many practical situations such as chemical engineering and polymer extrusion processes. The effect of different parameters like thermal radiation parameter, visco-elastic parameter, chemical reaction parameter, magnetic field parameter, permeability parameter, Schmidt number and Prandtl number are discussed. It is observed that the momentum and thermal boundary layer thickness decreases owing to an increase in the value of the radiation parameter. An increase in the Prandtl number is found to decrease the velocity and temperature but increasing in Nusselt number for air and water.

Interaction of magnetic field with heat and mass transfer in free convection flow of a Walters’-B fluid

The heat and mass transfer phenomenon is studied in the unsteady free convection flow of a Walters’-B fluid in the presence of a transverse magnetic field. The problem is modelled in terms of partial differential equations with some physical conditions. Exact solutions for velocity, temperature and concentration are obtained via Laplace transform method. They satisfy imposed initial and boundary conditions. As a special case for $ \Gamma \rightarrow 0$ , these solutions can be be reduced to the similar solutions for Newtonian fluids. The shear stress at the boundary is evaluated from the velocity solution. Numerical results of velocity and shear stress are portrayed through graphs and discussed for various embedded parameters.

Analysis of von Kármán’s swirling flow on a rotating disc in Bingham fluids

In this article, the flow above a rotating disc, which was first studied by von Kármán for a Newtonian fluid, has been investigated for a Bingham fluid in three complementary but separate ways: by computational fluid dynamics (CFD), by a semi-analytical approach based on a new transformation law, and by another semi-analytical approach based on von Kármán’s transformation. The full equations, which consist of a set of partial differential equations, are solved by CFD simulations. The semi-analytical approach, in which a set of ordinary differential equations is solved, is developed here by simplifying the full equations invoking several assumptions. It is shown that the new transformation law performs better and reduces to von Kármán’s transformation as a limiting case. The present paper provides a closed-form expression for predicting the non-dimensional moment coefficient which works well in comparison with values obtained by the full CFD simulations. Detailed variations of tangential, axial, and radial components of the velocity field as a function of Reynolds number (Re) and Bingham number (Bn) have been determined. Many subtle flow physics and fluid dynamic issues are explored and critically explained for the first time in this paper. It is shown how two opposing forces, viz., the viscous and the inertial forces, determine certain important characteristics of the axial-profiles of non-dimensional radial velocity (e.g., the decrease of maxima, the shift of maxima, and the crossing over). It has been found that, at any Re, the maximum value of the magnitude of non-dimensional axial velocity decreases with an increase in Bn, thereby decreasing the net radial outflow. A comparison between the streamline patterns in Newtonian and Bingham fluids shows that, for a Bingham fluid, a streamline close to the disc-surface makes a higher number of complete turns around the axis of rotation. The differences between the self-similarity in a Newtonian fluid flow and the non-similarity in a Bingham fluid flow are expounded with the help of a few compelling visual representations. Some major differences and similarities between the flow of a Newtonian fluid above a rotating disc and that of a Bingham fluid, deduced in the present investigation, are brought together in a single table for ready reference. Two limiting cases, viz. Bn → 0 and Re → ∞, are considered. The present results show that the Bingham fluid solution progressively approaches the von Kármán’s solution for a Newtonian fluid as the Bingham number is progressively reduced to zero (Bn → 0). It is also established here that, for finite values of Bn, the Bingham fluid solution progressively approaches the von Kármán’s solution for a Newtonian fluid as the non-dimensional radius and Reynolds number increase. The higher the value of Bn, the higher is the required value of Re at which convergence with the solution for Newtonian fluid occurs.

Rheological characterization of cellular blood in shear

AbstractA hybrid lattice-Boltzmann spectrin-link (LB–SL) method is used to simulate dense suspensions of red blood cells (RBCs) for investigating rheological properties of blood. RBC membranes are modelled using a coarse-grained SL method and are filled with a viscous Newtonian fluid solution with viscosity five times that of the suspending fluid. Relative viscosities, normal stress differences, and particle pressures are reported for a range of capillary numbers at a physiologically realistic haematocrit value of approximately 42.5 %. Viscosity shear thinning is demonstrated for shear rates ranging from 14 to 440 s−1 and is shown to be affected by the orientation and bending modulus of RBCs. The particle-phase pressure undergoes a change in sign from positive to negative as the shear rate is increased. The particle-phase normal stress tensor values show that there is a transition from compressive to tensile states in the flow direction as the shear rate is increased. The normal stress differences are notably different from those recently reported for deformable capsule suspensions using a similar methodology, which suggests that the bending stiffness and the biconcave shape of RBCs affect the rheology of blood.

