Thermal analysis of nonsymmetric stress tensor on a partially ionized viscoelastic non-Newtonian fluid flow with convective boundary conditions (A numerical study)

Reduced-order models have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably reduced computational cost. In contrast, the reduced-order modeling of non-Newtonian viscoelastic fluid flows remains relatively unexplored. This work leverages the sparse identification of nonlinear dynamics (SINDy) algorithm to develop interpretable reduced-order models for a broad class of viscoelastic flows. In particular, we explore a benchmark oscillatory viscoelastic flow on the four-roll mill geometry using the classical Oldroyd-B fluid. This flow exemplifies many canonical challenges associated with non-Newtonian flows, including transitions, asymmetries, instabilities, and bifurcations arising from the interplay of viscous and elastic forces, all of which require expensive computations in order to resolve the fast timescales and long transients characteristic of such flows. First, we demonstrate the effectiveness of our data-driven surrogate model in predicting the transient evolution on a simplified representation of the dynamical system. We then describe the ability of the reduced-order model to accurately reconstruct spatial flow field in a basis obtained via proper orthogonal decomposition. Finally, we develop a fully parametric, nonlinear model that captures the dominant variations of the dynamics with the relevant nondimensional Weissenberg number. This work illustrates the potential to reduce computational costs and improve design, optimization, and control of a large class of non-Newtonian fluid flows with modern machine learning and reduced-order modeling techniques.

Reduced-order models (ROMs) have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably reduced computational cost. In contrast, the reduced-order modelling of non-Newtonian viscoelastic fluid flows remains relatively unexplored. This work leverages the sparse identification of nonlinear dynamics (SINDy) algorithm to develop interpretable ROMs for viscoelastic flows. In particular, we explore a benchmark oscillatory viscoelastic flow on the four-roll mill geometry using the classical Oldroyd-B fluid. This flow exemplifies many canonical challenges associated with non-Newtonian flows, including transitions, asymmetries, instabilities, and bifurcations arising from the interplay of viscous and elastic forces, all of which require expensive computations in order to resolve the fast timescales and long transients characteristic of such flows. First, we demonstrate the effectiveness of our data-driven surrogate model to predict the transient evolution and accurately reconstruct the spatial flow field for fixed flow parameters. We then develop a fully parametric, nonlinear model capable of capturing the dynamic variations as a function of the Weissenberg number. While the training data are predominantly concentrated on a limit cycle regime for moderate , we show that the parametrized model can be used to extrapolate, accurately predicting the dominant dynamics in the case of high Weissenberg numbers. The proposed methodology represents an initial step in applying machine learning and reduced-order modelling techniques to viscoelastic flows.

Simulations of variable concentration aspects in a fractional nonlinear viscoelastic fluid flow

A novel finite volume method about the boundary layer flow and heat transfer of fractional viscoelastic fluid over a moving plate with convective boundary condition is developed. The fractional Maxwell model and fractional Fourier's law are employed in the constitutive relations. Numerical solutions are obtained and validated by exact solutions of special case with source terms. The effects of fractional parameters on the flow and heat transfer characteristics are analyzed. Results show that the viscoelastic fluid performs shear-thickening property with the increase of fractional parameter. Moreover, the variations of the average Nusselt number demonstrate that the viscoelastic fluid characterized by fractional Fourier's law has short memory in heat conduction process.

