Peristaltic Blood Flow of Couple Stress Fluid Suspended with Nanoparticles under the Influence of Chemical Reaction and Activation Energy

Unsteady hybrid nanofluid (Cu-UO2/blood) with chemical reaction and non-linear thermal radiation through convective boundaries: An application to bio-medicine

This study is focused on modeling and simulations of hybrid nanofluid flow. Uranium dioxide UO2 nanoparticles are hybrid with copper Cu, copper oxide CuO and aluminum oxide Al2O3 while considering blood as a base fluid. The blood flow is initially modeled considering magnetic effect, non-linear thermal radiation and chemical reactions along with convective boundaries. Then for finding solution of the obtained highly nonlinear coupled system we propose a methodology in which q-homotopy analysis method is hybrid with Galerkin and least square Optimizers. Residual errors are also computed in this study to confirm the validity of results. Analysis reveals that rate of heat transfer in arteries increases up to 13.52 Percent with an increase in volume fraction of Cu while keeping volume fraction of UO2 fixed to 1% in a base fluid (blood). This observation is in excellent agreement with experimental result. Furthermore, comparative graphical study of Cu,CuO and Al2O3 for increasing volume fraction is also performed keeping UO2 volume fraction fixed. Investigation indicates that Cu has the highest rate of heat transfer in blood when compared with CuO and Al2O3. It is also observed that thermal radiation increases the heat transfer rate in the current study. Furthermore, chemical reaction decreases rate of mass transfer in hybrid blood nanoflow. This study will help medical practitioners to minimize the adverse effects of UO2 by introducing hybrid nano particles in blood based fluids.

Entropy Generation Analysis in Magnetohydrodynamic Couple Stress Nanofluid Flow Through an Oblique Microchannel in a Permeable Medium with Thermal Radiation

The present work examines the flow and thermal energy process in conducting couple stress nanofluid flows through an oblique microchannel. The microchannel is embedded with permeable medium and thermal radiation is implemented. The microchannel boundaries retain the slip boundary conditions. The impact of buoyancy force and magnetic field are incorporated. The temperature dependent heat source effect was also taken into account. The momentum equation has been made by the permeability of the porous medium. The equations are modeled and non-dimensionalized using non-dimensional entities and further solved with the aid of the Runge-Kutta Fehlberg method and the shooting procedure. The detailed discussions about the importance of the effective parameters on entropy generation, the Bejan number have been observed through graphs. The findings of the examination depict that rise in radiation parameter augments the entropy generation and the Bejan number in the channel. The entropy generation and Bejan number diminishes with inflation of the permeability parameter.

Peristaltic transfer of nanofluid with motile gyrotactic microorganisms with nonlinear thermic radiation

In situated theoretical article, a study of peristaltic transition of Jeffery nanofluid comprising motile gyrotactic microorganisms is exposed. The movement floods due to anisotropically stenosed endoscope influenced by Hall current, Joule heating during Darcy-Forchheimer feature. Influences of nonlinear thermic radiation, chemical interactions as well as Soret and Dufour scheme are exhibited. To ameliorate the competence of this article, activation energy has been appended to concentration of nano-particles due to the amended Arrhenius scheme and Buongiorno type. The slip stipulation is deemed relative to the speed scheme. Meanwhile, convective stipulation is reckoned for temperature. The proposition of protracted wavelength besides subdued Reynolds numeral is regulated to transit the manner of partial differential formulations that judges the fluid movement to ordinary one. Homotopy perturbation manner is tackled to manage the traditional solutions of generated neutralizations. Influences of assorted factors of the issue are debated and schematically showed with a class of charts. The situated study grants a medication for the malign cells and clogged arteries of the heart by manner of penetrating a slender tube (catheter). Also, this study may represent the depiction of the gastric juice movement in small intestine when an endoscope is permeating across it.

Heat and mass transfer for MHD peristaltic flow in a micropolar nanofluid: mathematical model with thermophysical features

According to a survey of the literature, nanofluids are superior to traditional fluids at transferring heat. A detailed analysis of the models mentioned above is crucial since there are large gaps in the illumination of current solutions for improving heat transfer in nanomaterials. The ongoing investigation's purpose is to ascertain the tiny size gold particles drift in free with the heat and mass transfer, buoyancy forces, thermophoresis, and Brownian motion of a micropolar nanofluid being transported through a porous medium in an asymmetric channel with a uniform magnetic field using a long-wavelength and low Reynolds number approximation. The resulting dimensionless nonlinear governing equations have been numerically solved using a MATLAB software and the Runge-Kutta-Fehlberg integration scheme. Two comparisons with previously investigated problems are also made to confirm our findings, and an excellent concurrence is discovered. As a result, trustworthy results are being given. Numerical solutions are used to describe the effects of different thermal-fluidic parameters on velocity profiles, temperature, concentration, micropolar rotation, pressure gradient, shear stress, heat flux, and nanoparticle volume flux, etc. Tables, graphs, and bar charts are used to present and discuss numerical results that have been produced. A comparison of the resulting numerical solution to earlier literature also reveals a satisfactory level of agreement. Insight into real-world applications such nanofluidic, energy conservation, friction reduction, and power generation are provided by this work. Furthermore, the Brownian and thermophoresis parameters behave significantly differently in a concentration field. On the other hand, the study puts forward an important note that for peristaltic flow of a micropolar fluid with nanoparticles can be controlled by suitably adjusting the micropolar parameter, thermophoresis parameter, nanoparticle Grashof number, and Brownian motion parameter.