Starting Solutions for Motion of a Maxwell Fluid Over an Infinite Plate that Applies an Oscillating Shear to the Fluid

Unsteady motion of a Maxwell fluid over an infinite plate that applies an oscillating shear to the fluid is studied by means of integral transforms. The obtained solutions satisfy all initial and boundary conditions. They are presented as a sum of steady-state and transient solutions and can easily be reduced to the similar solutions for Newtonian fluids. They describe the motion of the fluid some time after its initiation. After that time, when the transients disappear, the motion of the fluid is described by the steady-state solutions which are periodic in time and independent of the initial conditions. However, they satisfy the governing equations and boundary conditions. Finally, the required time to reach the steady-state, as well as a comparison between models, is determined by graphical illustrations.

Unsteady Magnetohydrodynamic Oscillatory Flow of Viscoelastic Fluids in a Porous Channel with Heat and Mass Transfer

In this paper, we analyze the effects of slip condition on the unsteady magnetohydrodynamic (MHD) flow of incompressible viscoelastic fluids in a porous channel under the influence of transverse magnetic field and Hall current with heat and mass transfer. The channel flow is induced due to external pressure gradient of oscillatory form. The governing equations for the velocity field, temperature and concentration distributions, are solved using perturbation technique. We present the results for skin friction, Nusselt number and Sherwood number. The numerical results are also computed for skin friction in tabular form. The effects of various indispensable flow parameters are displayed using several graphs. The numerical results show the effects of the physical parameters on the fluid flow as well as on heat and mass transfer and skin friction. The solutions for Newtonian fluids can be obtained as a limiting case from our general solutions when the viscoelastic parameter is zero.

EXACT SOLUTION FOR RAYLEIGH−STOKES PROBLEMS OF AN OLDROYD-B FLUID IN A POROUS MEDIUM AND ROTATING FRAME

The aim of this paper is to determine the new exact solution of a magnetohydrodynamic (MHD) and rotating flow of the Maxwell fluid induced by a suddenly moved plate in its own plane. This is accomplished by using the Fourier sine and Laplace transforms. Based on the modified Darcy’s law, the expression for the velocity field is obtained. It is found that similar solutions for Newtonian fluid appear as limiting cases of our solutions. Finally some graphical results of the velocity profiles are presented for different values of the material constants.

Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid and both the cylinders are at rest and at t = 0+, cylinders suddenly begin to oscillate around their common axis in a simple harmonic way having angular frequencies ω1 and ω2. The obtained solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for Newtonian fluid are also obtained as limiting cases of our general solutions.

Some Exact Solutions for Helical Flows of Maxwell Fluid in an Annular Pipe due to Accelerated Shear Stresses

Some exact solutions corresponding to helical flows of Maxwell fluid between two infinite coaxial circular cylinders are determined by means of finite Hankel transform, presented in series form, satisfied all imposed initial and boundary conditions. The motion is produced by the inner cylinder that applies the torsional and longitudinal time-dependent accelerated shear stresses to the fluid. The corresponding solutions for Newtonian fluid and large-time solutions are also obtained as limiting cases and effect of material parameters on the large-time solutions are discussed. Finally, the influence of pertinent parameters as well as a comparison between Maxwell and Newtonian fluids on the velocity components and shear stresses profiles is also examined by graphical illustrations.

