Search Results (35)

Rheological complex models of various elastoviscous and viscoelastic fractional-type substances with polarized piezoelectric properties are of interest due to the widespread use of viscoelastic–plastic bodies under loading. The word “overview” used in the title means and corresponds to the content of the manuscript and aims to emphasize that it presents an overview of a new class of complex rheological models of the fractional type of ideal elastoviscous, as well as viscoelastic, materials with piezoelectric properties. Two new elementary rheological elements were introduced: a rheological basic Newton’s element of ideal fluid fractional type and a basic Faraday element of ideal elastic material with the property of polarization under mechanical loading and piezoelectric properties. By incorporating these newly introduced rheological elements into classical complex rheological models, a new class of complex rheological models of materials with piezoelectric properties described by differential fractional-order constitutive relations was obtained. A set of seven new complex rheological models of materials are presented with appropriate structural formulas. Differential constitutive relations of the fractional order, which contain differential operators of the fractional order, are composed. The seven new complex models describe the properties of ideal new materials, which can be elastoviscous solids or viscoelastic fluids. The purpose of the work is to make a theoretical contribution by introducing, designing, and presenting a new class of rheological complex models with appropriate differential constitutive relations of the fractional order. These theoretical results can be the basis for further scientific and applied research. It is especially important to point out the possibility that these models containing a Faraday element can be used to collect electrical energy for various purposes. Full article

Artificial intelligence (AI) is employed in fluid flow models to enhance the simulation’s accuracy, to more effectively optimize the fluid flow models, and to realize reliable fluid flow systems with improved performance. Jeffery fluid flow through the interstice of a cone-and-disk system is considered in this study. The mathematical description of this flow involves converting a partial differential system into a nonlinear ordinary differential system and solving it using a neurocomputational technique. The fluid streaming through the disk–cone gap is investigated under four contrasting frameworks, i.e., (i) passive cone and spinning disk, (ii) spinning cone and passive disk, (iii) cone and disk rotating in the same direction, and (iv) cone and disk rotating in opposite directions. Employing the recently developed technique of artificial neural networks (ANNs) can be effective for handling and optimizing fluid flow exploits. The proposed approach integrates training, testing and analysis, and authentication based on a locus dataset to address various aspects of fluid problems. The mean square error, regression plots, curve-fitting graphs, and error histograms are used to evaluate the performance of the least mean square neural network algorithm (LMS-NNA). The results show that these equations are consistently aligned, and agreement is, on average, in the order of 10⁻⁸. While the resting parameters were kept static, the transverse velocity distribution, in all four cases, exhibited an incremental decreasing behavior in the estimates of magnetic and Jeffery fluid factors. Furthermore, the results obtained were compared with those in the literature, and the close agreement confirms our results. To train the model, 80% of the data were used for LMS-NNA, with 10% used for testing and the remaining 10% for validation. The quantitative and qualitative outputs obtained from the neural network strategy and parameter variation were thoroughly examined and discussed. Full article

This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey’s fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional forms with appropriate boundary conditions. The study also utilizes dynamic systems theory to analyze the effects of the parameters on the streamline and to investigate the position of critical points and their local and global bifurcation of flow. The research presents numerical and analytical methods to illustrate the impact of flow rate and amplitude changes on fluid transport. It identifies three types of streamline patterns that occur: backwards, trapping, and augmented flow resulting from changes in the value of flow rate parameters. Full article

The issue of Jeffrey nanofluid peristaltic flow in an asymmetric channel being affected by an induced magnetic field was studied. In addition, mixed convection and viscous dissipation were considered. Under the supposition of a long wave length and a low Reynolds number, the problem was made simpler. The system and corresponding boundary conditions were solved numerically by using the built-in package NDSolve in Mathematica software. This software ensures that the boundary value problem solution is accurate when the step size is set appropriately. It computes internally using the shooting method. Axial velocity, temperature distribution, nanoparticle concentration, axial induced magnetic field, and density distribution were all calculated numerically. An analysis was conducted using graphics to show how different factors affect the flow quantities of interest. The results showed that when the Jeffrey fluid parameter is increased, the magnitude of axial velocity increases at the upper wall of the channel, while it decreases close to the lower walls. Increasing the Hartmann number lads to increases in the axial velocity near the channel walls and in the concentration of nanoparticles. Additionally, as the Brownian motion parameter is increased, both temperature and nanoparticle concentration grow. Full article

