Upper-convected Maxwell Fluid Research Articles

Impact of chemical reaction on the Cattaneo–Christov heat flux model for viscoelastic flow over an exponentially stretching sheet

In this article, the numerical solutions for the heat transfer flow of an upper-convected Maxwell fluid across an exponentially stretched sheet with a chemical reaction on the Cattaneo–Christov heat flux model have been investigated. Using similarity transformation, the controlling system of nonlinear partial differential equations was transformed into a system of ordinary differential equations. The resulting converted equations were solved numerically by a successive linearization method with the help of MATLAB software. A graphic representation was created to analyze the physical insights of the relevant flow characteristics. The findings were presented in the form of velocity, temperature, and concentration profiles. As the relaxation time parameter varied, the local Nusselt number increased. The thermal relaxation time was shown to have an inverse relationship with fluid temperature. Furthermore, the concentration boundary layer becomes thinner as the levels of the reaction rate parameter increase. The results of this model can be applicable in biological fluids and industrial situations. Excellent agreement exists between the analysis's findings and those of the previous studies.

Thermal stratification and heat generation/absorption impacts on stagnation point flow of MHD UCM fluid through a permeable medium

We investigated two dimensional magnetohydrodynamic (MHD) stagnation point upper-convected Maxwell (UCM) fluid flow through a stretch sheet in a porous medium having the effects of heat generation/absorption and thermal stratification. Utilizing suitable similarity transformations, the governing partial differential equations (PDEs) of the fluid flow and heat transfer phenomena are converted to nonlinear dimensionless ordinary differential equations (ODEs). We numerically solved these nonlinear ODEs and compared our results of skin friction and Nusselt number with previous work which demonstrated accuracy of the presented solutions. We also illustrated the graphical behavior of dependent variables that is of the velocity and temperature fields versus the key parameters involved. It showed that velocity field decreases for Deborah number, porosity and magnetic parameters. The temperature of the fluid showed an increasing behavior for Deborah number, magnetic, porosity, and heat source/sink parameters while declining for thermal stratification and velocity ratio parameters.

Numerical analysis of inclined magnetic force impact on cross liquid flowing with widening shallow and heat generating

ABSTRACT The creation, utilisation, conversion, and exchange of thermal energy are all covered under the thermal engineering subject of heat transfer. Heat transfer plays a major role in engineering and industrial sectors like food packaging, food additive manufacturing, electronic cooling, microturbine, etc. Scientists across the world have tried to explore the impact of heat transfer on fluid past an expandable surface due to its exciting applications in industries like polymer production, paper production, crystal glass manufacturing, etc. This article has unique exploration, and it emphasises interpreting the Cross fluid flow along stretching surface with convective heat transport analysis by using the Lie group methodology. We investigated the implication of inclined upper-convected Maxwell fluid magnetohydrodynamic (MHD) movement through a penetrable strained plate. To solve nonlinear differential equations and clearly determine their absolute invariants, the Lie group approach is introduced. For the numerical solution of non-linear ordinary differential equations with boundary conditions, the fourth-order Runge–Kutta procedure with shelling performance is utilised. Plots showing the impacts of motivated and non-motivated MHD are researched and examined for the alterations of many parameters, and statistical graphs are given to explain the physical values. It is evident that opposing behaviour occurs in connection to temperature captivation and generation parameters together with motivated and non-motivated MHD. Under an amplified, heat-generating parameter and Deborah number, the rate of heat transmission increases. The Lie group investigation of Cross liquid in the presence/absence of inclined and non-inclined has not been investigated yet in the available literature.

Induced upper-convected Maxwell fluid flow in a cylinder oscillating longitudinally and torsionally with slip at the boundary

Induced upper-convected Maxwell fluid flow in a cylinder oscillating longitudinally and torsionally with slip at the boundary

MHD Darcy–Forchheimer flow and double-diffusive modeling of Maxwell fluid over rotating stretchable surface: A computational study

In this work, the Cattaneo–Christov double diffusion model is used to analyze the three-dimensional boundary layer flow of an upper-convected Maxwell fluid flowing over a bi-directional stretching surface. The model assumes that the fluid’s diffusivity is concentration-dependent, whereas dynamic viscosity and thermal conductivity are temperature-dependent; and the model takes into account the influence of the magnetic field of uniform strength. The problem is formulated using the conservation rules of mass, momentum, and energy as well as the boundary layer approximation. The resulting nonlinear system is then numerically solved using the bvp4c procedure in MATLAB. The obtained results are set forth graphically to illustrate the variations of different parameters. It is contemplated that the increase in thermal relaxation parameter results in a drop in fluid temperature while there is an enhancement in the concentration profile. Also, the temperature field has a direct relationship with the temperature-dependent viscosity. This research has proven its utility in industries where there is a need to analyze fluid flow over surfaces that can stretch in two directions.