Magnetic Nanoparticles for Drug Delivery through Tapered Stenosed Artery with Blood Based Non-Newtonian Fluid

Nanoparticles play an essential role in biomedical applications. A most promising area in nanomedicine is drug targeting which is done with the aid of magnetized nanoparticles. In this study, the hemodynamics of hybrid nanofluid flow with gold and copper nanoparticles suspended in it is investigated. This research primarily focuses on magnetic drug delivery which is propagated through a tapered stenosed artery under three situations, including converging, diverging, and non-tapering arteries. To explore the rheological characteristics of blood, a Sutterby fluid, which is a non-Newtonian fluid, is postulated. The energy equation also incorporates the effects of the magnetic field and joule heating, as well as the viscous dissipation function. Lubrication theory provides a mathematical framework for model formulation. The hypothesized modeling is simplified to a set of nonlinear differential equations that are then solved using a perturbation method up to the second order of approximation. Graphs are used to describe the outcomes of different evolving parameters. The Sutterby fluid parameter opposes the flow negligibly, whereas the Hartmann number and thermal Grashof number strengthen the flow field. Copper nanoparticles (in the absence of gold nanoparticles) are observed to deplete the thermal profile substantially more than gold nanoparticles. Nevertheless, the thermal profile is enhanced by the presence of both nanoparticles (hybrid nanofluids). For greater values of the Sutterby fluid parameter, the wall shear stress has been observed to rise considerably, whereas the inverse is true for the Hartmann number and the thermal Grashof number. The present results have been improved to give significant information for biomedical scientists who are striving to study blood flow in stenosis situations, as well as for those who will find the knowledge valuable in the treatment of different diseases.

Trace of Chemical Reactions Accompanied with Arrhenius Energy on Ternary Hybridity Nanofluid Past a Wedge

Heat transfer is a vital fact of daily life, engineering, and industrial mechanisms such as cryogenic systems, spaceborne thermal radiometers, electronic cooling, aircraft engine cooling, aircraft environmental control systems, etc. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and keeps the symmetry of the flowing structure. Purpose: In this attempt, the effect of endothermic/exothermic chemical reactions accompanied by activation energy on a ternary hybrid nanofluid with the geometry of a wedge is taken into consideration. The mathematical form of PDEs is obtained by Navier–Stokes equations, the second law of thermodynamics, and Fick’s second law of diffusion. The geometric model is therefore described using a symmetry technique. Formulation: The MATLAB built-in Lobatto III A structure is utilized to find the computational solution of the dimensionless ODEs. All computational outcomes are presented by graphs and statistical graphs in order to check the performance of various dimensionless quantities against drag force factor and Nusselt quantity. Finding: the addition of tri-hybridizing nanomolecules in the standard liquid improves the thermic performance of the liquid much better in comparison to simple hybrid nanofluids. Wedge angle parameter α brings about a decrement in fluid velocity and augmentation in thermal conductivity ϵ, thermal radiation Rd, thermophoresis parameter Nt and endothermic/exothermic reaction Ω, and fitted rate constant n accelerates the heat transmission rate. Novelty: The effect of tri-hybridizing nanomolecules along with endothermic/exothermic reactions on the fluid past a wedge have not been investigated before in the available literature.

Effects of Double Diffusive Convection and Inclined Magnetic Field on the Peristaltic Flow of Fourth Grade Nanofluids in a Non-Uniform Channel

This study explored the impact of double diffusive convection and inclined magnetic field in nanofluids on the peristaltic pumping of fourth grade fluid in non-uniform channels. Firstly, a brief mathematical model of fourth grade fluid along inclined magnetic fields and thermal and concentration convection in nanofluids was developed. A lubrication approach was used to simplify the highly non-linear partial differential equations. An analytical technique was then used to solve the highly non-linear differential equations. The exact solutions for the temperature, nanoparticle volume fraction and concentration were calculated. Numerical and graphical outcomes were also examined to see the effects of the different physical parameters of the flow quantities. It was noted that as the impact of Brownian motion increased, the density of the nanoparticles also increased, which led to an increase in the nanoparticle fraction. Additionally, it could be observed that as the effects of thermophoresis increased, the fluid viscosity decreased, which lowered the fraction of nanoparticles that was made up of less dense particles.

The Role of Double-Diffusion Convection and Induced Magnetic Field on Peristaltic Pumping of a Johnson-Segalman Nanofluid in a Non-Uniform Channel

The peristaltic propulsion of a Johnson–Segalman nanofluid under the dependency of a double-diffusion convection and induced magnetic field was investigated in this study. On the premise of continuity, linear momentum, solute concentration, thermal energy, and nanoparticle concentration, a flow issue was proposed. The lubrication methodology was used to carry out mathematical modelling. Numerical techniques were used to solve the corresponding highly nonlinear partial differential equations. The exact solution of concentration, temperature, and nanoparticle were computed. The manifestations of all relevant constraints were theoretically and graphically evaluated. The current study develops a theoretical model that can predict how various parameters affect the characteristics of blood-like fluid flows.

