Grade Fluid Research Articles

Peristaltic pump with heat and mass transfer of a fractional second grade fluid through porous medium inside a tube

In magnetic resonance imaging (MRI), this MRI is used for the diagnosis of the brain. The dynamic of these particles occurs under the action of the peristaltic waves generated on the flexible walls of the brain. Studying such fluid flow of a Fractional Second-Grade under this action is therefore useful in treating tissues of cancer. This paper deals with a theoretical investigation of the interaction of heat and mass transfer in the peristaltic flow of a magnetic field fractional second-grade fluid through a tube, under the assumption of low Reynolds number and long-wavelength. The analytical solution to a problem is obtained by using Caputo's definition. The effect of different physical parameters, the material constant, magnetic field, and fractional parameter on the temperature, concentration, axial velocity, pressure gradient, pressure rise, friction forces, and coefficient of heat and mass transfer are discussed with particular emphasis. The computed results are presented in graphical form. It is because the nature of heat and mass transfer coefficient is oscillatory which is following the physical expectation due to the oscillatory nature of the tube wall. It is perceived that with an increase in Hartmann number, the velocity decreases. A suitable comparison has been made with the prior results in the literature as a limiting case of the considered problem.

Development and Internal Validation of the ARISE Prediction Models for Rebleeding After Aneurysmal Subarachnoid Hemorrhage.

Aneurysmal rerupture is one of the most important determents for outcome after aneurysmal subarachnoid hemorrhage and still occurs frequently because individual risk assessment is challenging given the heterogeneity in patient characteristics and aneurysm morphology. To develop and internally validate a practical prediction model to estimate the risk of aneurysmal rerupture before aneurysm closure. We designed a multinational cohort study of 2 prospective hospital registries and 3 retrospective observational studies to predict the risk of computed tomography confirmed rebleeding within 24 and 72 hours after ictus. We assessed predictors with Cox proportional hazard regression analysis. Rerupture occurred in 269 of 2075 patients. The cumulative incidence equaled 7% and 11% at 24 and 72 hours, respectively. Our base model included hypertension, World Federation of Neurosurgical Societies scale, Fisher grade, aneurysm size, and cerebrospinal fluid drainage before aneurysm closure and showed good discrimination with an optimism corrected c-statistic of 0.77. When we extend the base model with aneurysm irregularity, the optimism-corrected c-statistic increased to 0.79. Our prediction models reliably estimate the risk of aneurysm rerupture after aneurysmal subarachnoid hemorrhage using predictor variables available upon hospital admission. An online prognostic calculator is accessible at https://www.evidencio.com/models/show/2626 .

High order numerical method for the simulation of Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative on regular and irregular domains

High order numerical method for the simulation of Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative on regular and irregular domains

An accurate computational method for two-dimensional (2D) fractional Rayleigh-Stokes problem for a heated generalized second grade fluid via linear barycentric interpolation method

This paper deals with the development and analysis of an efficient method for the numerical solution of the two-dimensional (2D) fractional Rayleigh-Stokes problem for a heated generalized second grade fluid. The fractional time derivative that occurs in the problem is in the Riemann-Liouville sense and is discretized using a finite difference approach that is convergent with order of convergence O(τ1+β) and unconditionally stable. After discretization of time variable, linear barycentric interpolation method is used to discretize space variables. In this way, a fully discrete scheme is obtained, which can be used to solve the problem numerically. The numerical solution is compared with exact solution to see how accurate it is. Also L∞ error norm is reckoned and compared with those of other numerical methods in the literature to see performance of the method. Numerical simulations verify that the suggested method is accurate and workable for similar 2D fractional problems.

Mittag-Leffler form solutions of natural convection flow of second grade fluid with exponentially variable temperature and mass diffusion using Prabhakar fractional derivative

In this article, heat source impact on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer second grade fluid near an exponentially accelerated vertical plate with exponentially variable velocity, temperature and mass diffusion through a porous medium. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on newly introduced Prabhakar fractional operator with generalized Fourier's law and Fick's law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical second grade model, classical Newtonian model and fractional Newtonian model are recovered from Prabhakar fractional second grade fluid. Moreover, compare the results between second grade and Newtonian fluids for both fractional and classical which shows that the movement of the viscous fluid is faster than second grade fluid. Additionally, it is visualized that for both classical second grade and viscous fluid have relatively higher velocity as compared to fractional second grade and viscous fluid.