The bioconvective flow of a Jeffrey fluid conveying tiny particles under the effect of an oscillating stretched bidirectional surface is considered in this paper. The effects of thermal radiation and a porous medium are also investigated. The Cattaneo–Christov diffusion theories are used to analyze the heat and mass transfer phenomena. The activation energy effects are included in the concentration equation. The solved dimensionless equations system is established, based on non-dimensional variables. The analytical findings are evaluated using the homotopic analysis technique. The convergence of solutions is ensured. The results are validated by already available published findings and a good concordance is encountered. The fundamental physical aspect of flow parameters is graphically evaluated. The main results reveal that the velocity is reduced by increasing the permeability of the porous medium. An increase in the temperature occurs when the viscosity of the fluid is varied. The obtained results can be useful in thermal systems, energy production, heat transfer devices, solar systems, biofuels, fertilizers, etc. Full article

The dynamics of non-Newtonian Jeffrey fluid in conjunction with a spinning disk surface can be problematic in heating systems, polymer technology, microelectronics, advanced technology, and substantive disciplines. Therefore, the significance of the Hall current and Coriolis forces in terms of the dynamics of Jeffrey fluid flowing across a gyrating disk subject to non-Fourier heat flux was investigated in this study. A temperature-related heat source (TRHS) and exponential-related heat source (ERHS) were incorporated into the model to improve the thermal characteristics. Thermal radiation and multiple slip effects were employed in the flow system. The connected non-linear PDEs governing the transport were transmuted into non-linear ODEs and solved using the Runge–Kutta shooting technique (RKST). The results of the RKST were substantiated in previous studies and found to have adequate reliability. The numerical values of the coefficient of friction and the Nusselt number were simulated. The non-Fourier heat flux was found to have a higher rate of heat transfer (HTR) than with traditional Fourier heat flux. Furthermore, both TRHS and ERHS phenomena support the progression of HTR. The swelling effects of the Hall current influence the velocities, whilst the temperature of the Jeffrey fluid shows the opposite tendency. Furthermore, asymptotic variances were detected for larger Hall parameter values. Full article

This article examines the effects of entropy generation, heat transmission, and mass transfer on the flow of Jeffrey fluid under the influence of solar radiation in the presence of copper nanoparticles and gyrotactic microorganisms, with polyvinyl alcohol–water serving as the base fluid. The impact of source terms such as Joule heating, viscous dissipation, and the exponential heat source is analyzed via a nonlinear elongating surface of nonuniform thickness. The development of an efficient numerical model describing the flow and thermal characteristics of a parabolic trough solar collector (PTSC) installed on a solar plate is underway as the use of solar plates in various devices continues to increase. Governing PDEs are first converted into ODEs using a suitable similarity transformation. The resulting higher-order coupled ODEs are converted into a system of first-order ODEs and then solved using the RK 4th-order method with shooting technique. The remarkable impacts of pertinent parameters such as Deborah number, magnetic field parameter, electric field parameter, Grashof number, solutal Grashof number, Prandtl number, Eckert number, exponential heat source parameter, Lewis number, chemical reaction parameter, bioconvection Lewis number, and Peclet number associated with the flow properties are discussed graphically. The increase in the radiation parameter and volume fraction of the nanoparticles enhances the temperature profile. The Bejan number and entropy generation rate increase with the rise in diffusion parameter and bioconvection diffusion parameter. The novelty of the present work is analyzing the entropy generation and solar radiation effects in the presence of motile gyrotactic microorganisms and copper nanoparticles with polyvinyl alcohol–water as the base fluid under the influence of the source terms, such as viscous dissipation, Ohmic heating, exponential heat source, and chemical reaction of the electromagnetohydrodynamic (EMHD) Jeffrey fluid flow. The non-Newtonian nanofluids have proven their great potential for heat transfer processes, which have various applications in cooling microchips, solar energy systems, and thermal energy technologies. Full article

