non-Newtonian Viscoelastic Fluid Research Articles

Numerical investigation on the enhanced heat transfer characteristics of non-Newtonian viscoelastic fluids in microchannel with chip arrays

Elastic turbulence is an efficient heat transfer method at microscale. In this work, we conduct a systematic investigation on the flow and heat transfer performances of viscoelastic polymer solutions in microchannels with chip arrays by means of high-fidelity numerical simulations. Focusing on the effects of fluid elasticity [i.e. polymer relaxation time (λ)] and flow Reynolds number (Re), we find that the synergistic interplay between inertial and elastic forces is strategically exploited to amplify convection, thereby facilitating an enhanced heat transfer performance. For highly elastic fluid, the Nusselt number (Nu) can be improved by 76.13 % compared to that of less elastic fluid, while the pressure drop is reduced appropriately. In addition, as the fluid elasticity increases, the pressure drop decreases and eventually converges to a constant. In the zone of elastic turbulence, the fluid reinforces the convective heat transfer, which can be ascribe to the deformation of long-chain polymer molecules. Particularly, we consider the effect of temperature-dependent λ on the heat transfer performance. Our results demonstrate that the increased temperature-dependent λ decreases the value of Nu, and the variation between values of variable and constant λ is reduced with increasing Re or λ. Hence, in some cases of large fluid elasticity or high Re, it is possible to safely ignore the impact of temperature-dependent λ with an acceptable accuracy. The present work provides important insights into the enhanced heat transfer via elastic turbulence, which could guide the applications in the field of chip cooling.

Improving the prediction of turbulent kinetic energy for drag reduction in turbulent viscoelastic pipe flow

Reducing turbulence in pipe flows using polymer additives is crucial for industrial applications like crude oil, water, and sewage transportation. While previous research has accurately predicted friction factor and velocity profiles, none has fully understood turbulent kinetic energy (TKE) behavior in such fluids. Authors are now focusing on exploring turbulence models to better understand the TKE behavior. In this research, we have introduced a model to improve the behavior of TKE in a modified generalized Newtonian fluid (GNF). The developed model aims to simulate the viscoelastic effects of fluids that result in drag reduction in turbulent pipe flow. The work is noteworthy as it integrates turbulence and viscoelastic components, offering a comprehensive understanding of the phenomenon. By incorporating the rheological properties of viscoelastic fluids and replacing the damping function with a non-Newtonian alternative proposed by Cruz and Pinho, the Launder–Sharma k–ε turbulence model is now suitable for simulating dilute non-Newtonian viscoelastic fluids. The viscoelastic aspect of the model employs the modified GNF model. The developed model has been subjected to simulations using the computational fluid dynamics software. The results obtained for fluid TKE demonstrate a significant improvement in comparison to our previous research and the findings of other researchers. Furthermore, the model's prediction for the Darcy friction factor has been enhanced, resulting in an average error of only 3.71% in this section. It is noteworthy that the model consistently maintains a high level of accuracy in predicting other essential flow parameters such as mean axial velocity and Reynolds stresses. The provided model advances our understanding of viscoelastic fluid behavior in turbulent pipe flow by applying the modified GNF model.

Viscoelastic nanofluids flow through Darcy–Forchheimer porous media with Newtonian conditions

This research is conducted by considering the Darcy–Forchheimer viscoelastic non-Newtonian fluids (NNF) generated by the movement of surface. Two types NNF namely Walter’s liquid B (WLB) and second grade (SG) fluids are chosen as the working fluids. Cattaneo–Christov energy diffusion model is carried out for the energy transmission analysis. Newtonian heating (NH) and Newtonian concentration (NC) conditions are imposed for the solutal and thermal analysis. The model is formulated by the application of boundary layer technique. These equations are converted into non dimensional model by the implication of similarity variables. The numeric solutions are executed by the utilization of Runge–Kutta–Fehlberg-45 order scheme. The results are presented by numeric benchmarks and graphical illustrations. A comparative discussion of WLB and SG fluids is reported. A comparative visualization shows that the higher velocity profile is achieved for SG fluid case while temperature and concentration profiles are larger in the case of SG fluid. The Brownian movement and thermophoretic constraints have similar influences on temperature. The Brownian movement constraint has reverse trends on concentration and temperature.