Tricritical state and quasi-periodicity triggered by the non-linear elasticity in an Upper Convected Maxwell fluid confined between two co-oscillating cylinders about zero-mean

The effects of harmonically co-oscillating the inner and outer cylinders about zero mean rotation in a Taylor–Couette flow are examined numerically using Floquet theory, for the case where the fluid confined between the cylinders obeys the upper convected Maxwell model. Although stability diagrams and mode competition involved in the system were clearly elucidated recently by Hayani Choujaa et al. (2021) in weakly elastic fluids, attention is focused, in this paper, on the dynamic of the system at higher elasticity with emphasis on the nature of the primary bifurcation. In this framework, we are dealing with pure inertio-elastic parametric resonant instabilities where the elastic and inertial mechanisms are considered of the same order of magnitude. It turns out, on the one hand, that the fluid elasticity gives rise, at the onset of instability, to the appearance of a family of new harmonic modes having different axial wavelengths and breaking the spatio-temporal symmetry of the base flow: invariance in the axial direction generating the O(2) symmetry group and a half-period-reflection symmetry in the azimuthal direction generating a spatio-temporal Z2 symmetry group. On the other hand, new quasi-periodic flow emerging in the high frequency limit and other interesting bifurcation phenomena including bi and tricritical states are also among the features induced by the fluid elasticity. Lastly, and in comparison with the Newtonian configuration of this system, the fluid elasticity leads to a total suppression of the non-reversing flow besides emergence of instabilities with lower wavelengths. Such a comparison provides insights into the dynamics of elastic hoop stresses in altering the flow reversal in modulated Taylor–Couette flow.

Analysis of MHD and Heat Transfer Characteristics of Thermally Radiative Upper-Convected Maxwell Fluid Flow between Moving Plates: Semi-Analytical and Numerical Solution

The current paper studies the MHD and heat transfer characteristics of radiative upper-convected Maxwell fluid flow between two plates approaching or receding from each other with injection at the fixed lower porous plate. The governing momentum and energy equations are reduced into non-linear ordinary differential equations employing similarity transformations. With the help of the Homotopy Perturbation Method (HPM), an approximate analytic solution is obtained. This work aims to determine the effects of Reynolds number (R), Deborah number (De), Radiation parameter (Rd), Magnetic parameter (M), and Prandtl number (Pr) on the velocity and temperature profiles. It is observed that the Deborah number has a direct impact on the velocity profile when there is a squeezed flow. It is also observed that the magnetic parameter shows an indirect impact on the temporal distribution for both the upper plate moving away and towards the lower. The variations in the significant physical parameters on the coefficient of skin friction and heat transfer rates are also calculated. The results are then compared with the classical finite difference method and are in excellent agreement. It is found that larger the magnetic parameter, the dominance of viscous forces retards the velocity in the core region, and the increase in radiation parameter suppresses the heat transfer rates. This study is helpful in industrial applications, specifically in polymer processing.

Radiation Effect on Heat Transfer Analysis of MHD Flow of Upper Convected Maxwell Fluid between a Porous and a Moving Plate

Radiation Effect on Heat Transfer Analysis of MHD Flow of Upper Convected Maxwell Fluid between a Porous and a Moving Plate

A comparative study on the rheological properties of upper convected Maxwell fluid along a permeable stretched sheet

