Unsteady Flow Of non-Newtonian Fluid Research Articles

COMPUTATIONAL ANALYSIS OF NONLINEARIZED THERMAL RADIATION & LORENTZ FORCE ON UNSTEADY FLOW OF NON-NEWTONIAN FLUID IN POROUS MEDIUM

An extensive analysis of nonlinearized thermal radiation & Lorentz force on an unsteady flow of Non-Newtonian fluid taking the Maxwell model over a permeable nonuniform stretchable sheet in a porous media has been presented. Appropriate analogous transformations are introduced to develop the ordinary differential equations from the fluid flow governing equations. Numerical method Lobatto IIIa is used to solve these ODEs and programmed in mathematical software MATLAB to obtain the graphical and numerical details. The effectiveness of non-linearity in thermal radiation, unsteadiness of the flow and magnetic field on Nusselt number, skin friction, heat & fluid motion are tabulated and represented in graphs with an elaborate discussion of the consequences. It is found that the Lorentz force and nonlinearity in thermal radiation have an adverse impression on the heat propagation throughout the flow. Further, a comparative inspection is also carried out proving the relevance of the current technique.

Unsteady non-Newtonian fluid flow with heat transfer and Tresca\u2019s friction boundary conditions

We consider an unsteady non-isothermal flow problem for a general class of non-Newtonian fluids. More precisely the stress tensor follows a power law of parameter p, namely sigma = 2 mu ( theta , upsilon , | D(upsilon ) |) |D( upsilon ) |^{p-2} D(upsilon ) - pi mathrm{Id} where θ is the temperature, π is the pressure, υ is the velocity, and D(upsilon ) is the strain rate tensor of the fluid. The problem is then described by a non-stationary p-Laplacian Stokes system coupled to an L^{1}-parabolic equation describing thermal effects in the fluid. We also assume that the velocity field satisfies non-standard threshold slip-adhesion boundary conditions reminiscent of Tresca’s friction law for solids. First, we consider an approximate problem (P_{delta }), where the L^{1} coupling term in the heat equation is replaced by a bounded one depending on a small parameter 0 < delta ll 1, and we establish the existence of a solution to (P_{delta }) by using a fixed point technique. Then we prove the convergence of the approximate solutions to a solution to our original fluid flow/heat transfer problem as δ tends to zero.

Mix convection non- boundary layer flow of unsteady MHD oblique stagnation point flow of nanofluid

This article demonstrates the analysis of hydrodynamics in the existence of a magnetic field. Heat transfer is analyzed for the unsteady flow of non-Newtonian fluid. The thermal conductivity is enhanced by introducing nanoparticles in the non-Newtonian fluid. Magnetohydrodynamics is introduced to control the turbulence in the flow. The dimensional equations satisfying the stated assumptions of the fluid flow and the motion of nanoparticles are presented. Fourier law is incorporated in the evaluation of heat flux. The analysis is tested in the fixed frame of reference. The mathematical coupled equations of motion are solved numerically. It is concluded that the Casson parameter leads to enhance velocity profile whereas the temperature profile is declined.

Convection-diffusion in unsteady non-Newtonian fluid flow in an annulus with wall absorption

The present study investigates the combined effects of non-Newtonian rheology and unsteady nature of the fluid on dispersion of a soluble substance between two coaxial cylinders having wall permeability at the outer wall with the flowing fluid is modelled as Casson fluid. Generalized dispersion method in combination with a finite difference scheme is used to study the dispersion phenomenon. Using the generalized dispersion model, the entire process of dispersion is expressed in terms of three transport coefficients viz., absorption, convection, and dispersion (effective diffusion) coefficients. These transport coefficients are evaluated numerically using Crank-Nicolson finite difference method. The mean concentration is expressed in terms of these transport coefficients. Effects of annular gap, yield stress, Womersley frequency parameter, amplitude of the pressure pulsation, and the absorption parameter on the transport coefficients and mean concentration are studied. Flow unsteadiness is observed influencing the dispersion coefficient both quantitatively and qualitatively. It is observed that, as Womersley number increases the fluctuation of the dispersion coefficient increases and the magnitude of dispersion coefficient decreases for small values of time (< 0.5) and increases for later values of time.

Finite Volume Solution of Non-Newtonian Casson Fluid Flow in A Square Cavity

A two dimensional unsteady flow of non-Newtonian fluid in a square cavity is investigated numerically by using finite volume method based on staggered grids. The discretized equations are integrated by using second order Adams-Bashforth time advancement scheme togather with pressure correction approach. Error history for velocities and pressure are recorded for high Reynolds number when grid resolution is \(128\times128\). The results are also compared with already published work for special case. An excellent agreement is observed. The behavior of velocity components are studied for different values of non-Newtonian parameter $\beta$, the Casson fluid parameter.