To seal a wound, caterpillars transform blood from a viscous to a viscoelastic fluid in a few seconds

In insects vulnerable to dehydration, the mechanistic reaction of blood after wounding is rapid. It allows insects to minimize blood loss by sealing the wound and forming primary clots that provide scaffolding for the formation of new tissue. Using nano-rheological magnetic rotational spectroscopy with nickel nanorods and extensional rheology, we studied the properties of blood dripping from the wound of caterpillars of the Carolina sphinx moth (Manduca sexta) with a high concentration of blood cells. We discovered that wound sealing followed a two-step scenario. First, in a few seconds, the Newtonian low-viscosity blood turns into a non-Newtonian viscoelastic fluid that minimizes blood loss by retracting the dripping blood back into the wound. Next, blood cells aggregate, starting from the interfaces and propagating inward. We studied these processes using optical phase-contrast and polarized microscopy, X-ray imaging, and modeling. Comparative analyses of the cell-rich and cell-poor blood of different insects revealed common features of blood behavior. These discoveries can help design fast-working thickeners for vertebrate blood, including human blood.

Elastoviscoplasticity intensifies the unstable flows through a micro-contraction geometry

This study focuses on the two-dimensional numerical investigation of complex fluid flows through a micro-contraction geometry in the creeping flow regime, specifically examining elastoviscoplastic (EVP) fluids. These fluids exhibit a combination of viscous, elastic, and plastic behaviors. The governing equations, including mass and momentum, are solved using a finite volume method-based discretization technique. Saramito’s constitutive model is utilized to accurately represent the viscous, elastic, and plastic responses of the EVP fluid. The present results demonstrate significant differences in flow dynamics, such as vortex dynamics and transitions between flow regimes (e.g., steady to unsteady), when compared to simple Newtonian and non-Newtonian viscoelastic (VE) or viscoplastic (VP) fluids. This study reveals that when the yield strain (ϵy) exceeds a critical value, approximately ranging from 0.79 to 0.89, the flow transits from a steady to an unsteady state for the EVP fluids. Importantly, the present study shows that EVP fluids exhibit intensified chaotic flow dynamics and increased instability compared to VE and VP fluids under similar flow conditions. However, the presence of shear-thinning behavior in EVP fluids suppresses this instability. The analysis of local velocity fields and flow deformation in this study highlights the impact on the stretching of fluid microstructure and elastic stresses, which ultimately contribute to the origin of this intensified unstable flow condition for EVP fluids. The finding from this study holds significant potential for enhancing heat or mass transfer rates and mixing efficiency in micro-scale systems, where the prevailing steady and laminar flow conditions often hinder these transport processes.

Inverse problems for nonlinear Navier–Stokes–Voigt system with memory

This paper deals with the unique solvability of some inverse problems for nonlinear Navier–Stokes–Voigt (Kelvin–Voigt) system with memory that governs the flow of incompressible viscoelastic non-Newtonian fluids. The inverse problems that study here, consist of determining a time dependent intensity of the density of external forces, along with a velocity and a pressure of fluids. As an additional information, two types of integral overdetermination conditions over space domain are considered. The system supplemented also with an initial and one of the boundary conditions: stick and slip boundary conditions. For all inverse problems, under suitable assumptions on the data, the global and local in time existence and uniqueness of weak and strong solutions were established.