The objective of this paper is to examine the flow of a non-Newtonian Maxwell fluid induced by a permeable stretching sheet in motion within a porous medium. The research incorporates the Cattaneo-Christov heat flux model to study the heat transfer process. The utilization of the Cattaneo-Christov heat flux approach becomes relevant in scenarios involving materials with high thermal conductivity or during short time intervals. Consequently, the current investigation holds significant importance. It is assumed that the viscosity of the Maxwell fluid changes exponentially as the temperature changes. The modeling of the physical phenomena being investigated takes into account the effects of a magnetic field, thermal radiation, velocity, and thermal slip conditions. In this study, the viscous dissipation phenomenon is taken into account because it can have notable impacts on the temperature and viscosity of the fluid, and is known to play a crucial role in fluid flow phenomena. The equations developed to model fluid flow are transformed into nonlinear ordinary differential equations through the use of appropriate similarity transformations. The focus of the research revolves around investigating the numerical solution of ordinary differential equations accompanied by boundary conditions using the shooting technique. The findings are then showcased via tables and graphs and scrutinized in order to arrive at conclusions. Furthermore, the precision of the present findings was evaluated by contrasting the heat transfer rate with outcomes that were previously published. Based on the obtained outcomes, it can be concluded that both the Eckert number and thermal radiation have a comparable enhancing influence, whereas the thermal relaxation parameter and thermal slip parameter exhibit opposing effects.

Chemically Radiative and Slip Effects on MHD Heat and Mass Transfer Flow of Maxwell Nanofluid across an Inclined Surface

In both the laboratory and the manufacturing setting, nanofluids play a crucial role in improving the thermal properties of pure fluids. The heat and mass transmission of an incompressible upper-convected Maxwell fluid along a stretched sheet in the midst of heat radiation, chemical changes, and suction is investigated. The nonlinear slip condition for the Maxwell fluid is put into account herein. The diffusion model for mass and heat transfer introduced by Cattaneo and Christov is incorporated in the modelling process. The partial differential equations that regulate the system are reduced into a more fundamental form via similarity transformations. Mathematica's NDSolve technique is implemented to do a numerical treatment of the dimensionless equations once they have been translated. The upsides of this strategy lie in its ability to automatically track errors and select the best algorithm. Assessments are taken of velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number, among others. Graphs are used to quickly illustrate and clarify how various material qualities affect the flow of mass and heat transmission. Thermal relaxation and chemical reaction parameters minimize temperature and concentration fields. It is observed that greater Maxwell parameters implies a rise in the intensity of skin friction, whereas a spike in the slip parameter generates a decrease. Nusselt and Sherwood numbers diminish with Maxwell parameter.

Steady-state simulation of the film-casting process for Newtonian and viscoelastic fluids

Thin polymeric films are usually produced in an extensional flow between an extrusion head and a chill roll. The final product is prone to several defects, such as reduced width and non-uniform thickness, and a better understanding of the whole process can improve the final product quality and reduce wastes. This work revisits the film-casting process by exploring the scaling relation between different variables, with particular focus on the width reduction (neck-in). The numerical simulations are carried out for Newtonian, Upper-Convected Maxwell and Giesekus fluids in isothermal and steady-state conditions, for varying film aspect ratio (AR; film width over length), draw ratio (DR) and Deborah number (De). The governing equations are discretized with finite-volumes in their full form (3D model) and using an approximate 2.5D model. However, the latter has been mainly used in this study, as it offered similar accuracy as the 3D model, at a much lower computational cost. The results show that the normalized film shape is independent of the aspect ratio for sufficiently high values of this parameter and that the film thickness scales with DR according to the theoretical prediction for planar and uniaxial extensional flows, in the centre and edge regions, respectively. The neck-in grows logarithmically with the draw ratio for high AR, with a De-dependent growth rate (higher De leads to lower neck-in and lower dependence on DR). There is a reasonable correlation between the neck-in and the ratio between the planar and uniaxial extensional viscosities, as well as between the neck-in and dimensionless variable M = ln(DR)/(De+δ), where δ is a constant which depends on the fluid rheology. However, none of the correlations offer a perfect fit to the neck-in and the search for such a correlation (or master curve) shall be pursued in future works.