Non fourier heat transfer enhancement in power law fluid with mono and hybrid nanoparticles

Several polymers like ethylene glycol exhibit non-Newtonian rheological behavior. Ethylene glycol is a world-widely used engine coolant and therefore, investigation of thermal enhancement by dispersing mono and hybrid nanoparticles in ethylene glycol is worthful. Since ethylene glycol has shear rate-dependent viscosity and it obeys the power-law rheological model. Therefore, based on these facts, the power-law rheological model with thermophysical properties is augmented with basic law of heat transfer in fluid for the modeling of the considered physical situation. [Formula: see text] are taken as mono-nanoparticles where [Formula: see text] and [Formula: see text] are taken as hybrid nanoparticles. Comparative study for the enhancement of thermal performance of MoS2 ethylene glycol and [Formula: see text]-[Formula: see text]- ethylene glycol is done. For energy conservation, non-Fourier's law of Cattaneo-Christov is used. The power-law fluid becomes more heat generative due to the dispersion of [Formula: see text] and [Formula: see text]. However, [Formula: see text]-power-law fluid is less heat generative relative to [Formula: see text]- [Formula: see text]-nanofluid. Thermal relaxation time is found proportional to the ability of the fluid to restore its thermal equilibrium.

Crossbreed impact of double-diffusivity convection on peristaltic pumping of magneto Sisko nanofluids in non-uniform inclined channel: A bio-nanoengineering model

The consequences of double-diffusivity convection on the peristaltic transport of Sisko nanofluids in the non-uniform inclined channel and induced magnetic field are discussed in this article. The mathematical modeling of Sisko nanofluids with induced magnetic field and double-diffusivity convection is given. To simplify PDEs that are highly nonlinear in nature, the low but finite Reynolds number, and long wavelength estimation are used. The Numerical solution is calculated for the non-linear PDEs. The exact solution of concentration, temperature and nanoparticle are obtained. The effect of various physical parameters of flow quantities is shown in numerical and graphical data. The outcomes show that as the thermophoresis and Dufour parameters are raised, the profiles of temperature, concentration, and nanoparticle fraction all significantly increase.

Bioconvection Due to Gyrotactic Microorganisms in Couple Stress Hybrid Nanofluid Laminar Mixed Convection Incompressible Flow with Magnetic Nanoparticles and Chemical Reaction as Carrier for Targeted Drug Delivery through Porous Stretching Sheet

In this paper, the steady electrically conducting hybrid nanofluid (CuO-Cu/blood) laminar-mixed convection incompressible flow at the stagnation-point with viscous and gyrotactic microorganisms is considered. Additionally, hybrid nanofluid flow over a horizontal porous stretching sheet along with an induced magnetic field and external magnetic field effectsthat can be used in biomedical fields, such as in drug delivery and the flow dynamics of the microcirculatory system. This investigation can also deliver a perfect view about the mass and heat transfer behavior of blood flow in a circulatory system and various hyperthermia treatments such as the treatment of cancer. The simple partial differential equations (PDEs) are converted into a series of dimensional ordinary differential equations (ODEs), which are determined using appropriate similarities variables (HAM). The influence of the suction or injection parameter, mixed convection, Prandtl number, buoyancy ratio parameter, permeability parameter, magnetic parameter, reciprocal magnetic prandtl number, bioconvection Rayleigh number, coupled stress parameter, thermophoretic parameter, Schmidt number, inertial parameter, heat source parameter, and Brownian motion parameter on the concentration, motile microorganisms, velocity, and temperature is outlined, and we study the physical importance of the present problem graphically.

Slip Effects on a Ree-Eyring Liquid Peristaltic Flow Towards an Inclined Channel and Variable Liquid Properties

The current paper aims to model the flow of blood in narrow arteries by taking non-Newtonian Ree-Eyring fluid. The impact of wall properties, slip, mass, and heat transport are considered. In earlier studies, the viscosity of blood was considered a constant parameter. However, many researchers have claimed that the blood’s viscosity in the peripheral region is less than that of the core region. Thus, the present model incorporates the variation in thermal conductivity and viscosity, which takes a vital character in scrutinizing blood flow in narrow arteries. The mathematical model is developed on low Reynold’s number approximation and long wavelength, leading to the governing non-linear equations representing the flow phenomena. The governing non-linear partial differential equations are resolved by utilizing the series solution method (perturbation technique). MATLAB programming has been used to plot the pictorial representation of all the parameters through the flow quantities. The investigation shows that the variable velocity slip parameter and viscosity develops the velocity profiles. Further, the liquid parameter can be used to control the dimension of the trapped bolus. Moreover, the obtained outcomes aid in recognizing the flow of blood in micro arteries.

Magnetohydrodynamic mixed convective peristaltic slip transport of carbon nanotubes dispersed in water through an inclined channel with Joule heating

Carbon nanotubes are considered to be the latest nanotechnology innovation because of their remarkable physical and mechanical properties. Recently, researchers have shown great interest in the peristaltic transport of nanotube‐based nanofluid as this process involves a wide range of uses in the bioengineering, biomechanics, and medical fields. In this investigation, influence of single‐walled carbon nanotubes (SWCNTs) on magnetohydrodynamic mixed convective peristalsis through an inclined and asymmetric channel is analyzed. The additional physical mechanisms such as velocity slip, viscous dissipation, thermal slip, Joule heating, and heat consumption/injection are also encountered. The principal equations are formulated under the estimation of long wavelength and low Reynolds number. Perturbation method is operated to evaluate the solutions of subsequent nonlinear system of equations for small Brinkman number. To deeply analyze the characteristics of embedded parameters, graphs are presented and comprehensive interpretation is provided. Rate of heat transfer is augmented for higher proportion of SWCNTs in base fluid water. At the center of channel, increasing volume fraction of SWCNTs and strong Lorentz force retard the motion of fluid while flow is accelerated in more inclined channel. Volume fraction of SWCNTs, Grashof number, and inclination parameter encourage the pressure gradient at wider part of the channel. The size of bolus is contracted by strong Lorentz force and large volume fraction of SWCNTs. Three basic models named as Maxwell's, Hamilton‐Crosser's, and Xue's model are utilized to forecast the thermal conductivity of nanofluid and succeeding numerical computations for heat transfer rate are presented through table. It is found that the Xue's model is most effective to anticipate the thermal conductivity of nanofluids. Moreover, the addition of a heat sink in the system significantly influences the heat transfer process and plays a supportive role to rapidly cool down the channel.