Viscoelastic fluids are a type of non-Newtonian fluids which are formed by complex internal structures and high-molecular-weight, whose typical examples are the polymer solutions and molten polymers. Also, the viscoleastic fluid flow presents a combination of two fluid properties: viscosity and elasticity. The main characteristic regarding the behavior of these flows is the strong dependence of the stresses on the flow history. Due to this complexity, computing the viscoelastic fluid flow involves a wide range of difficulties, in particular when elasticity becomes dominant, i.e., when the dimensionless Weissenberg number is high. These difficulties are considered one of the biggest challenges in computational rheology; this is known as the High Weissenberg Number Problem (HWNP). This study presents different strategies to deal with the numerical shortcomings that appear when the viscoelastic fluid is particularly elastic. These strategies are carried out in the Finite Element (FE) framework and by using the Variational Multiscale (VMS) formulation as stabilization approach. A term-by-term is also design. The cornerstone of this work is the application of a reformulation of the equations associated to the standard formulation, namely, the logarithmic reformulation, which permits simulating more elastic flows due to the fact that it eliminates the exponential stress profiles in the vicinity of stress singularities. Another topic addressed in this work is the study of the effect of temperature in viscoelastic fluid flow, where a two-way strategy is considered: the viscoelastic properties have now a dependence with the temperature, and the energy equation takes into account has to consider the viscous dissipation. That study is particularly interesting due to the fact that non-isothermal flow in many industrial applications. On the other hand, the incorporation of time-dependent subscales for solving the viscoelastic fluid flow problem is crucial to address two issues: the first one related with the instability produced when solving anisotropic space-time discretizations, and the second, the already mentioned exponential growth typical in viscoelastic flows with high Weissenberg number. In this work, time-dependent subgrid-scales are presented for both formulations: standard and logarithmic. Finally, as the logarithmic formulation is particularly expensive, above all when the scheme considered is monolithic, a fractional step for this formulation is designed, in which the system of equations is defined in a fully decoupled manner. This algorithm is especially useful when purely elastic instabilities need to be captured. These instabilities lead in some cases to elastic turbulence: a physical phenomenon in which the fluid flow becomes chaotic even for low Reynolds numbers. Los fluidos viscoelásticos son un tipo específico de fluidos no Newtonianos formados por una estructura interna muy compleja con alto peso molecular. Los ejemplos típicos de este tipo de fluidos son las soluciones y líquidos poliméricos. Además, los fluidos viscoelásticos presentan la combinación de dos propiedades específicas de los fluidos: viscosidad y elasticidad. Sin embargo, la principal característica relacionada con el comportamiento para estos flujos es la dependencia de la tensiones a la historia del fluido. Debido a su estructura y la complejidad de su comportamiento, resolver el problema de flujo viscoelástico se convierte en algo bastande difícil de abordar, en particular cuando el flujo es elástico, o en otras palabras, cuando el número adimensional Weissenberg es alto. Afrontar estas dificultades se considerada uno de los mayores retos de la reología computacional, y es conocido como el Problema de Alto Número de Weissenberg (HWNP). Este estudio presenta diferentes estrategias con el fin de evitar las dificultades numéricas que aparecen en estos casos, en que la componente elástica del fluido es muy dominante. Estas estrategias se abordan desde el marco de los Elementos Finitos cuyo método de estabilización será el de Subscalas Variacionales (VMS). Además, se diseña la estabilización término a término basada en estos métodos, que se aplicará a las formulaciones desarrolladas. Sin embargo, la piedra angular de este trabajo es la aplicación de una reformulación de las ecuaciones que describen el flujo viscoelástico, llamada formulación logaritmica, y que permite la simulación de casos más elásticos debido a que, básicamente, elimina el crecimiento exponencial de las tensiones cerca de singularidades. Otro tema que se trata en este trabajo es el efecto de la temperatura en los flujos viscoelásticos, donde se considerará un acople bidireccional con el problema térmico. Por un lado, ahora las propiedades del fluido dependen de la temperatura, y por otro, en la ecuación de energía tenemos que considerar la disipación viscosa como fuente térmica. Este estudio es interesante debido a que los fluidos viscoelásticos son sometidos a altas temperaturas en muchas aplicaciones industriales. Por otra parte, también se explora la incorporación de subescalas dependientes del tiempo en el método de estabilización. Este cambio será crucial para paliar dos tipos de problemas: el primero relacionado con la inestabilidad que se produce cuando resolvemos discretizaciones anisotropicas espacio-tiempo, y la segunda para tratar con el mencionado crecimiento exponencial que aparece cuando los flujos viscoelásticos tienen alto número de Weissenberg. Esta estrategia se aplica tanto a la formulación estándar de las ecuaciones como a la logaritmica. Finalmente, como la computación de la formulación logaritmica es cara computacionalmente, sobre todo cuando el esquema es de tipo monolítico, se ha diseñado un esquema de paso fraccionado en que el sistema de ecuaciones para esta formulación se desacopla. Este algoritmo resulta especialemnte útil para capturar inestabilidades púramente elásticas. Estas inestabilidades pueden desembocar en turbulencia elástica, que es un fenómeno físico en que el flujo se vuelve caótico a pesar de contar con un bajo número de Reynolds.