Analysis of the unsteady upper-convected Maxwell fluid having a Cattaneo–Christov heat flux model via two-parameters Lie transformations

Analysis of the unsteady upper-convected Maxwell fluid having a Cattaneo–Christov heat flux model via two-parameters Lie transformations

Squeeze flow of a Maxwell fluid between two parallel disks or two spheres

In this study, we investigated the squeeze flow of an upper convected Maxwell fluid between two rigid disks or spheres. It has been proved that the velocity field of the Maxwell squeeze flow between two disks is similar to Newtonian at low Deborah numbers. Based on the Newtonian fluid velocity field, we analyze the pressure distribution between two parallel disks and develop a theoretical model of normal squeeze force. We also use the same method to analyze the interaction between two nearly contacting, arbitrary rigid spheres. We obtained the analytical expression of the pressure distribution and normal squeeze force, which can be implemented into the contact model for the discrete element simulation of a wet particle system with the Maxwell fluid.

Mathematical Modeling on Magnetohydrodynamics Upper Convected Maxwell Fluid Flow Past a Flat Plate Using Spectral Relaxation Approach

The focus of this treatise is on the scrutiny of MHD heat and mass transfer motion of upper convection Maxwell (UCM) fluid in a thermally radiated flat plate. The models of the flow equations were considered when there is a temperature difference: the Cattaneo-Christov model and the Soret-Dufour mechanisms. A magnetic field of firmness was inflicted in opposition to the flow. The flow inspection is controlled by partial differential equations (PDEs). Suitable similarity variables were utilised on the PDEs to obtain a set of nonlinear ordinary differential equations (ODEs). The simplified set of ODEs shall be answered by exploiting the spectral relaxation method (SRM). The SRM is a numerical technique that solves differential equations by utilising the repetition of a sequence of operations that is iterated iteratively by first decoupling the coupled systems of equations. The magnetism was found to decline the velocity and hydrodynamic boundary layer due to the Lorentz force. The Deborah number was found to enhance the velocity contour. The Eckert number was discovered to improve the temperature profile due to the production of heat energy within the boundary layer. An increase in Prandtl number was found to enhance the hydrodynamic and thermal boundary layer thickness. The local skin friction and Nusselt number were found to be elevated by the increase in the Dufour parameter.

MHD gyrotactic microorganisms upper convected Maxwell fluid flow in the presence of nonlinear thermal radiation: numerical approach Lobatto IIIA technique

MHD gyrotactic microorganisms upper convected Maxwell fluid flow in the presence of nonlinear thermal radiation: numerical approach Lobatto IIIA technique

Entropy formation analysis for magnetized UCM fluid over an exponentially stretching surface with PST and PSHF wall conditions

<abstract> <p>This article aims to demonstrate the formation of entropy due to variable thermal conductivity, radiation, and fluid friction irreversibilities for a three-dimensional upper-convected Maxwell (UCM) fluid. The fluid motion occurs as a result of exponential stretching sheets. Separate discussions are held regarding the entropy generation related to the prescribed surface temperature and prescribed surface heat flux. Additionally, the heat transport mechanism is examined in the presence of thermal radiation. The governing physical situation is first modeled and then solved by using the homotopy analysis method to acquire the solution. The physical importance of relevant flow parameters is shown graphically and in tabular form. It is noted that the entropy generated is reduced with an increase in the thermal radiation parameter. Streamline patterns are also drawn for two- and three-dimensional UCM fluid models. Finally, the current analytical solution is found to be in agreement with the solutions in the literature.</p> </abstract>

RADIATIVE AND MHD DISSIPATIVE HEAT EFFECTS ON UPPER-CONVECTED MAXWELL FLUID FLOW AND MATERIAL TIME RELAXATION OVER A PERMEABLE STRETCHED SHEET

Combined investigation of the generalized paradox of fluid flow and heat flux with upper-convected Maxwell (UCM) fluid and the Cattaneo-Christov model over a porous stretchable sheet is considered. In proffering an effective fluid flow and heat conduction, Fourier's law proved faulty. Consequently, a true estimation of non-Newtonian fluid characterizations is required due to their wide application in the biomedical science and engineering industries, among others. To these, nonlinear coupled partial differential equations (PDEs) governing the aforementioned conditions are modeled and transformed to ordinary differential equations (ODEs) using adequate similarity transformation. The solutions of these ODEs were obtained using Legendre collocation method (LCM). The results identified that a rise in geometrical inclination retards the velocity field, and an increase of the Deborah number brings about retardation in the flow fields, thus indicating a highly viscous fluid. Since fluids with high Deborah number are highly elastic, there exists flow friction, hence resulting in large heat accumulation. Therein, the material relaxation phenomenon explains that more time will be needed for successful circulation/transfer of heat from one medium to another.