Some generalized results for Maxwell fluid flow over porous oscillatory surface with modified Fourier and Fick’s theories

This study intends to elaborate heat and mass transportation characteristics in unsteady flow of non-Newtonian fluid caused by oscillatory surface. The rheological behavior of non-Newtonian fluid is addressed by using Maxwell model. Further, heat transportation is characterized through consideration of Cattaneo–Christov theory of heat diffusion. Secondly, the generalized Fick’s law is implemented for investigation of mass transfer. The independent variables in the governing expressions are decreased with suitable transformations. The homotopic procedure is adopted for the solutions of well-defined problem. The validity of obtained solution is verified in limiting case. The graphical explanations for both linear and oscillatory stretching surface are presented. The comparison of $$f^{{\prime \prime }} (0,\tau )$$ with proposed results for linear stretching surface is recovered. Furthermore, the numerical values of flow feature parameters on local Nusselt and local Sherwood numbers are also highlighted and expressed in tabular form.

Effect of thermal radiation and chemical reaction on non-Newtonian fluid through a vertically stretching porous plate with uniform suction

Abstract In this work, we discuss the unsteady flow of non-Newtonian fluid with the properties of heat source/sink in the presence of thermal radiation moving through a binary mixture embedded in a porous medium. The basic equations of motion including continuity, momentum, energy and concentration are simplified and solved analytically by using Homotopy Analysis Method (HAM). The energy and concentration fields are coupled with Dankohler and Schmidt numbers. By applying suitable transformation, the coupled nonlinear partial differential equations are converted to couple ordinary differential equations. The effect of physical parameters involved in the solutions of velocity, temperature and concentration profiles are discussed by assign numerical values and results obtained shows that the velocity, temperature and concentration profiles are influenced appreciably by the radiation parameter, Prandtl number, suction/injection parameter, reaction order index, solutal Grashof number and the thermal Grashof. It is observed that the non-Newtonian parameter H leads to an increase in the boundary layer thickness. It was established that the Prandtl number decreases thee thermal boundary layer thickness which helps in maintaining system temperature of the fluid flow. It is observed that the temperature profiles higher for heat source parameter and lower for heat sink parameter throughout the boundary layer. Fromm this simulation it is analyzed that an increase in the Schmidt number decreases the concentration boundary layer thickness. Additionally, for the sake of comparison numerical method (ND-Solve) and Adomian Decomposition Method are also applied and good agreement is found.

Unsteady flows of non-Newtonian fluids in generalized Orlicz spaces

Our purpose is to show existence of weak solutions to unsteady flow of non-Newtonian incompressible nonhomogeneous fluids with nonstandard growth conditions of the stress tensor. We are motivated by the fluids of anisotropic behaviour and characterised by rapid shear thickening. Since we are interested in flows with the rheology more general than power-law-type, we describe the growth conditions with the help of an $x$--dependent convex function and formulate our problem in generalized Orlicz spaces.

Numerical modelling of the motion of rapid, flow-like landslides for hazard assessment

Computer methods for analysis of stresses, strains and displacements of soil structures have made spectacular advances in recent years. Now, a new field of analysis with substantial practical significance is opening up. This is the quantitative analysis of motion of rapidly moving masses of earth and fragmented rock in landslides such as debris avalanches, debris flows, flow slides and rock avalanches. The new methods accept an unstable body of material on the slope as input (the “landslide source”) and map its propagation down the slope in terms of flow depth and velocity. This allows outlining the extent of potential hazard areas and the distribution of hazard intensity parameters within them as needed for detailed hazard mapping, estimation of risks and design of remedial measures such as deflecting walls, dykes or barriers. Two advanced numerical solutions based on integrated “shallow-flow” Lagrangian theory of unsteady flow of non-Newtonian fluid are described in terms of their theoretical background, assumptions regarding the type of flow and rheological characteristics, as well as examples of a variety of results. The two models are the pseudo-three dimensional code DAN and its extension into three dimensions, DAN3D. Both codes have the following main capabilities: 1) Open rheological kernel, allowing the choice of a variety of rheological relationships to suit a particular character of the moving mass; 2) ability to change rheology during the flow; 3) non-hydrostatic, anisotropic internal stress distribution controlled by longitudinal strain; and 4) ability to entrain material during the flow. Both codes are highly efficient and both produce similar results when applied to the same example.

Numerical study of the unsteady flow of non-Newtonian fluid through differently shaped arterial stenoses

The problem of non-Newtonian and nonlinear pulsatile flow through an irregularly stenosed arterial segment is solved numerically where the non-Newtonian rheology of the flowing blood is characterized by the generalized Power-law model where both the shear-thinning and shear-thickening models of the streaming blood are taken into account. The combined influence of an asymmetric shape and surface irregularities (roughness) of the constriction has been explored in a study of blood flow with 48% areal occlusion. The vascular wall deformability is taken to be anisotropic, linear, viscoelastic, incompressible circular cylindrical membrane shell. The effect of the surrounding connective tissues on the motion of the arterial wall is also paid due attention. Results are obtained for a smooth stenosis model and also for a stenosis model represented by the cosine curve. The present analytical treatment has the potential to calculate the rate of flow, the resistive impedance and the wall shear stress without excessive computational complexity by exploiting the appropriate physiologically realistic prescribed conditions in nonuniform nonstaggered grids, and to estimate the effects of surface roughness as well as asymmetry of stenosis shape for both shear-thinning and shear-thickening models of Power-law fluid, representing the streaming blood through graphical representations in order to validate the applicability of the present improved mathematical model.