A mathematical analysis has been performed for heat and mass transfer of a time-dependent MHD flow of an electrically conducting viscoelastic fluid in nonuniform vertical channel with convective boundary condition. The fluid flow is considered between a vertical long wavy wall and a parallel flat wall saturated with the porous medium. The effects of thermal radiation, heat absorption, chemical reaction, and Hall current are taken into account. The prevailing nonlinear partial differential equations are derived by considering Boussinesq approximation, and the same equations are solved analytically using perturbation technique. Further the expressions for skin friction, Nusselt number, and Sherwood number are presented. The effects of various pertinent parameters on different flow fields are analyzed graphically and tabularly. It is found that effects of Hall parameter and Biot number are unfavorable on velocity profiles, but this trend is reverse for the effect of thermal and solutal Grashof numbers. The expressions of different flow fields satisfy the imposed boundary conditions, which is shown in all graphs; this implies accuracy of the solution.

Due to the increasing importance in processing industries and elsewhere when materials whose flow behavior cannot be characterized by Newtonian relationships, a new stage in the evolution of fluid dynamics theory is in progress. An intensive effort, both theoretical and experimental, has been devoted to problems of non-Newtonian fluids. The study of MHD flow of viscoelastic fluids over a continuously moving surface has wide range of applications in technological and manufacturing processes in industries. This concerns the production of synthetic sheets, aerodynamic extrusion of plastic sheets, cooling of metallic plates, etc. (Crane, 1970) considered the laminar boundary layer flow of a Newtonian fluid caused by a flat elastic sheet whose velocity varies linearly with the distance from the fixed point of the sheet. (Chang, 1989; Rajagopal et al., 1984) presented an analysis on flow of viscoelastic fluid over stretching sheet. Heat transfer cases of these studies have been considered by (Dandapat & Gupta, 1989, Vajravelu & Rollins, 1991), while flow of viscoelastic fluid over a stretching surface under the influence of uniform magnetic field has been investigated by (Andersson, 1992). Thereafter, a series of studies on heat transfer effects on viscoelastic fluid have been made by many authors under different physical situations including (Abel et al., 2002, Bhattacharya et al., 1998, Datti et al., 2004, Idrees & Abel, 1996, Lawrence & Rao, 1992, Prasad et al., 2000, 2002). (Khan & Sanjayanand, 2005) have derived similarity solution of viscoelastic boundary layer flow and heat transfer over an exponential stretching surface. (Cortell, 2006) have studied flow and heat transfer of a viscoelastic fluid over stretching surface considering both constant sheet temperature and prescribed sheet temperature. (Abel et al., 2007) carried out a study of viscoelastic boundary layer flow and heat transfer over a stretching surface in the presence of non-uniform heat source and viscous dissipation considering prescribed surface temperature and prescribed surface heat flux. (Khan, 2006) studied the case of the boundary layer problem on heat transfer in a viscoelastic boundary layer fluid flow over a non-isothermal porous sheet, taking into account the effect a continuous suction/blowing of the fluid, through the porous boundary. The effects of a transverse magnetic field and electric field on momentum and heat transfer characteristics in viscoelastic fluid over a stretching sheet taking into account viscous dissipation and ohmic dissipation is presented by (Abel et al., 2008). (Hsiao, 2007) studied