Analysis of unsteady non-Newtonian Jeffrey blood flow and transport of magnetic nanoparticles through an inclined porous artery with stenosis using the time fractional derivative

In the present study, a Caputo–Fabrizio (C–F) time-fractional derivative is introduced to the governing equations to present the flow of blood and the transport of magnetic nanoparticles (MNPs) through an inclined porous artery with mild stenosis. The rheology of blood is defined by the non-Newtonian visco-elastic Jeffrey fluid. The transport of MNPs is used as a drug delivery application for cardiovascular disorder therapy. The momentum and transport equations are solved analytically by using the Laplace transform and the finite Hankel transform along with their inverses, and the solutions are presented in the form of Laplace convolutions. To display the solutions graphically, the Laplace convolutions are solved using the numerical integration technique. The study presents the impacts of different governing parameters on blood and MNP velocities, volumetric flow rate, flow resistance, and skin friction. The study demonstrates that blood and MNP velocities boost with an increase in the fractional order parameter, Darcy number, and Jeffrey fluid parameter. The volumetric flow rate decreases and flow resistance increases with enhancement in stenosis height. The non-symmetric shape of stenosis and the rheology of blood decrease skin friction, whereas enhancement in MNP concentration increases skin friction. A comparison of the present result with the previous work shows excellent agreement. The present study will be beneficial for the field of medical science to further study atherosclerosis therapy and other similar disorders.

The HAN method for a thermal analysis of forced non-Newtonian MHD Reiner-Rivlin viscoelastic fluid motion between two disks

In this article, the semi-analytical technique of the Hybrid Analytical and Numerical Method (the HAN Method) is used to study the non-transient forced non-Newtonian MHD Reiner-Rivlin viscoelastic fluid motion that is constrained between two plates. The magnetic field is also present in this model. The governing equations are in the PDE form and by using the Von Kármán similarity variables, they transformed into a set of ODEs. The HAN-method is applied to solve the ODEs and their associated boundary conditions, analytically. In addition, for the validation, the HAN solution results were compared with the HPM and numerical technique of Runge-Kutta results. And finally, new results were extracted from the HAN solutions in a quantitative form.

Spectral Collocation Technique for Solving Two-Dimensional Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Model

Applications of non-Newtonian fluids have been widespread across industries, accompanied by theoretical developments in engineering and mathematics. This paper studies a two-dimensional multi-term time fractional viscoelastic non-Newtonian fluid model by using two autonomous consecutive spectral collocation strategies. A modification of the spectral approach is implemented, leading to an algebraic system of equations able to obtain an approximate symmetric solution for the model. Numerical examples illustrate the effectiveness of the technique in terms of accuracy and convergence.

THE PROBLEM OF THE FLOW OF ONE TYPE OF NON-NEWTONIAN FLUID THROUGH THE BOUNDARY OF A MULTI-CONNECTED DOMAIN

In this paper, the existence of a weak solution of the initial boundary value problem for the equations of motion of a viscoelastic non-newtonian fluid in a multi-connected domain with memory along the trajectories of a non-smooth velocity field and an inhomogeneous boundary condition. The study assumes the approximation of the original problem by Galerkin-type approximations followed by a passage to the limit based on a priori estimates. The theory of regular Lagrangian flows is used to study the behavior of trajectories of a non-smooth velocity field.

Transport mechanism under temperature and concentration gradient for nano-sized species in Maxwell viscoelastic fluid over cylindrical object moving with non-uniform velocity

Non-Newtonian fluids have a wide range of engineering applications, which has drawn researchers to study their puzzling rheology as well as the transport of thermal and somatic energy behaviors. The researchers provide a variety of empirical models to describe the behavior of the non-Newtonian fluids because non-Newtonian fluids alter their flow behavior in response to the applied stress. This study considered a two-dimensional transport mechanism in viscoelastic fluid over convectively heated surface moving with non-uniform velocity is modelled via simplified conservation laws by considering temperature and concentration gradients. Axisymmetric PDEs are further transformed into their dimensionless forms under similarity principle. The associated set of models are solved numerically using finite element numerical technique. Convergent mesh free solutions are further utilized in exploring the underlying physics. The significant role of temperature gradient in transporting species observed whereas impact of compositional gradient in transferring the heat energy is investigated. Brownian motion of solid nano-sized structures in viscoelastic non-Newtonian fluid is rheological observed to strongly impact the simultaneous transport of heat and mass. Convectively heated surface is also responsible for thermal enhancement. Convective transport is being accelerated by convectively varying amount of species at the convectively heat surface of cylindrical body.