Fractional order model of thermo-solutal and magnetic nanoparticles transport for drug delivery applications

We examine the capturing efficiency of magnetic nanoparticles bound with drug molecules infused into the blood stream and monitored them by the application of an external magnetic field. We analyzed the motion of the nanoparticles along with the blood velocity through a porous medium vessel under the effect of periodic vibration. The thermo-solutal transport with Caputo-Fabrizio fractional-order derivative is modeled with non-Newtonian biviscosity fluid, Soret and Dufour effect, thermal radiation, and linear variation of the chemical reaction. The Laplace transform, finite Hankel transform and their inverse techniques are used to find analytical solutions. The study shows that both the velocity of blood and nano-particles increase with the increase of particle mass and the concentration parameter, while the opposite behaviour is observed with increasing the fractional parameter, magnetic field effect, and thermal radiation. The heat and mass transfer rates at the wall are enhanced with an increase in the Peclet number and the metabolic heat source. Thermal radiation effect signifies the higher rate of heat transfer at the vessel wall. The study bears potential applications in drug delivery with magnetic nanoparticles at the targeted region.

Biologically Inspired Intra-Uterine Nanofluid Flow under the Suspension of Magnetized Gold (Au) Nanoparticles: Applications in Nanomedicine

The present analysis deals with the intra-uterine nanofluid flow of a Jeffrey fluid through a finite asymmetric channel filled with gold nanoparticles. Gold nanoparticles are helpful in biomedicine to treat various diseases and locate blood flow motion through tiny vessels. The governing fluid is electrically conducting due to the presence of an extrinsic magnetic field while the magnetic Reynolds number is small; therefore, the induced magnetic effects are neglected. The thermal radiation and viscous dissipation effects are also contemplated with the energy equation. The lubrication approach has been utilized by taking a long wavelength and ignoring the inertial forces. The formulated equations are coupled and nonlinear; therefore, a perturbation approach is used to derive the series results. The results are obtained up to the second-order and plotted against various parameters for velocity mechanism, trapping profile, pressure rise, and temperature profile.

Mixed convection stagnation point flow of the blood based hybrid nanofluid around a rotating sphere

In this new world of fluid technologies, hybrid nanofluid has become a productive subject of research among scientists for its potential thermal features and abilities, which provides an excellent result as compared to nanofluids in growing the rate of heat transport. Our purpose here is to introduce the substantial influences of magnetic field on 2D, time-dependent and stagnation point inviscid flow of couple stress hybrid nanofluid around a rotating sphere with base fluid is pure blood, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{TiO}}_{2} \,\,{\text{and}}\,\,{\text{Ag}}$$\end{document}TiO2andAg as the nanoparticles. To translate the governing system of partial differential equations and the boundary conditions relevant for computation, some suitable transformations are implemented. To obtain the analytical estimations for the corresponding system of differential expression, the innovative Optimal Homotopy Analysis Method is used. The characteristics of hybrid nanofluid flow patterns, including temperature, velocity and concentration profiles are simulated and analyzed in detail due to the variation in the evolving variables. Detailed research is also performed to investigate the influences of relevant constraints on the rates, momentum and heat transport for both \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{TiO}}_{2} + {\text{Ag}} + Blood$$\end{document}TiO2+Ag+Blood and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{TiO}}_{2} + Blood$$\end{document}TiO2+Blood. One of the many outcomes of this analysis, it is observed that increasing the magnetic factor will decelerate the hybrid nanofluid flow velocity and improve the temperature profile. It may also be demonstrated that by increasing the Brownian motion factor, significant improvement can be made in the concentration field of hybrid nanofluid. The increase in the nanoparticle volume fraction from 0.01 to 0.02 in the case of the hybrid nanofluid enhances the thermal conductivity from 5.8 to 11.947% and for the same value of the nanoparticle volume fraction in the case of nanofluid enhance the thermal conductivity from 2.576 to 5.197%.

Fractional order model for thermochemical flow of blood with Dufour and Soret effects under magnetic and vibration environment

We examine the effect of the Caputo-Fabrizio derivative of fractional-order model on the flow of blood in a porous tube having thermochemical properties under the magnetic and vibration mode. Blood is considered as the biviscosity non-Newtonian fluid having thermal radiation and chemical reaction properties to observe its impact on energy flux and mass flux gradients. We provided analytical solution via the Laplace, finite Hankel transform, and the corresponding inverse techniques. The study shows that blood velocity and temperature both decrease in ascending values of the fractional-order parameter as memory effect. The permeability of blood flow medium resists to drive the fluid fast. The chemical reaction causes an increase in wall shear stress. Dufour effect influences to rise in the Nusselt number. Thus the study may help to explore further information about the fractional-order model, adsorption of nutrients and their strong correlation with the surface chemistry and applied them in pathology.