Some Exact Solutions for Helical Flows of Maxwell Fluid in an Annular Pipe due to Accelerated Shear Stresses

Some exact solutions corresponding to helical flows of Maxwell fluid between two infinite coaxial circular cylinders are determined by means of finite Hankel transform, presented in series form, satisfied all imposed initial and boundary conditions. The motion is produced by the inner cylinder that applies the torsional and longitudinal time-dependent accelerated shear stresses to the fluid. The corresponding solutions for Newtonian fluid and large-time solutions are also obtained as limiting cases and effect of material parameters on the large-time solutions are discussed. Finally, the influence of pertinent parameters as well as a comparison between Maxwell and Newtonian fluids on the velocity components and shear stresses profiles is also examined by graphical illustrations.

Helical flows of second grade fluid due to constantly accelerated shear stresses

The helical flows of second grade fluid between two infinite coaxial circular cylinders is considered. The motion is produced by the inner cylinder that at the initial moment applies torsional and longitudinal constantly accelerated shear stresses to the fluid. The exact analytic solutions, obtained by employing the Laplace and finite Hankel transforms and presented in series form in term of usual Bessel functions of first and second kind, satisfy both the governing equations and all imposed initial and boundary conditions. In the limiting case when α → 0, the solutions for Newtonian fluid are obtained for the same motion. The large-time solutions and transient solutions for second grade fluid are also obtained, and effect of material parameter α and kinematic viscosity ν is discussed. In the last, the effects of various parameters of interest on fluid motion as well as the comparison between second grade and Newtonian fluids are analyzed by graphical illustrations.

Helical flows of Maxwell fluid between coaxial cylinders with given shear stresses on the boundary

Helical flows for a Maxwell fluid are studied between two infinite coaxial circular cylinders, at time t = 0 + ; the inner cylinder begins to rotate around its axis and to slide along the same axis due to the torsional and longitudinal time dependent shear stresses. Exact solutions obtained with the help of finite Hankel transform and, presented under series form, satisfy all imposed initial and boundary conditions. The corresponding solutions for Newtonian fluid are also given as limiting cases. Finally, the influence of pertinent parameters–as well as a comparison between Maxwell and Newtonian fluids–on the velocity components and shear stresses is also analyzed by graphical illustrations.

Exact solutions for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit

The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.

On the energetic balance for the flow of a Maxwell fluid due to a constantly accelerating plate

Dissipation, the power due to the shear stress at the wall and the boundary layer thickness for the motion of a Maxwell fluid, induced by a constantly accelerating plate, are established in exact and approximate forms. The corresponding solutions for Newtonian fluids, performing the same motion, are obtained as limiting cases of our solutions. In comparison with the Newtonian model, the dissipation and the boundary layer thickness decrease.

A finite element formulation for laminar flow of a fluid with microstructure

AbstractA finite element formulation for the steady laminar flow of an incompressible fluid with microstructure has been developed. The particular fluids considered are commonly known as micropolar fluids, in which case suspended particulate microstructures are modelled by an ‘extended’ continuum formulation. The particle microspin is a new kinematic variable which is independent of the classical vorticity vector and thereby allows relative rotation between particles and the surrounding fluid. This formulation also gives rise to couple stresses in addition to classical force or traction stresses. The finite element formulation utilizes a variational approach and imposes conservation of mass through a penalty function. A general boundary condition for microspin has been incorporated whereby microspin at a solid boundary is constrained to be proportional to the fluid vorticity. The proportionality constant in this case can vary from zero to unity. Sample solutions are presented for fully developed flow through a straight tube and compared with an analytical solution. Results are also generated for flow through a constricted tube and compared with a Newtonian fluid solution.

DAMPED OSCILLATIONS IN A BINGHAM PLASTIC FLUID

Abstract Stokes' second problem, the propagation and damping of waves into a semi-infinite fluid generated by harmonic oscillations of a flat pate on the surface, is solved for the simple Bingham Theological constitutive model. The solution reveals the existence of “windows” in the distance-time-stress space in which shearing is possible whereas outside these restricted regions no shearing can occur. Within these restricted regions the wave forms developed are exponentially damped, traveling waves which propagate from the excitation plane into the fluid and disappear along definitely prescribed boundaries determined by the yield condition. The most significant consequence of the existence of these “windows” of shear is that even very small yield stresses will radically modify the induced velocity wave patterns from that which would be expected based upon the classical Newtonian fluid solution of Stokes’ second problem. At least in this physical setting, it is not necessary for shear to occur globally for ...