CFD-PBM simulation of PET and supercritical CO2 microcellular foaming

By loading Cross model and Oldroyd-B model with User-defined Function (UDF) program, a method to simulate the extrusion flow of viscoelastic non-Newtonian fluid in Fluent software was proposed. In the homogeneous solution of Polyethylene terephthalate (PET) and supercritical CO2, the microscopic bubble growth kinetics model was coupled with the Population Balance Module (PBM), analysis effect of shear rate on bubble nucleation and growth, numerically simulated of the nucleation and growth of bubbles in the extrusion die of PET microcellular foam sheet. Through analysis, the bubble size distribution is more uniform under the condition of 60° template convergence angle. The larger the extrusion speed, the wider the uniform distribution range of bubble density at the outlet position. The initial concentration of CO2 has the greatest impact on the bubble density. Increasing the initial concentration of CO2 can improve the bubble density, but appropriately reducing the initial concentration of CO2 can improve the effective distribution range of bubble density of foam sheet.

Flow of Viscoelastic Fluid with Microrotation at a Boundary Layer Flow of a Horizontal Circular Cylinder

In this study, the dynamics of the non-Newtonian viscoelastic fluid with microrotation at a boundary layer of a horizontal circular cylinder is investigated. For this case, Lorentz force is induced by external magnetic field positioned at right angle of the fluid flow, hence the magnetohydrodynamic effect is embedded in the momentum equation of the proposed model in addition to other governing parameters. The constitutive equations are converted to dimensionless form along with the associated boundary conditions before the resulting partial differential equations are solved using finite difference technique in Fortran programming. Results are validated before the velocity and microrotation profiles are examined and the effects of material, viscoelastic and magnetohydrodynamic parameter on the flow is discussed.

Determination of pressure from nonlinear equations of nonhomogeneous non-newtonian fluids

In this paper, the initial-boundary problem for a system of nonlinear equations modified by p-laplacian diffusion and nonlinear damping term, in which describe the motion of a non-homogeneous (with unknown and non constant density ) incompressible viscoelastic non-Newtonian fluids is considered. Usually, a pressure does not include in the definition of weak generalized solution to equations of hydrodynamics for incompressible fluids, because weak solutions consider in the solenoidal space due to the incompressibility (continuity) equation. In the classical hydrodynamic equations, after determining a velocity and a density, a pressure can be determined by using the theorem of a representation of the space L2(Ω) into the direct sum of two orthogonal subspaces. The recovering of a pressure from the nonlinear equations of hydrodynamics modified by p-laplacian and nonlinear damping term requires a new approches. Here, under a suitable conditions on the data of the problem, a pressure has been uniquelly determined from the initial-boundary value problem for the system of nonlinear modified equations describing the motion of nonhomogeneous (with unknown and non constant density ) incompressible viscoelastic non-Newtonian fluids. The main functional spaces and necessary axuillary conclusions are introduced. A space of generalized weak solutions is identified. The pressure uniquelly recovered by using the known de-Ram lemma.

Computation of MHD flow of three-dimensional mixed convection non-Newtonian viscoelastic fluid with the physical aspect of gyrotactic microorganism

The present work is established for the examination of the MHD flow of three-dimensional mixed convection non-Newtonian viscoelastic nanofluid containing the gyrotactic microorganism toward the stretched sheet in a porous media. The Darcy-Forchheimer along with thermal radiation effects are evaluated. For the computation of the heat transmission mechanism, the theory of the Cattaneo-Christov heat flux in place of classical Fourier’s law is used. The effect of the thermal relaxation time parameter over the boundary layer is predicted by using this theory of the Cattaneo-Christov heat flux problem. Further, the study of Brownian motion and thermophoretic influence are scrutinized. The problem formulation is formulated in the form of momentum equations in and directions, energy, mass and gyrotactic microorganism equations under the convective boundary condition. The analytical simulations of the current problem are performed by using the homotopic analysis scheme in a MATHEMATICA 12 software. The graphical investigation of the velocities in the directions of and axes, temperature, concentration and gyrotactic microorganism profiles of the nanofluid for numerous estimations of the distinct flow parameters are also elaborated. The physical aspect of the skin friction coefficients, Nusselt number, Sherwood number and density number of microorganisms are accomplished versus different flow parameters in a pictorial form. Some of the main results of the current problem are that intensifying estimations of the viscoelastic fluid parameter and magnetic field parameter increased the nanofluid velocity in direction. It is noted that the temperature of the nanoliquid is lesser for larger estimations of the Prandtl number and thermal relaxation time parameter. It is scrutinized that the Nusselt number of the nanoliquid is increased due to the increasing of radiation parameter.