Numerical investigation of non-Newtonian blood flow within an artery with cone shape of stenosis in various stenosis angles

BACKGROUND AND OBJECTIVE

In this work, a numerical study is done on the blood flow inside an artery with a cone shape of stenosis. An artery has different stenosis angles. Also, blood flow is energized by constant heat flux which is applied on the wall. The finite volume method is employed to determine blood properties on the basis of a Sisko fluid model with different constant parameters.

METHODS

Firstly, the effects of applying constant heat flux of q'' = 4 W/m² are studied on the velocity profile of blood flow inside an artery with stenosis angles of φ = 0.5°. Afterward, effects of different stenosis angles of φ = 0.25, φ = 0.5, φ = 0.75, φ = 1 and φ = 1.25 is studied on blood flow temperature profile. Then, different values of the Sisko model are employed to investigate influences of Newtonian and non-Newtonian behaviors of blood fluid on the temperature profiles of blood flow inside an artery with stenosis angle of φ = 0.5°.

RESULTS

It is reported that with increasing stenosis angles, blood flow temperature is decreased due to velocity enhancement. This phenomenon is convinced by non-slip condition and sticking non-Newtonian blood fluid to the internal surface of artery wall which reduce velocity from wall surface region to central region of vessel. Also, it is concluded that changing behavior of blood fluid from non-Newtonian to Newtonian behaviors can empower the capability of blood in thermal energy transfer inside human body vessels.

CONCLUSIONS

Any treatment by balloon angioplasty, percutaneous transluminal angioplasty, and serum injection, which changes the behavior of blood flow inside body veins, can be effective on blood flow temperature.

Study of Activation Energy on the Movement of Gyrotactic Microorganism in a Magnetized Nanofluids Past a Porous Plate

The present study deals with the swimming of gyrotactic microorganisms in a nanofluid past a stretched surface. The combined effects of magnetohydrodynamics and porosity are taken into account. The mathematical modeling is based on momentum, energy, nanoparticle concentration, and microorganisms’ equation. A new computational technique, namely successive local linearization method (SLLM), is used to solve nonlinear coupled differential equations. The SLLM algorithm is smooth to establish and employ because this method is based on a simple univariate linearization of nonlinear functions. The numerical efficiency of SLLM is much powerful as it develops a series of equations which can be subsequently solved by reutilizing the data from the solution of one equation in the next one. The convergence was improved through relaxation parameters in the study. The accuracy of SLLM was assured through known methods and convergence analysis. A comparison of the proposed method with the existing literature has also been made and found an excellent agreement. It is worth mentioning that the successive local linearization method was found to be very stable and flexible for resolving the issues of nonlinear magnetic materials processing transport phenomena.

Mathematical Analysis of Entropy Generation in the Flow of Viscoelastic Nanofluid through an Annular Region of Two Asymmetric Annuli Having Flexible Surfaces

In this manuscript, the authors developed the mathematical model for entropy generation analysis during the peristaltic propulsion of Jeffrey nanofluids passing in a midst of two eccentric asymmetric annuli. The model was structured by implementation of lubrication perspective and dimensionless strategy. Entropy generation caused by the irreversible influence of heat and mass transfer of nanofluid and viscous dissipation of the considered liquid was taken into consideration. The governing equations were handled by a powerful analytical technique (HPM). The comparison of total entropy with the partial entropy was also invoked by discussing Bejan number results. The influence of various associated variables on the profiles of velocity, temperature, nanoparticle concentration, entropy generation and Bejan number was formulated by portraying the figures. Mainly from graphical observations, we analyzed that, in the matter of thermophoresis parameter and Brownian motion parameter, entropy generation is thoroughly enhanced while inverse readings were reported for the temperature difference parameter and the ratio of temperature to concentration parameters.

Signalling molecule transport analysis in lacunar-canalicular system

Mechanical loading-induced fluid flow in lacunar-canalicular space (LCS) of bone excites osteocyte cells to release signalling molecules which initiate osteo-activities. Theoretical models considered canaliculi as a uniform and symmetrical space/channel in bone. However, experimental studies reported that canalicular walls are irregular and curvy resulting in inhomogeneous fluid motion which may influence the molecular transport. Therefore, a new mathematical model of LCS with curvy canalicular walls is developed to characterize cantilever bending-induced canalicular flow behaviour in terms of pore-pressure, fluid velocity, and streamlines. The model also analyses the mobility of signalling molecules involved in bone mechanotransduction as a function of loading frequency and permeability of LCS. Inhomogeneous flow is observed at higher loading frequency which amplifies mechanotransduction; nevertheless, it also promotes trapping of signalling molecules. The effects of shape and size of signalling molecules on transport behaviour are also studied. Trivially, signalling molecules larger in size and weight move slower as compared to molecules small in size and weight which validates the findings of the present study. The outcomes will ultimately be useful in designing better biomechanical exercise in combination with pharmaceutical agents to improve the bone health.

Unsteady Radiative Natural Convective MHD Nanofluid Flow Past a Porous Moving Vertical Plate with Heat Source/Sink

In this research article, we investigated a comprehensive analysis of time-dependent free convection electrically and thermally conducted water-based nanofluid flow containing Copper and Titanium oxide (Cu and TiO 2 ) past a moving porous vertical plate. A uniform transverse magnetic field is imposed perpendicular to the flow direction. Thermal radiation and heat sink terms are included in the energy equation. The governing equations of this flow consist of partial differential equations along with some initial and boundary conditions. The solution method of these flow interpreting equations comprised of two parts. Firstly, principal equations of flow are symmetrically transformed to a set of nonlinear coupled dimensionless partial differential equations using convenient dimensionless parameters. Secondly, the Laplace transformation technique is applied to those non-dimensional equations to get the close form exact solutions. The control of momentum and heat profile with respect to different associated parameters is analyzed thoroughly with the help of graphs. Fluid accelerates with increasing Grashof number (Gr) and porosity parameter (K), while increasing values of heat sink parameter (Q) and Prandtl number (Pr) drop the thermal profile. Moreover, velocity and thermal profile comparison for Cu and TiO 2 -based nanofluids is graphed.