Rotating MHD flow of second grade fluid through porous medium between two vertical plates with chemical reaction, radiation absorption, Hall, and ion slip impacts

Rotating MHD flow of second grade fluid through porous medium between two vertical plates with chemical reaction, radiation absorption, Hall, and ion slip impacts

Analysis of fuzzified boundary value problems for MHD Couette and Poiseuille flow

In an uncertain atmosphere, the magnetohydrodynamics (MHD) flow in three principal flows of the third grade fluid across two parallel plates is presented. Fuzzy differential equations are constructed by manipulating dimensionless differential equations. The prime purpose of the current article is to use a semi-analytical approach fuzzy-based Adomian decomposition method to achieve numerical results for nonlinear FDEs with fuzzy boundary conditions. Triangular fuzzy numbers are used in fuzzy BCs with help of alpha {text{-cut}} approach. This strategy is linked to the membership function. In a graphic and tabular depiction, the effect of alpha and other constraints on fuzzy velocity profiles is explored. The current findings are in good agreement with their previous numerical and analytical results in a crisp environment.

Insight into the relationship between the Fourier's law of heat conduction and Fick's law over a Riga device: Fourth grade analysis

Mixed convective flow of fourth grade (Non-Newtonian) fluid model by a Riga stretchable plate is addressed. The aim of the current research work is therefore to explain the role of the fourth grade (Non-Newtonian) fluid model in the field of fluid dynamics. Energy and concentration equations are modeled subject to both Fourier's law of heat conduction and Fick's law. Radiation aspects and heat source/sink phenomenon are also accounted. Entropy analysis is discussed through second thermodynamics law. The (OHAM) approach is used to achieve a meaningful solution. Finally, the emerging variables behavior on the velocity, temperature, concentration and entropy rate are discussed graphically. Here, velocity enhances for increasing range of fourth grade variable. Temperature boosts against rising radiation and thermal relaxation variables, but opposite trend is noted for solutal relaxation parameter on concentration.

A note on the multiphase flow of third grade fluid with wall properties

The present study addresses the missing theoretical idea regarding multiphase suspensions. There has been no attempt to highlight the chemical and pharmaceutical application of bi-phase flows. In this fruitful study, different types of multiphase flows are modeled and analyzed through the parametric survey. From the future perspective, highly thick non-Newtonian multiphase suspensions are a common phenomenon, which is more suitable for the coating process in the pharmaceutical and chemical industries. Moreover, a chemical conversion coating applies a superficial layer that contains the metal compound. It offers economical protection against corrosion and a surface suitable for powder coating and painting.

Combined Effect of Radiant Heat, Local Nusselt Number and Skin Friction Coefficient of a Third Grade Fluid through a Channel Flow in a Saturated Porous Medium

This paper investigates the combined effects of radiant heat, local Nusselt number and Skin friction coefficient on a channel flow of third grade fluid in the presence of saturated porous medium. It is assumed that the fluid has temperature-dependent variable viscosity and thermal conductivity. The non-linear governing differential equations are obtained and tackled numerically using Spectral element technique and C++ programming language. Increase in the values of radiation parameter and third grade material parameter consequently increase the local Nusselt number and skin friction coefficient. Graphical results showing the effects of various physical parameters are presented and discussed quantitatively. It is concluded that Williamson’s fluid parameter served as a cooling factor in diverse improved technological processes in order to avoid different machines from overheating and enhance their efficiencies.

Analytic simulation of thermophoretic second grade fluid flow past a vertical surface with variable fluid characteristics and convective heating

The study considers the effect of thermophoresis particle deposition on the flow properties of second grade fluid with variable viscosity, variable thermal conductivity and variable concentration diffusivity subjected to a convective boundary condition. To further describe the transport phenomenon, the special case of assisting and opposing flows is explored. Using similarity transformations, the governing equations of the fluid model are transformed and parameterized into a system of nonlinear ordinary differential equations. The approximate analytic solution of a dimensionless system is obtained through the Optimal Homotopy Analysis Method (OHAM). It is observed that velocity and temperature distributions are decreasing functions of the second grade parameter for both assisting and opposing flows. When the thermophoretic parameter is increased, the concentration distributions at the first and fourth orders of chemical reaction decrease. For both opposing and assisting flows, velocity distributions are enhanced due to larger temperature-dependent viscous parameters.