Linear instability of interfacial Hele-Shaw flows of viscoelastic fluids

We present a theoretical study on the role of elasticity in causing fingering or fracturing instability during the immiscible displacement process of a viscoelastic fluid by another viscoelastic fluid in a rectilinear Hele-Shaw cell. Upper convected Maxwell (UCM) models are used for both fluid layers and linear stability analysis is performed in the regime of moderate to large Deborah number. This is a generalization of Hai and Daripa (2022) where the case of a Newtonian fluid displacing an UCM fluid is considered. The elastic effect of the displacing layer has a significant impact on the overall flow stability. The dispersion relation is implicitly given by a quartic polynomial equation with coefficients depending on a modified wavenumber k ˆ , viscosity contrast η r / η l (displaced/displacing fluid), relaxation time contrast λ r / λ l and a composite parameter β inversely proportional to the flow speed U (depth averaged). Viscous effect is still the dominant mechanism in determining long wave stability (unstable if η r / η l > 1 ). The elastic effect of the displacing layer always destabilizes short waves (unstable if wavelength is shorter than λ l U ). In addition, three types of singular behaviors are found all of which are associated with elastic effects: (i) velocity becomes singular at infinitely many isolated wavenumbers (precise values are inversely proportional to λ l U or λ r U ); (ii) stress becomes singular if wavenumber exceeds certain value (can happen even for slow flow); and (iii) growth rate becomes singular at up to two wavenumbers if η r / η l , λ r / λ l and β fall within a certain range but this can always be avoided if flow is slow enough. The special cases of an UCM fluid displacing air or a viscous Newtonian fluid are also considered. • Analytic solutions for perturbations. • Explicit formulas for the dispersion relations. • Viscous effect dominates long wave stability. • The elastic effect of the displacing fluid destabilizes short waves. • Singularities associated with elasticity in connection with fracturing instability.

Convective Flow of Radiative Maxwell Nanofluid with Variable Thermo-Physical Properties

In this article, analysis has been executed to find the impact of radiation, varied thermal conductivity and varied viscosity on the steady 2 dimensional flows of nanoparticles existing Maxwell fluid past a flat surface that can be stretched. The partial differential equations which govern this flow are modified by using similarity transformations in order to form ordinary differential equations. Employing bvp4c of MATLAB software the transformed equations are solved and the results for velocity, temperature and species concentration are depicted through graphs for varying parametric values. Comparisons with previous published data of analytical methods are carried out, thereby validating the present numerical results. It has been observed that thermal conductivity as well as viscosity enhances the temperature of the fluid and nanoparticles species concentration. Also the nanoparticles existence in the fluid slows down the fluid motion. In various engineering processes and nanoscience technology, the inferences of this present study can find its applications.
 HIGHLIGHTS
 
 Investigation has been carried out on a 2 dimensional steady flow of upper-convected Maxwell fluid under the existence of the radiation and nanoparticles
 The thermo-physical properties of the fluid flow such as thermal conductivity and viscosity are taken as variable quantity
 Bvp4c solver of the software MATLAB has been used to solve the governing transformed ODEs
 With the rise in thermal conductivity and fluid viscosity, the temperature of the fluid boost up
 The existence of nanoparticles in the fluid results in deceleration of the fluid motion

Modeling and Mathematical Investigation of Blood-Based Flow of Compressible Rate Type Fluid with Compressibility Effects in a Microchannel.

In this investigation, the compressibility effects are visualized on the flow of non-Newtonian fluid, which obeys the stress–strain relationship of an upper convected Maxwell model in a microchannel. The fundamental laws of momentum and mass conservation are used to formulate the problem. The governing nonlinear partial differential equations are reduced to a set of ordinary differential equations and solved with the help of the regular perturbation method assuming the amplitude ratio (wave amplitude/half width of channel) as a flow parameter. The axial component of velocity and flow rate is computed through numerical integration. Graphical results for the mean velocity perturbation function, net flow and axial velocity have been presented and discussed. It is concluded that the net flow rate and increase in case of the linear Maxwell model, while they decrease in case of the convected Maxwell model. The compressibility parameter shows the opposite results for linear and upper convected Maxwell fluid.