Special Issue on Symmetry and Fluid Mechanics

This Special Issue invited researchers to contribute their original research work and review articles on “Symmetry and Fluid Mechanics” that either advances the state-of-the-art mathematical methods through theoretical or experimental studies or extends the bounds of existing methodologies with new contributions related to the symmetry, asymmetry, and lie symmetries of differential equations proposed as mathematical models in fluid mechanics, thereby addressing current challenges. In response to the call for papers, a total of 42 papers were submitted for possible publication. After comprehensive peer review, only 25 papers qualified for acceptance for final publication. The rest of the papers could not be accommodated. The submissions may have been technically correct but were not considered appropriate for the scope of this Special Issue. The authors are from geographically distributed countries such as the USA, Australia, China, Saudi Arabia, Iran, Pakistan, Malaysia, Abu Dhabi, UAE, South Africa, and Vietnam. This reflects the great impact of the proposed topic and the effective organization of the guest editorial team of this Special Issue.

Effects of Double Diffusion Convection on Third Grade Nanofluid through a Curved Compliant Peristaltic Channel

Nanofluids are potential heat transfer fluids with improved thermophysical properties and heat transfer performance. Double diffusion convection plays an important role in natural processes and technical applications. The effect of double convection by diffusion is not limited to oceanography, but is also evident in geology, astrophysics, and metallurgy. For such a vital role of such factors in applications, the authors have presented the analytical solutions of pumping flow of third-grade nanofluid and described the effects of double diffusion convection through a compliant curved channel. The model used for the third-grade nanofluid includes the presence of Brownian motion and thermophoresis. Additionally, thermal energy expressions suggest regular diffusion and cross-diffusion terms. The governing equations have been constructed for incompressible laminar flow of the non-Newtonian nanofluid along with the assumption of long wavelength. The obtained analytical expressions for velocity, temperature, and nanoparticle concentration have been sketched for various considerable parameters. The effects of regular buoyancy ratio, buoyancy parameter, modified Dufour parameter, and Dufour-solutal Lewis number have been analyzed along with wall properties and pumping characteristics. This study concludes that fluid becomes hotter with increase in regular buoyancy ratio and a modified Dufour parameter, but a decrease in temperature is observed for the buoyancy parameter. Moreover, the solutal concentration is behaving inversely against the Defour-Solutal Lewis number.

Darcy–Boussinesq Model of Cilia-Assisted Transport of a Non-Newtonian Magneto-Biofluid with Chemical Reactions

The model developed in this study presents a mathematical approach to the physiological transport of seminal liquid due to ciliary movements, which are attached with the lumen of the ductile efferent in the male reproductive system. The rheological properties of the seminal liquids were described using the Jeffrey liquid model. The problem described an electromagnetic mixed convective flow of a Jeffrey liquid through a vertical channel with heat and mass transfers. The effects of chemical reactions and the external heat generation were included in the formulation. The flow took place through an active porous medium (due to thick cilia mat and other deposits) and was influenced by the Lorentz magnetic force. Four basic conservation laws of mass, momentum, energy, and concentration were utilized in the mathematical modeling. These are highly nonlinear equations, which were simplified due to a physiologically valid approach known as LAT (lubrication approximation theory). Analytical solutions for temperature, concentration, and velocity profiles were evaluated. The expressions describing the pressure–volume flow rate relationships were also obtained. Analysis of various physical and geometrical factors affecting the pressure–volume (pumping) characteristics was also presented. One of the main findings of our study is that the difference between our calculated values of the flow rate and the estimated values of the flow rate in the ductile efferent was negligibly small. Moreover, our results can be implemented in the artificial cilia pumping systems in microchannels.

Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects

BACKGROUND

In last few decades, a new class of working materials which comprises from two solid materials dispersed in a continuous phase liquid was established and deeply scrutinized. These materials are called hybrid nanomaterials. This research article aims to investigate entropy optimization in hybrid nanomaterial flow through a rotating peristaltic channel walls. Flow behavior is analyzed between the channels which is caused by propagation of sinusoidal waves. Viscosity of fluid is considered variable instead of constant characteristics. Fluid saturates through porous attributes of channel walls. Nonliear radiative flux and convective condition are considered. Slip conditions are imposed at the boundary of walls.

METHODS

Built-in-Shooting technique is employed to obtain the numerical outcomes for the considered flow problem.

RESULTS

Impacts of sundry variables on the entropy, temperature and velocity are scrutinized through different graphs. Numerical result presents that the axial velocity escalates with the inclusion of hybrid nanomaterial. The temperature of fluid enhances through higher estimations of hybrid nanoparticles.

CONCLUSIONS

Here the flow behavior is discussed between the channels which are caused by propagation of sinusoidal waves with speed c. Entropy generation rate is minimum for variable viscosity and maximum for hybrid nanoparticles. Hybrid nanoparticles increase the temperature of fluid. Bejan number presents the similar impact for variable viscosity and thermal slip parameters. Temperature field decays through higher values of Brinkman number.