Many non-Newtonian visoous fluids are recently used in practice, and in consequence the chances of handling these fluids have increased in many fields. However, at present the rheological equation is not yet established for the viscoelastic non-Newtonian fluids. Experimental studies are required, therefore, of viscoelastic flow concerning its stress analysis. One of the most efficient experimental methods is considered to be the photoelastic procedure, in view of the fact that the viscoelastic fluids with velocity gradients have birefringence effect.In this paper, the results of photoelastic measurements of viscoelastic flows through narrowed portions are reported. The flow was produced in rectangular vessels as two-dimentional flow by applying pressure to the fluid, and the narrowed portions were formed by applying triangular or rectangular projections to the two opposite walls. As the viscoelastic fluid, taking the homogeneity, fluidity and transparency as well as the birefringence effect of the material into consideration, Epikote fluid was employed. An ordinary photoelastic apparatus was used, and clear isochromatic and isoclinic patterns of stressed viscoelastic fluid were obtained. The experimental results may be summarized as follows. In general, the shear stress plays an important role for the mechanical degradation of highpolymer fluids. It is significant, therefore, to predict the amount of shear stress in the flow of such fluids, In the viscoelastic flows through the narrowed portions experimented in this study, the maximum shear stress appeared at the corner of each projection. Moreover, the shear stresses along the flow direction midway between both the projections showed peak values at the points a short distance ahead or behind the corners of the projections.

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 x - and y - 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 x - and y - 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 x - 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.

Viscoelastic fluid flow over a moving vertical cone and flat plate with variable electric conductivity

The temperature variation within two elastic bodies in perfect thermoelastic contact may cause the contact area to become convex and hence lead to a reduction in the size of the contacting surface. In receding thermoelastic contact problems, the final size of the contact zone is independent of the applied loads, being only affected by the thermomechanical properties of the solids. However, the final size of the contact zone can also be affected by the conductive and convective boundary conditions at the separation zones of the contacting surfaces. In those regions, the heat flux is a function of the separation between the solids, so the thermal and the thermoelastic problems are highly coupled. For this reason, this work studies the three-dimensional receding thermomechanical contact problem under conductive and convective boundary conditions at the interstitial zones of the contact area. After the validation of the numerical scheme presented to solve this problem, several examples are presented and discussed in detail. The results reveal that conductive and convective interstitial boundary conditions have a significant effect not only on the size of the contact zone, but also on the resulting tractions, temperature and heat flux distributions.

Experimental study on the characteristics of heat transfer and flow resistance in turbulent pipe flows of viscoelastic-fluid-based Cu nanofluid

The present paper deals with the investigation of the internal heat sink and magnetic field effects on natural convection oscillatory heat and mass transfer of an electrically conducting micropolar fluid flow over a vertical plate in a porous medium in the presence of chemical reaction and thermal radiation with convective boundary condition. The governing equations are converted into their dimensionless form by using non-similar transformations. The governing coupled non-linear partial differential equations are then converted into ordinary differential equations using perturbation analysis. These equations are then solved analytically with appropriate convective thermal and solutal boundary conditions valid at the porous interface. The effect of Prandtl number, heat sink parameter, Schmidt number, thermal radiation, magnetic field, chemical reaction and permeability parameter are analyzed on the temperature and concentration distributions, and local Nusselt number. The results obtained from the computation of analytical results are depicted graphically. The results show that the effects of viscosity ratio, magnetic field and internal heat sink decrease the frictional coefficient and concentration distribution at the wall whereas reverse effects are seen on the local Nusselt number.

This article reports the magnetohydrodynamic (MHD) three-dimensional flow of viscoelastic fluid over a stretching surface with heat transfer. Mathematical analysis is formulated using convective boundary conditions. Computations of dimensionless velocity and temperature fields are presented. The tabulated values show excellent agreement between present and previous limiting analysis. Graphical results show the impact of embedded parameters entering into the problem.

In the present paper we have Analysis of hydro magnetic flow of visco elastic fluid. Hydro magnetic visco elastic fluid flow between two horizontal infinite parallel porous plates with time varying sinusoidal pressure gradient and magnetic field has been discussed in the present study. The visco elasticity in an effective approach to modeling the dissipative mechanism. Some interesting observations are low-frequency oscillating pressure gradient Prevents back flow, significant reduction in skin frictions is observed by embedding the channel in porous medium and magnetic field and elasticity decelerate the fluid flow and also in this paper a Theoretical Analysis is carried out of study the visco elastic effects on hydro magnetic heat & mass transfer in a vertical channel. The two vertical plates are in porous medium and non-uniform wall temperatures. A magnetic field of uniform strength is applied in the direction perpendicular to the plates. The visco elastic fluid flow is characterized by second order fluid. The effects of different flow parameters on skin friction are analyzed and illustrated graphically.