non-Newtonian Viscoelastic Fluid Flow Research Articles

Two Models on the Unsteady Heat and Fluid Flow Induced by Stretching or Shrinking Sheets and Novel Time-Dependent Solutions

Abstract This study sheds light on unsteady heat and fluid flow problems over stretching and shrinking surfaces, enriching our understanding of these complex phenomena. We derive two mathematical models using a rigorous approach. The first model aligns with the model commonly employed by researchers in this field, but its steady-state solution remains trivial. The second model, introduced in this work, demonstrably captures the physically relevant steady-state solutions well-studied in the literature. Notably, we introduce new similarity solutions for the temperature field specifically within the first model. We further demonstrate that a uniform wall temperature condition leads to the optimal heat transfer rate. While similarity solutions can be derived for specific cases with the second model, nonsimilar solutions may be necessary for more general scenarios. We discuss the implications of our analysis for stagnation-point flow and non-Newtonian viscoelastic fluid flow problems, illuminating future research directions in the open literature.

On MHD Flow of Non-newtonian Viscoelastic Fluid over a Stretched Magnetized Surface

The purpose of this research is to investigate heat and mass transport in a magnetohydrodynamic (MHD) flow of a non-Newtonian viscoelastic fluid on a stretched magnetized surface. The investigations involve modelling the governing partial differential equations with respect to the Cartesian coordinate system. The models are then transformed into a set of coupled ordinary differential equations. Numerical and graphical solutions were obtained using similarity analysis. The effect of the magnetized sheet on the flow behavior; local skin friction, Nusselt, and Sherwood numbers, are presented in tables. It was observed that an enhanced thickening of the thermal boundary layer was due to the induced magnetization of the sheet. This leads to a significant decline in the heat transfer rate. Certain significant discoveries reported in this research discloses that the effect of viscous dissipation and the non-uniform heat transmission have momentous impact in controlling the rate of heat transfer in the boundary layer region. Again, from the outcome of the analysis it is seen that, the effect of appreciating the Soret number or lessening the Dufour number tends to decrease the velocity and temperature profiles while enhancing the concentration dissemination. Magnetizing the surface shows similar effects on the local skin friction, Nusselt number, and Sherwood number. It is concluded that magnetized surfaces significantly influence the rate of cooling and hence the quality of the penultimate product.

Similarity solution of second grade fluid flow over a moving cylinder

Stagnation point flow of viscoelastic second grade fluid over a stretching cylinder under the thermal slip and magnetic hydrodynamics effects are studied. The mathematical model has been developed under the assumption of non-Newtonian viscoelastic fluid flow over a stretching cylinder by means of the boundary layer approximations. The developed model further reduced through the similarity transformations and constructs the model of nonlinear ordinary differential equations. The system of nonlinear differential equations is dimensionless and solved through the numerical technique bvp5c methods. The results of the physical parameters are found and interpreted in the form of tables and graphs. The velocity shows that the graph of curves enhances away from the surface when the values material parameter [Formula: see text] increase, which means the momentum boundary layer increases for enhancing the material parameter [Formula: see text]. The temperature gradient reduced due enhancing the values of material parameter [Formula: see text] because thermal boundary layer reduced for higher values of material parameter [Formula: see text].

Powell–Eyring fluid flow towards an isothermal sphere in a non-Darcy porous medium