Mathematical Analysis on an Asymmetrical Wavy Motion of Blood under the Influence Entropy Generation with Convective Boundary Conditions

In this article, we discuss the entropy generation on the asymmetric peristaltic propulsion of non-Newtonian fluid with convective boundary conditions. The Williamson fluid model is considered for the analysis of flow properties. The current fluid model has the ability to reveal Newtonian and non-Newtonian behavior. The present model is formulated via momentum, entropy, and energy equations, under the approximation of small Reynolds number and long wavelength of the peristaltic wave. A regular perturbation scheme is employed to obtain the series solutions up to third-order approximation. All the leading parameters are discussed with the help of graphs for entropy and temperature profiles. The irreversibility process is also discussed with the help of Bejan number. Streamlines are plotted to examine the trapping phenomena. Results obtained provide an excellent benchmark for further study on the entropy production with mass transfer and peristaltic pumping mechanism.

Impact of Velocity Second Slip and Inclined Magnetic Field on Peristaltic Flow Coating with Jeffrey Fluid in Tapered Channel

The peristaltic flow of velocity second slip boundary conditions and inclined magnetic field of Jeffrey fluid by means of heat and mass transfer in asymmetric channel was inspected in the present study. Leading equations described the existing flow were then simplified under lubrication approach. Therefore, exact solutions of stream function, concentration and temperature were deduced. Further, the numerical solutions of pressure rise and pressure gradient were computed using Mathematica software. Furthermore, the effect of the second slip parameter was argued via graphs. It has been depicted that this kind of slip is mandatory and very imperative to foresee the physical model. On the other hand, false results will be obtained.

Keller-Box Analysis of Buongiorno Model with Brownian and Thermophoretic Diffusion for Casson Nanofluid over an Inclined Surface

The key objective of the study under concern is to probe the impacts of Brownian motion and thermophoresis diffusion on Casson nanofluid boundary layer flow over a nonlinear inclined stretching sheet, with the effect of convective boundaries and thermal radiations. Nonlinear ordinary differential equations are obtained from governing nonlinear partial differential equations by using compatible similarity transformations. The quantities associated with engineering aspects, such as skin friction, Sherwood number, and heat exchange along with various impacts of material factors on the momentum, temperature, and concentration, are elucidated and clarified with diagrams. The numerical solution of the present study is obtained via the Keller-box technique and in limiting sense are reduced to the published results for accuracy purpose.

Numerical simulation of electroosmosis regulated peristaltic transport of Bingham nanofluid

The effects of slip condition and Joule heating on the peristaltic flow of Bingham nanofluid are investigated. The flow is taken in a porous channel with elastic walls. Mathematical formulation is presented under the assumption of long wavelength and small Reynolds number. The transformed equations for the flow are solved to seek values for the nanoparticles velocity, concentration and temperature along the channel length. Graphs are plotted to evaluate the behavior of various physical parameters on flow quantities in both slip and no-slip cases. The main features of the physical parameters are highlighted on the inclined non uniform channel. The results show an increment in velocity with rise in inclination and porosity while it reduces with magnetic field. Moreover, nanofluid favors the heat transfer and decline the concentration.

Darcy–Forchheimer Radiative Flow of Micropoler CNT Nanofluid in Rotating Frame with Convective Heat Generation/Consumption

Since 1991, from the beginning of the carbon nanotube era, this has been a focus point for investigation due to its synthetic and simple nature. Unique properties like good stiffness, high surface area, and resilience of carbon nanotubes (CNTs) have been investigated in many engineering applications such as hydrogen storage, composite material, energy storage, electrochemical super-capacitors, transistors, sensors, and field-emitting devices. Keeping in view these applications, we investigate single and multi-walled CNTs nanofluid flow having water as the base fluid between parallel and horizontal rotating plates with microstructure and inertial properties. The thermal radiation effect is considered for variable phenomenon of heat generation/consumption. The principal equations are first symmetrically transformed to a system of nonlinear coupled ordinary differential equations (ODEs), and then, Homotopy Analysis Technique (HAM) and numerical method are employed for solving these coupled equations. The obtained analytical and numerical results are explained graphically and through different tables. The HAM and numerical results show an excellent agreement. The Skin friction and the Nusselt number are numerically calculated and then analyzed with the already published results, and these results are found to be in agreement with one another. The impact of important parameters are shown graphically.

Effect of the Variable Viscosity on the Peristaltic Flow of Newtonian Fluid Coated withMagnetic Field: Application of Adomian Decomposition Method for Endoscope

In the present analysis, peristaltic flow was discussed for MHD Newtonian fluid through the gap between two coaxial tubes, where the viscosity of the fluid is treated as variable. In addition, the inner tube was considered to be at rest, while the outer tube had the sinusoidal wave traveling down its motion. Further, the assumptions of long wave length and low Reynolds number were taken into account for the formulation of the problem. A closed form solution is presented for general viscosity using the Adomian decomposition method. Numerical illustrations that show the physical effects and pertinent features were investigated for different physical included phenomenon. It was found that the pressure rise increases with an increase in Hartmann number, and frictional forces for the outer and inner tube decrease with an increase in Hartmann number when the viscosity is constant. It was also observed that the size of the trapping bolus decreases with an increase in Hartmann number, and increases with an increase in amplitude ratio when the viscosity is parameter.