A Thermodynamical Description of Third Grade Fluid Mixtures

Abstract A complete thermodynamical analysis for a non-reacting binary mixture exhibiting the features of a third grade fluid is analyzed. The constitutive functions are allowed to depend on the mass density of the mixture and the concentration of one of the constituents, together with their first and second order gradients, on the specific internal energy of the mixture with its first order gradient, and on the symmetric part of the gradient of barycentric velocity. Compatibility with the second law of thermodynamics is investigated by applying the extended Liu procedure. An explicit solution of the set of thermodynamic restrictions is obtained by postulating a suitable form of the constitutive relations for the diffusional mass flux, the heat flux, and the Cauchy stress tensor. Taking a first order expansion in the gradients of the specific entropy, the expression of the entropy flux is determined. It includes an additional contribution due to non-local effects.

Magneto-hydrodynamics second grade compressible fluid flow in a wavy channel under peristalsis: Application to thermal energy

The present work is aimed to explore the peristaltic transport characteristics of a compressible fluid under the impact of magnetic field inside a wavy channel. The interior of channel is filled with the second grade fluid. To explore the details of fluid dynamics analytically, a perturbation expansion for sufficiently small values of amplitude ratio is applied. The consequence of pertinent parameters on net axial velocity, perturbation function and net flow rate are portrayed and examined. It is inferred that the compressibility of the fluid has a strong impact on net axial velocity. Perturbation in mean axial velocity appeared to be of order of magnitude 10−2 for different values of Reynolds number. Wall shear stress changes its behavior at χ = 0.3 and χ = 0.6. A decrement in the flow rate as well as in the net axial velocity with second grade fluid parameter is also revealed.

Uniqueness for optimal control problems of two-dimensional second grade fluids

Uniqueness for optimal control problems of two-dimensional second grade fluids

Different families of new exact solutions for planar and nonplanar second grade fluid flows

Three different families of new exact solutions for second grade fluid flows are derived in this paper. First family of two dimensional exact solutions are obtained by assuming a novel form for the stream function and these solutions contain spatially periodic as well as non-periodic solutions. The subclass of periodic solutions extends the rectangular array of Taylor vortices to more complex structures of two dimensional vortices. Second family of planar solutions are also having vortex structures similar to Taylor vortices. Third family of exact solutions are pseudo planar flows of second kind. All these exact solutions reduce to corresponding new exact solutions for Newtonian fluid flows when the normal stress moduli are absent.

Computational approach and dynamical aspects of fractional second grade fluid with heat and mass transport in cylindrical domain

The purpose of the present article is to set up some new exact derivations for velocity, temperature, and concentration fields correlating with unsteady, incompressible model of second-order fluid near an infinitely placed vertical cylinder with the influence of heat and mass transfer. With help of appropriate similarity conversions, governing system of partial differential equations as well as boundary constraints are reduced to dimensionless form. The fractional calculus approach is used to study the memory effects on the fluid flow behavior. Laplace along with Hankel transforms are accustomed to investigate the general form of closed solutions for velocity, temperature, and mass fields. The influences of distinct physical parameters are presented through graphical discussion and tables. The main findings through graphical sketch are that the Grashof number and Prandtl number show opposite correspondence to velocity distribution. Furthermore, the temperature distribution is decreasing function with respect to Prandtl number.