Error Bounds of a Finite Difference/Spectral Method for the Generalized Time Fractional Cable Equation

We present a finite difference/spectral method for the two-dimensional generalized time fractional cable equation by combining the second-order backward difference method in time and the Galerkin spectral method in space with Legendre polynomials. Through a detailed analysis, we demonstrate that the scheme is unconditionally stable. The scheme is proved to have min{2−α,2−β}-order convergence in time and spectral accuracy in space for smooth solutions, where α,β are two exponents of fractional derivatives. We report numerical results to confirm our error bounds and demonstrate the effectiveness of the proposed method. This method can be applied to model diffusion and viscoelastic non-Newtonian fluid flow.

AN INITIAL-BOUNDARY VALUE PROBLEM FOR KELVIN-VOIGT EQUATIONS WITH (p(x), q(x),m(x))- STRUCTURE

The proof of the global in time existence of solutions of initial-boundary value problems for nonlinear equations in many The proof of the global in time existence of solutions of initial-boundary value problems for nonlinear equations in many cases,  is not easy, even in some cases it is impossible. However, by showing some qualitative properties of its solution, one can find answers to such questions. For example, by establishing the blow up in a finite time property of a solution, one can show that a solution does not exist globally in time. Such way, in last years, the investigating the quality properties of solutions as localization and/or blow up in a finite time, has been developing rapidly In this paper, we study the initial-boundary value problem for the Kelvin-Voigt equations with both of diffusion and relaxation term, modified by (p(x),q(x))-Laplacian, respectively, and with the variable exponent damping term. The damping term in the equation realizes as nonlinear source term. In this work, we study the nonlinear initial-boundary value problem for generalized Kelvin-Voigt equations describing the motion of incompressible viscoelastic non-Newtonian fluids. The equations generalized by replacing the diffusion and relaxation terms in equation with p(x)-Laplacian and q(x)-Laplacian, respectively, and adding a nonlinear absorption term with variable exponents and coefficients. The definition of a weak solution is given. Under suitable conditions for variable exponents and coefficients, and data of the problem, the blow up of weak solutions are established.

Double diffusive convective motion in a reactive porous medium layer saturated by a non-Newtonian Kuvshiniski fluid

The impact of chemical reactions on the double-diffusive convective motion in a non-Newtonian viscoelastic fluid (Kuvshiniski type) saturated porous layer is examined applying both linear and nonlinear stability techniques. The Darcy model that includes the Kuvshiniski type viscoelastic effect of viscoelastic fluid and the Boussinesq estimation is employed as the momentum equation. The conditions for the occurrence of the stationary and oscillatory style of convective motions are determined by applying linear stability theory in terms of a critical thermal Rayleigh–Darcy number. Using the weakly nonlinear stability analysis, the convective heat and mass transfers are calculated. It is observed that the occurrence of oscillatory convection is possible only if the value of the solute Rayleigh–Darcy number is negative and also depends on other involved physical parameters. With rising values of the Kuvshiniski parameter and the heat capacity ratio, the range of the solute Rayleigh–Darcy number in which oscillatory convection is privileged diminishes, whereas it grows with the chemical reacting parameter and the Lewis number. The critical thermal Rayleigh–Darcy number at which the convective motion occurs increased nearly 3% with a 15% increase in the value of the Kuvshiniski parameter. Furthermore, the convective heat and mass transfers are reduced by growing the Kuvshiniski parameter and the heat capacity ratio, while both are enhanced by increasing the thermal Rayleigh–Darcy number and the solute Rayleigh–Darcy number.

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].