Numerical Simulation and Mathematical Modeling of Electro-Osmotic Couette–Poiseuille Flow of MHD Power-Law Nanofluid with Entropy Generation

The basic motivation of this investigation is to develop an innovative mathematical model for electro-osmotic flow of Couette–Poiseuille nanofluids. The power-law model is treated as the base fluid suspended with nano-sized particles of aluminum oxide (Al2O3). The uniform speed of the upper wall in the axial path generates flow, whereas the lower wall is kept fixed. An analytic solution for nonlinear flow dynamics is obtained. The ramifications of entropy generation, magnetic field, and a constant pressure gradient are appraised. Moreover, the physical features of most noteworthy substantial factors such as the electro-osmotic parameter, magnetic parameter, power law fluid parameter, skin friction, Nusselt number, Brinkman number, volume fraction, and concentration are adequately delineated through various graphs and tables. The convergence analysis of the obtained solutions has been discussed explicitly. Recurrence formulae in each case are also presented.

Peristaltic Pumping of Nanofluids through a Tapered Channel in a Porous Environment: Applications in Blood Flow

In this study, we present an analytical study on blood flow analysis through with a tapered porous channel. The blood flow was driven by the peristaltic pumping. Thermal radiation effects were also taken into account. The convective and slip boundary conditions were also applied in this formulation. These conditions are very helpful to carry out the behavior of particle movement which may be utilized for cardiac surgery. The tapered porous channel had an unvarying wave speed with dissimilar amplitudes and phase. The non-dimensional analysis was utilized for some approximations such as the proposed mathematical modelling equations were modified by using a lubrication approach and the analytical solutions for stream function, nanoparticle temperature and volumetric concentration profiles were obtained. The impacts of various emerging parameters on the thermal characteristics and nanoparticles concentration were analyzed with the help of computational results. The trapping phenomenon was also examined for relevant parameters. It was also observed that the geometric parameters, like amplitudes, non-uniform parameters and phase difference, play an important role in controlling the nanofluids transport phenomena. The outcomes of the present model may be applicable in the smart nanofluid peristaltic pump which may be utilized in hemodialysis.

Significance of Velocity Slip in Convective Flow of Carbon Nanotubes

The present article inspects velocity slip impacts in three-dimensional flow of water based carbon nanotubes because of a stretchable rotating disk. Nanoparticles like single and multi walled carbon nanotubes (CNTs) are utilized. Graphical outcomes have been acquired for both single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). The heat transport system is examined in the presence of thermal convective condition. Proper variables lead to a strong nonlinear standard differential framework. The associated nonlinear framework has been tackled by an optimal homotopic strategy. Diagrams have been plotted so as to examine how the temperature and velocities are influenced by different physical variables. The coefficients of skin friction and Nusselt number have been exhibited graphically. Our results indicate that the skin friction coefficient and Nusselt number are enhanced for larger values of nanoparticle volume fraction.

Two-Phase Couette Flow of Couple Stress Fluid with Temperature Dependent Viscosity Thermally Affected by Magnetized Moving Surface

The Couette–Poiseuille flow of couple stress fluid with magnetic field between two parallel plates was investigated. The flow was driven due to axial pressure gradient and uniform motion of the upper plate. The influence of heating at the wall in the presence of spherical and homogeneous Hafnium particles was taken into account. The temperature dependent viscosity model, namely, Reynolds’ model was utilized. The Runge–Kutta scheme with shooting was used to tackle a non-linear system of equations. It was observed that the velocity decreased by increasing the values of the Hartman number, as heating of the wall reduced the effects of viscous forces, therefore, resistance of magnetic force reduced the velocity of fluid. However, due to shear thinning effects, the velocity was increased by increasing the values of the viscosity parameter, and as a result the temperature profile also declined. The suspension of inertial particles in an incompressible turbulent flow with Newtonian and non-Newtonian base fluids can be used to analyze the biphase flows through diverse geometries that could possibly be future perspectives of proposed model.

Thermally Charged MHD Bi-Phase Flow Coatings with Non-Newtonian Nanofluid and Hafnium Particles along Slippery Walls

The present study is about the pressure-driven heated bi-phase flow in two slippery walls. The non-Newtonian couple stress fluid is suspended with spherically homogenous metallic particles. The magnetic susceptibility of Hafnium allures is taken into account. The rough surface of the wall is tackled by lubrication effects. The nonlinear coupled partial differential equations along with the associated boundary conditions are first reduced into a set of ordinary differential equations by using appropriate transformations and then numerical results were obtained by engaging the blend of Runge–Kutta and shooting techniques. The sway of physical quantities are examined graphically. An excellent agreement within graphical illustration and numerical results is achieved.

Effects of Radiative Electro-Magnetohydrodynamics Diminishing Internal Energy of Pressure-Driven Flow of Titanium Dioxide-Water Nanofluid due to Entropy Generation

The internal average energy loss caused by entropy generation for steady mixed convective Poiseuille flow of a nanofluid, suspended with titanium dioxide (TiO₂) particles in water, and passed through a wavy channel, was investigated. The models of thermal conductivity and viscosity of titanium dioxide of 21 nm size particles with a volume concentration of temperature ranging from 15 °C to 35 °C were utilized. The characteristics of the working fluid were dependent on electro-magnetohydrodynamics (EMHD) and thermal radiation. The governing equations were first modified by taking long wavelength approximations, which were then solved by a homotopy technique, whereas for numerical computation, the software package BVPh 2.0 was utilized. The results for the leading parameters, such as the electric field, the volume fraction of nanoparticles and radiation parameters for three different temperatures scenarios were examined graphically. The minimum energy loss at the center of the wavy channel due to the increase in the electric field parameter was noted. However, a rise in entropy was observed due to the change in the pressure gradient from low to high.