A numerical investigation of unsteady boundary layer flow with heat and mass transfer of non-Newtonian fluid model, namely, Jeffrey fluid subject, to the significance of Soret and Dufour effects is carried out by using the local nonsimilarity method and homotopy analysis method. An excellent agreement in the numerical results obtained by both methods is observed and we establish a new mathematical approach to obtain the solutions of unsteady-state flow with heat and mass transfer phenomenons. Similarity transformation is applied to governing boundary layer partial differential equations to obtain the set of self-similar, nondimensional partial differential equations. Graphical results for different emerging parameters are discussed. The dimensionless quantities of interest skin friction coefficient, Sherwood number, and Nusselt number are discussed through tabulated results. The main novelty of the current work is that the average residual error of the $mth$-order approximation of the OHAM scheme for steady-state solution is decreased for higher-order approximation. Further, a rapid development of the boundary layer thickness with the increasing values of dimensionless time $\tau$ is observed. It is noted that for large values of $\tau$, the steady state in the flow pattern is gained. It is worth mentioning that the magnitude of Sherwood number is increased with the increasing values of Schmidt number $Sc$ and Dufour number $D_f$. The magnitude of local Nisselt number is increased for the increasing values of Soret number, $Sr$. Full article

Free convection flow of non-Newtonian fluids over flat, heated surfaces is an important natural phenomenon that also occurs in human-made engineering processes under various physical and mechanical situations. In the current study, the free convection magnetohydrodynamic flow of Jeffrey fluid with heat and mass transfer over an infinite vertical plate is examined. Mathematical modeling is performed using Fourier’s and Fick’s laws, and heat and momentum equations have been obtained. The non-dimensional partial differential equations for energy, mass, and velocity fields are determined using the Laplace transform method in a symmetric manner. Later on, the Laplace transform method is employed to evaluate the results for the temperature, concentration, and velocity fields with the support of Mathcad software. The governing equations, as well as the initial and boundary conditions, satisfy these results. The impacts of fractional and physical characteristics have been shown by graphical illustrations. The obtained fractionalized results are generalized by a more decaying nature. By taking the fractional parameter $\beta ,\gamma \to 1$, the classical results with the ordinary derivatives are also recovered, making this a good direction for symmetry analysis. The present work also has applications with engineering relevance, such as heating and cooling processes in nuclear reactors, the petrochemical sector, and hydraulic apparatus where the heat transfers through a flat surface. Moreover, the magnetized fluid is also applicable for controlling flow velocity fluctuations. Full article

The proposed model of drug delivery has been developed as a medication methodology for the direct treatment of diseased body tissues. The mathematical model is built upon the particulate peristaltic transport of an electrical conducting Jeffrey fluid within an asymmetric duct. The flow takes place under the action of slip effects due to the occurrence of magnetohydrodynamics, which is generally known as electrical resistance and the energy released by charged particles as they make collisions with other particles. Transportation of drug particles along with Jeffry fluid due to peristaltic pumping in a rectangular duct is demonstrated. Magnetic force is utilized for the control of the process of pumping to the flow path at the right position. Taking into consideration the flow conditions and assumptions, the derivation of the system of partial differential equations of the flow is described. The eigenfunction expansion method is used to establish the solutions, and then the data are graphically displayed to imagine the effects of different parameters. It can be professed that the velocity component for Jeffrey fluid flow is decreased because of magnetic force, volume fraction size, and wall compliance. Heat and mass transfer with nanoparticles of different shapes of particles to extend this work. Full article

The existing work deals with the Jeffrey fluid having an unsteady flow, which is moving along a vertical plate. A fractional model with ternary, hybrid, and nanoparticles is obtained. Using suitable dimensionless parameters, the equations for energy, momentum, and Fourier’s law were converted into non-dimensional equations. In order to obtain a fractional model, a fractional operator known as the Prabhakar operator is used. To find a generalized solution for temperature as well as a velocity field, the Laplace transform is used. With the help of graphs, the impact of various parameters on velocity as well as temperature distribution is obtained. As a result, it is noted that ternary nanoparticles approach can be used to increase the temperature than the results obtained in the recent existing literature. The obtained solutions are also useful in the sense of choosing base fluids (water, kerosene and engine oil) for nanoparticles to achieved the desired results. Further, by finding the specific value of fractional parameters, the thermal and boundary layers can be controlled for different times. Such a fractional approach is very helpful in handling the experimental data by using theoretical information. Moreover, the rate of heat transfer for ternary nanoparticles is greater in comparison to hybrid and mono nanoparticles. For large values of fractional parameters, the rate of heat transfer decreases while skin friction increases. Finally, the present results are the improvement of the results that have already been published recently in the existing literature. Fractional calculus enables us to control the boundary layers as well as rate of heat transfer and skin friction for finding suitable values of fractional parameters. This approach can be very helpful in electronic devices and industrial heat management system. Full article