Non-Newtonian viscoelastic fluid flow past an isothermal sphere embedded in non-Darcy porous medium is examined numerically in this work. To be specific, the non-Newtonian Powell–Eyring fluid in the presence of both the heat and mass characteristics is mathematically modelled in terms of differential system. A non-Darcy drag force model is employed to simulate the effects of linear porous media drag and second-order Forchheimer drag. The surface of the sphere is maintained at a constant temperature and concentration. The numerical solution of the resultant system is reported via the Keller box method. Both tabular and graphical forms are adopted to identify the variations in Powell–Eyring fluid velocity, Powell–Eyring fluid temperature, and Powell–Eyring fluid concentration. In addition, the surface physical quantities, namely, skin friction and heat and mass transfer rates, are explored. The obtained observations are validated with earlier Newtonian studies. We found an excellent match in this regard. It is found that the velocity is reduced with increasing fluid parameter (ε), Forchheimer parameter (Λ), and tangential coordinate (ξ). In contrast, the temperature and concentration are increasing with increasing value of ε. A very slight increase in velocity is seen with an increase in the local non-Newtonian parameter, δ. But the temperature and concentration decrease slightly with an increase in δ. An increase in Darcy parameter enhances velocity but reduces both temperature and concentration. The present study finds an extensive array of applications in modern nuclear engineering, mineral and chemical process engineering, nuclear waste in geomaterial repositories, petroleum product filtration, and insulation systems.

Analysis of boundary layer in MHD flow of non-Newtonian visco-elastic fluid on stretching sheet

This article aims to the study of fluid flow and heat transfer in non-Newtonian viscoelastic fluid magnetic hydrodynamics steady laminar flow is expanded on a horizontal plane. Among the many processes in chemical engineering, metallurgy, polymer extrusion process involves cooling the molten liquid is drawn into the cooling system, the production of paper and glass. In this process, the rate of cooling and shrinking influences very much on the final quality of the product. Equations for fluid flow and heat transfer analysis solutions are helping homotopy analysis. In this regard and in order to validate the results of the homotopy analysis, we are comparing the results of this study and other researchers published the results will be accepted. Also, the influence of various parameters on curves, speed and temperature have been investigated.

Investigation of heat transfer for cooling turbine disks with a non-Newtonian fluid flow using DRA

A non-Newtonian viscoelastic fluid flow passes through the porous wall of an axisymmetric channel on a turbine disc for cooling application. The present article solves the couple equations (momentum and heat transfer) of a non-Newtonian fluid flow in an axisymmetric channel with a porous wall for turbine cooling applications by using the Duan–Rach Approach (DRA). The precious achievement of the present work is introducing a new and efficient approximate analytical technique that this method allows us to find a solution without using numerical methods to evaluate the undetermined coefficients. The approximate analytical investigation is carried out for different values of the embedding parameters namely: Reynolds number, Prandtl number, injection Reynolds number and power law index. The DRA results indicate that Nusselt number has direct relationship with Reynolds number, Prandtl number and power law index. Also the results were compared with numerical solution in order to verify the accuracy of the proposed method. It is seen that the current results in comparison with the numerical ones are in excellent agreement.

Analysis of Viscoelastic Fluid Flow over a Suddenly Moved Flat Plat

The velocity field and the associated tangential tension corresponding to the flow of the viscoelastic fluid over an infinite rigid plate are determined in this paper. The characteristic of the non-Newtonian viscoelastic fluid flow is analyzed using the Stehfest method of the numerical inversion of Laplace transform. It indicates that the flow of the viscoelastic fluid is very sensitive to the material constants. Finally, some comparative diagrams concerning the velocity and tangential tension profiles are presented.

Approximate solution of non-Newtonian viscoelastic fluid flow on a turbine disc for cooling purposes by using Adomian decomposition method

In this work, a powerful semi-analytical method, called Adomian decomposition method (ADM) is introduced to obtain the exact solution of heat transfer equation of a non-Newtonian fluid flow in an axisymmetric channel with a porous wall which is useful for turbine cooling applications. This method is employed to obtain the expressions for velocity and temperature fields. Then, the influence of the two dimensionless numbers: the Prandtl number (Pr) and the Reynolds number (Re) for the dynamic forces have been considered. Comparisons are made between the numerical method (NM) solution, Homotopy perturbation method (HPM), Variation iteration method (VIM) and the results of Adomian decomposition method (ADM). The results reveal that this method is very effective and simple and can be applied for other nonlinear problems.