Heat and mass transfer exploration of non-Newtonian fluid flow induced by the exponentially stretching Riga surface with the application of Generalized Fourier’s and Fick’s law

In the present article, the analysis of the transportation of thermal and solutal energy of a3D flow on second- grade fluid with porous medium by an exponentially stretching surface is presented. The chemical reaction and heat generation/absorption are considered the dominating agents for the transportation of mass and heat in the second-order fluid. Furthermore, slip boundary conditions are considered on the boundary of the surface. A novel concept of the Cattaneo-Christov heat flux theory of the flow of second-order fluid is used under the effects of the Joule heating across the Riga surface for this research examination. The prevailing nonlinear PDEs are changed into the nonlinear coupled ordinary differential equations by choosing the suitable similarity transformations. The Matlab approach Bvp4c is applied to solve the nonlinear ODEs. Physical consequences of the different emerging parameters on the thermal, concentration, and momentum boundary layer thickness are examined by graphs. The thermal and concentration profiles are decreased by enhancing the values of (thermal relaxation parameter of time) and the (parameter of solutal relaxation time), respectively.

How do artificial bacteria behave in magnetized nanofluid with variable thermal conductivity: application of tumor reduction and cancer cells destruction

PurposeThe study aims to determine an efficiency of external magnetic field on the bacteria surrounded by thousands of magnetic magnetite nanoparticles. The interstitial nanoliquid in which an artificial bacteria swims in biological cell is utilized with variable thermal conductivity. Two dimensions unsteady motion of second grade fluid are considered. The stretching wall is taken as a curved surface pattern.Design/methodology/approachThe mathematical results have been obtained by Chebyshev pseudospectral method.FindingsThe impact of the various governing parameters is described by numerical tables and diagrams. It is proven that the pure blood velocity curves are higher when compared with the magnetite/blood. It is demonstrated from clinical disease that dangerous tumors show diminished blood flow. This study concludes that the blood velocity profile increases by increasing the values of fluid parameters. This implies that the medication conveyance therapy lessens the tumor volume and helps in annihilating malignancy cells. The blood temperature distribution raises as the magnetite nanoparticles concentration increases. Consequently, the physical properties of the blood can be enhanced by immersing the magnetite nanoparticles. Further, the present outcomes cleared the thermal conductivity as, a variable function of the temperature, has an important role to enhance the heat transfer rate.Originality/valueTo the best of authors’ knowledge, this study is reported for the first time.

The role of enthalpy and activation energy on thermophysical properties of third grade fluid near a magnetized radioactive irregular wavy surface

The present article communicates mathematical and theoretical study of three dimensional mixed convection flow of an electrical conducting third grade fluid flow near a non-uniform irregular wavy surface. The flow field is incorporated with an applied magnetic field. Heat and mass transfer characteristics are scrutinized with combined impact of enthalpy change along with energy activation and non-linear thermal radiation. The prime structure of differential equations is achieved in momentum, energy, magnetic and concentration forms. We defined some new dimensionless functions which transformed non-linear PDEs into dimensionless ODEs. Lobatto(iiiA) formula based technique Bvp4c is used for graphical and numerical solution of governing equations. Features of different dimensionless parameters are studied for velocity, concentration, magnetic and energy distributions by using graphical approach. Skin friction coefficients, rate of heat and mass fluxes are calculated by changing the values of some dimensionless parameters. Comparative study of Nusselt number with previous published results are demonstrated to investigate the accuracy of current problem. Final outcome justifies that better agreement is achieved with existing published work.

Hall effects on MHD chemically reacting flow of second grade fluid past a vertical porous plate

AbstractThe scrutiny of the consequences of radiation‐absorption, chemical reaction impacts on unsteady magnetohydrodynamics heat and mass transportation laminar flow of a gelatinous, electrical conducting by the heat generation or absorption second grade fluid embedded past a half‐unlimited porous surface within a gyratory structure taking Hall effects into account have been discussed. The plate is assumed to as in the motion by the invariable velocity contained by the direction of fluid movement. A uniform magnetic field performed at perpendicular to the porous plate; this is engrossing the fluid with the suction velocity changing with definite instants of time. The corresponding dimensionless governing equations of current configuration are solved by making use of perturbation technique with reference to harmonic and nonharmonic idioms. The velocity, temperature, and concentration profiles are discussed and examined with references to various governing parameters in detail. The results are verified with the published work. The velocity components are increased with increasing permeability and Hall parameters. It is noticed that practical application of Hall effects is as, washing machine dial to select the type of washing moves very smoothly. This problem has also applications in biomedical and aerospace engineering.