Steady and unsteady flow of non-newtonian fluid in curved pipe with triangular

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

Steady and unsteady flow of non-newtonian fluid in curved pipe with triangular

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

Unsteady flow of a non-Newtonian fluid above a rotating disk with heat transfer

The unsteady flow of an incompressible viscous non-Newtonian fluid above an infinite rotating disk is studied with heat transfer. The effect of the non-Newtonian fluid characteristics on the velocity and temperature distributions as well as the heat transfer is considered. Numerical solutions for the non-linear partial differential equations which govern the hydrodynamics and energy transfer are obtained.

Computational intellectual analytical theory of computational analytical approach to rotating flow of non-Newtonian fluid

A combination of the computational symbolic calculation, mathematical approach and physico-mechanical model leads to a computational intellectual analytical approach developed by the author. There is a principal difference between the computer proof and the computer derivation completed by the computer, also difference between the numerical and symbolic calculations. In this investigation the computational analytical approach is extended, and an unsteady flow of non-Newtonian fluid in the gap between two rotating coaxial cylinders is studied. The Oldroyd fluid B model is used by which the Weissenberg effects are explained in a good comparison with the experiments. The governing equations are reduced to a partial differential equation of 3 rd order for the dimensionless velocity. Using the computer software Macsyma and an improved variational approach the problem with the intial and boundary conditions is then reduced to a problem of an ordinary differential equation for different approximations. The analytical solutions are given for the 1 st, 2 nd and 3 rd approximations. The present investigation shows the ability of the computational symbolic manipulation in solving the problems of non-Newtonian fluid flows. There is a possibility of that to solve the problems in mathematics and mechanics. An important conclusion can be drawn from the results that the transition from a steady state to another steady state is non-unique.

Inertia effects of the fluid and cylinder in coaxial cylindrical rheometer

The inertias of the fluid and the inner cylinder in coaxial cylinder rheometer (CACR) have great influence on the unsteady flow of non-Newtonian fluid. Even for the Newtonian fluid there exist the so called “stress overshoot” phenomenon. In the present article this phenomenon was studied in detail and a method correcting the measured results for an unsteady flow in the rheometer was proposed. It is found that the inertia effect of the fluid can be ignored when the gap between cylinders is small.

Recent Developments in Three-Dimensional Unsteady Flows of Non-Newtonian Fluids

Recent Developments in Three-Dimensional Unsteady Flows of Non-Newtonian Fluids

On the existence of diffusive waves in some non-linear unsteady flows of non-Newtonian fluids through porous media

We investigate the unsteady flow of power law fluids through porous media. We determine the pressure and velocity distributions when fluid is injected into a porous medium of infinite extend. We obtain solutions of progressive-wave type by means of a translation. We determine the necessary conditions for the existence of this type of solution regarding the prescribed pressure of injection and the initial pressure and velocity distributions in the porous medium. Similarity solutions are also obtained for the cases of a prescribed time dependent pressure of injection and a prescribed constant flow rate of injection. In the latter case the resulting ordinary differential equation is solved numerically. Point source solutions are also obtained for the case when an amount of fluid is instantaneously injected into the porous media. In all cases the rheological effects are presented and analyzed.

Similarity solutions to some unsteady flows of non-Newtonian fluids of power law behavior

The question of the non-linear effects in some unsteady flows of non-Newtonian fluids is addressed. Exact similarity solutions in closed form are presented for Stokes' first problem, for Couette rotating flow, for the spreading of a thin fluid layer and for unsteady flow through a porous medium. From these solutions the conditions for the existence of traveling-wave characteristics are found for the velocity, shear stress and pressure distributions.

On non-linear effects in unsteady flows of non-newtonian fluids through fractured porous media

The question of the non-linear effects on unsteady flows of non-Newtonian fluids through fractured porous media is addressed. These effects are illustrated on the pressure and velocity distributions for a power-law fluid of shear thinning behavior. The governing equations and their self-similar solutions, for the first boundary value problem, are presented. The rheological effects and those associated with the presence of a fracture network, into the porous medium, on the flow behavior are shown and discussed. The effects of non-Newtonian fracturing fluid on the fracture dimensions in hydraulic fracturing mechanism are also investigated. Contributed by W.F. Ames.

On non-linear effects in unsteady flows through porous media

The question of the non-linear effects on the unsteady flows of non-Newtonian fluids through porous media is addressed. The slightly compressible fluids of power law behavior are considered. The exact self-similar solutions in a closed form of the non-linear equations governing the flow, for the first boundary value problem, are presented. The implications of the non-linear effects on the propagation mechanism of pressure disturbances in a non-Newtonian fluid, flowing through a porous medium, are discussed. It is shown that these disturbances propagate with finite velocity, which is a monotonically decreasing function of time, due to the existence of a moving pressure front. This relevant result is obtained from exact analytical solutions which exhibit traveling wave characteristics in a shear thinning fluid.