Unsteady Flow of Non-Newtonian Visco-Elastic Fluid in Dual-Porosity Media with The Fractional Derivative

The fractional order derivative was introduced to the seepage flow research to establish the relaxation models of non-Newtonian viscoelastic fluids in dual porous media. The flow characteristics of non-Newtonian viscoelastic fluids through a dual porous medium were studied by using the Hankel transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions were obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation were also resulted. The pressure transient behavior of non-Newtonian viscoelastic fluids flow through an infinite dual porous media was studied by using Stehfest's inversion method of the numerical Laplace transform. It shows that the characteristics of the fluid flow are appreciably affected by the order of the fractional derivative.

Magnetohydrodynamic flow of non-Newtonian visco-elastic fluid through a porous medium near an accelerated plate

An exact solution is obtained for the unsteady flow of an electrically conducting visco-elastic incompressible fluid through a porous medium on an infinite flat plate. The fluid under consideration obeys the rheological equations of state due to the Walters stress–strain relation. The plate is accelerated in the presence of a uniform magnetic field. The analysis includes the case of a solid plate as well as a porous one. The solution of the equations of motion is obtained by the use of a Laplace transform. The effects of the elasticity, magnetic field, permeability of the porous medium, and the suction of the plate on the velocity distribution, as well as on skin friction, are discussed. The analytical results are confirmed numerically. It is found that the velocity distribution increases with an increase of both elasticity and permeability, while it decreases as the magnetic parameter increases. It is also found that the skin friction decreases with an increase in the magnetic field and elasticity parameters, while it increases with an increase of both the permeability of the porous medium and the suction of the plate.PACS Nos.: 47.50.+d, 47.55.Mh, 47.85.Dh

On the dispersion of a solute in Poiseuille flow of a third-grade fluid in a channel

Gill and Sankarasubramanian's analysis of the dispersion of Newtonian fluids in laminar flow between two parallel walls are extended to the flow of non-Newtonian viscoelastic fluid (known as third-grade fluid) using a generalized dispersion model which is valid for all times after the solute injection. The exact expression is obtained for longitudinal convective coefficient K 1( Γ), which shows the effect of the added viscosity coefficient Γ on the convective coefficient. It is seen that the value of the K 1( Γ) for Γ≠0 is always smaller than the corresponding value for a Newtonian fluid. Also, the effect of the added viscosity coefficient on the K 2( t, Γ) (which is a measure of the longitudinal dispersion coefficient of the solute) is explored numerically. Finally, the axial distribution of the average concentration C m of the solute over the channel cross-section is determined at a fixed instant after the solute injection for several values of the added viscosity coefficient.

Generalized flow analysis of non-Newtonian visco-elastic fluid flow through fractal reservoir

In this paper, fractal geometry theory is used to combine with the seepage flow mechanics to establish the relaxation models of non-Newtonian visco-elastic fluid flow in fractal reservoirs. A method to scale the fractal properties of a fractal reservoir by the double parameters (df, ds) and to describe the generalized flow characteristics of visco-elastic fluid by four parameters (df, ds, λ y , λ p ) are presented. Exact solutions and asymptotic solutions have been obtained by using the Laplace-Weber and Laplace-orthogonal transforms with both infinite and finite reservoirs. The pressure transient behavior of non-Newtonian visco-elastic fluid flow through a fractal reservoir are studied by using the numerical Laplace transform inversion and asymptotic solutions. The law of pressure change for various fractal parameters is obtained.

Viscoelastic Fluid Flow in the Entrance of A Tube

A semi-empirical method is presented which permits the prediction of the entrance length and entrance pressure drop of laminar flow of non-Newtonian viscoelastic fluid into the entrance of a circular tube. The only information required for this calculation is the knowledge of pipe diameter, mean velocity, and rheological parameters of the fluid. In addition, data are presented concerning the laminar flow of aqueous solutions of ET-597, a Dow Chemical long-chain polymer, both in the entrance region and in the established zone. Data for laminar flow in the established zone indicate that the Fanning friction factor, f , and the generalized non-Newtonian Reynolds number, R', have the relationship f = 16/R'. Also, it is found that above a certain mean velocity, which is a function of polymer concentration and pipe diameter, the pressure losses become less for polymeric solutions than for water.