In this paper, the electrokinetic energy conversion (EKEC) efficiency, streaming potential of viscoelastic fluids in microtubes under an external transversal magnetic field, and an axial pressure gradient are investigated. The Jeffreys fluid is applied to model the viscoelastic fluid, and the analytic solution of velocity field is obtained using the Green’s function method. The influence of different dimensionless parameters, for instance, the Deborah numbers De and De^*, which are related to the relaxation time and retardation time, respectively; the dimensionless electro-kinetic width K; the dimensionless frequency ω; the volume fraction of the nanoparticles φ and the dimensionless Hartmann number Ha; and three different imposed axial periodic pressure gradients (cosine, triangular, and square) on fluid dynamics are discussed. The physical quantities are graphically described, and the influence of different parameters on the EKEC is analyzed. The results indicate that De promotes the streaming potential and EKEC efficiency of the microtube, while De^* inhibits them. Full article

This paper investigates the mobility of cilia in a non-uniform tapered channel in the presence of an induced magnetic field and heat transfer. Thermal radiation effects are included in the heat transfer analysis. The Jeffrey model is a simpler linear model that uses time derivatives rather than convected derivatives as the Oldroyd-B model does; it depicts rheology other than Newtonian. The Jeffrey fluid model is used to investigate the rheology of a fluid with cilia motion. The proposed model examines the behavior of physiological fluids passing through non-uniform channels, which is responsible for symmetrical wave propagation and is commonly perceived between the contraction and expansion of concentric muscles. To formulate the mathematical modeling, the lubrication approach is used for momentum, energy, and magnetic field equations. The formulated linear but coupled differential equations have been solved analytically. Graphs for velocity profile, magnetic force function, induced magnetic field, current density, pressure rise, and heat profile are presented to describe the physical mechanisms of significant parameters. It is found that the eccentricity parameter of the cilia equations opposes the velocity and the magnetic force functions. The thermal radiation decreases the temperature profile while it increases for Prandtl and Eckert numbers. A promising impact of the magnetic Reynolds number and electric field on the current density profile is also observed. Full article

An analytical study is reported that highlights the physical aspects for a heated non-Newtonian Jeffrey liquid in a duct possessing sinusoidally moving ciliated walls. A comprehensive and specific convection analysis is conveyed for this ciliated elliptic duct problem by considering the viscous dissipation effects. The dimensional mathematical problem under consideration is transformed into its dimensionless form by means of appropriate and useful transformations. Then, velocity and temperature equations are exactly evaluated with given boundary conditions. The velocity profile is integrated over the elliptic cross-section and exact mathematical solution is obtained for the pressure gradient. Moreover, the distinct physical flow properties combined with the convection heat transfer phenomenon are discussed in detail through graphical outcomes. The illustrative streamline description shows an enhancing closed contour size with increasing $Q$ (dimensionless flow rate). Full article

The noteworthiness of double-diffusive convection with magneto-Jeffrey nanofluid on a peristaltic motion under the effect of MHD and porous medium through a flexible channel with the permeable wall has been theoretically examined. A non-linearized Rosseland approximation is utilized to show the thermal radiation effect. The governing equations are converted to standard non-linear partial differential equations by using suitable non-dimensional parameters. Solutions of emerging equations are obtained by using the multi-step differential transformation method (Ms-DTM). The differential transformation method (DTM) can be applied directly to nonlinear differential equations without requiring linearization and discretization; therefore, it is not affected by errors associated with discretization. The role of influential factors on concentration, temperature, volume fraction, and velocity are determined using graphs. A significant outcome of the present article is that the presence of double-diffusive convection can change the nature of convection in the system. The present results have a wide biological applicability, including for biomicrofluidic devices that regulate the fluid flow through a flexible endoscope and other medical pumping systems. Full article