Stagnation point flow of Maxwell nanofluid containing gyrotactic micro‐organism impinging obliquely on a convective surface

A numerical study is performed to discuss the nonaligned stagnation of a rate type fluid over a convective surface. The rheology of the fluid is presented by the constitutive equation of the Maxwell fluid model. Buongiorno's model is used to elaborate on the effects of Brownian motion and thermophoresis and motile microorganisms are introduced for the stability of the nanoparticles. The governing equations were solved by the implicit finite difference method. Graphical illustrations for velocity, temperature, nanoparticle concentration and motile microorganism profiles for various involved parameters are presented for both convective and nonconvective surfaces. It is depicted that the temperature, nanoparticle, and microorganism concentration profiles decease while both axial and tangential velocities increase with the velocity ratio parameter for both Newtonian and Maxwellian fluids. The magnitude of temperature, nanoparticle, and microorganism concentration profiles is large for the nonconvective surface as compared to the convective surface. The Nusselt number, Sherwood number, and motile organism number decrease as we move from Newtonian fluid to non‐Newtonian fluid. Furthermore, the increase in the Brownian motion parameter and thermophoresis parameter decreases the density of the motile organism over the convective as well as nonconvective surface.     

Simultaneous effects of radiation,magnetic field on peristaltic flow of Carreau nanofluid submerged in gyrotactic microorganisms with heat and mass transfer

Our study intends to examine the combined effects of radiation, magnetic field, and chemical reaction on the peristaltic flow of a non-Newtonian fluid containing gyrotactic microorganisms and nanoparticles. The system of our equations is understood numerically by using the Rung-Kutta-Merson method with Newton iteration in a shooting and matching procedure. The effect of physical implanted parameters is represented and discussed through a lot of charts for velocity, temperature, nanoparticle concentration, the density of motile microorganisms. From this discussion, we notice that the motile microorganisms profile is affected by the arising with the Brownian motion parameter and radiation parameter but the thermophoresis parameter, traditional Lewis number, and bioconvection of Peclet number are decremented the motile microorganisms profile.     

A model for entropy generation in stagnation‐point flow of non‐Newtonian Jeffrey,Maxwell, and Oldroyd‐B nanofluids

We present a generalized model to describe the flow of three non‐Newtonian nanofluids, namely, Jeffrey, Maxwell, and Oldroyd‐B nanofluids. Using this model, we study entropy generation and heat transfer in laminar nanofluid boundary‐layer stagnation‐point flow. The flow is subject to an external magnetic field. The conventional energy equation is modified by the incorporation of nanoparticle Brownian motion and thermophoresis effects. A hydrodynamic slip velocity is used in the initial condition as a component of the stretching velocity. The system of nonlinear equations is solved numerically using three different methods, a spectral relaxation method, spectral quasilinearization method, and the spectral local linearization method, first to determine the most accurate of these methods, and second as a measure to validate the numerical simulations. The residual errors for each method are presented. The numerical results show that the spectral relaxation method is the most accurate of the three methods, and this method is used subsequently to solve the transport equations and thus to determine the empirical impact of the physical parameters on the fluid properties and entropy generation.     

Flow and heat transfer in a porous medium saturated with a Sisko nanofluid over a nonlinearly stretching sheet with heat generation/absorption

This work is focused on steady flow and heat transfer in a porous medium saturated with a Sisko nanofluid (non‐Newtonian power‐law) over a nonlinearly stretching sheet in the presence of heat generation/absorption. Nonlinear PDEs are transformed into a system of coupled nonlinear ODEs with related boundary conditions using similarity transformation. The reduced equations are then solved numerically using the Runge–Kutta–Fehlberg fourth–fifth order method (RKF45) with Maple 14.0 software. The solutions depend on the power‐law index n and the effect of pertinent parameter such as the Brownian motion parameter, thermophoresis parameter, Lewis number, the permeability, and the heat generation/absorption on the dimensionless velocity, temperature, and nanoparticles volume fraction and also on the skin friction, local Nusselt, and Sherwood numbers are produced for values of the influence parameter. A rapprochement of the numerical results of the actual study with formerly published data detected an excellent agreement.     

Similarity solution of three‐dimensional MHD radiative Casson nanofluid motion over a stretching surface with chemical and diffusion‐thermo effects

In this study, we analyzed three‐dimensional magnetohydrodynamic non‐Newtonian and Newtonian fluid motion, transfer of heat and mass over a stretching surface with Brownian flow, thermophoresis, and Dufour effects. By Runge‐Kutta based shooting method, the transformed governing equations are solved numerically. With the facilitate of tables and graphs, momentum, energy and mass profiles along with the skin friction coefficient, local Nusselt number, and Sherwood number are analyzed in the influence of nondimensional parameters. It is established that enhance the stretching ratio parameter improves the energy and concentration transfer rate. The transfer of energy and concentration rate in the Newtonian fluid is relatively low while compared with non‐Newtonian fluid.     

Finite element analysis of non‐Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery

The present study considers two‐dimensional mathematical modeling of non‐Newtonian nanofluid hemodynamics with heat and mass transfer in a stenosed coronary artery in the presence of a radial magnetic field. The second‐grade differential viscoelastic constitutive model is adopted for blood to mimic non‐Newtonian characteristics, and blood is considered to contain a homogenous suspension of nanoparticles. The Vogel model is employed to simulate the variation of blood viscosity as a function of temperature. The governing equations are an extension of the Navier‐Stokes equations with linear Boussinesq's approximation and Buongiorno's nanoscale model (which simulates both heat and mass transfer). The conservation equations are normalized by employing appropriate nondimensional variables. It is assumed that the maximum height of the stenosis is small in comparison with the radius of the artery, and, furthermore, that the radius of the artery and length of the stenotic region are of comparable magnitude. To study the influence of vessel geometry on blood flow and nanoparticle transport, variation in the design and size of the stenosis is considered in the domain. The transformed equations are solved numerically by means of the finite element method based on the variational approach and simulated using the FreeFEM++ code. A detailed grid‐independence study is included. Blood flow, heat, and mass transfer characteristics are examined for the effects of selected geometric, nanoscale, rheological, viscosity, and magnetic parameters, that is, stenotic diameter (d), viscoelastic parameter (), thermophoresis parameter (), Brownian motion parameter (), and magnetic body force parameter (M) at the throat of the stenosis and throughout the arterial domain. The velocity, temperature, and nanoparticle concentration fields are also visualized through instantaneous patterns of contours. An increase in magnetic and thermophoresis parameters is found to enhance the temperature, nanoparticle concentration, and skin‐friction coefficient. Increasing Brownian motion parameter is observed to accelerate the blood flow. Narrower stenosis significantly alters the temperature and nanoparticle distributions and magnitudes. The novelty of the study relates to the combination of geometric complexity, multiphysical nanoscale, and thermomagnetic behavior, and also the simultaneous presence of biorheological behavior (all of which arise in actual cardiovascular heat transfer phenomena) in a single work with extensive visualization of the flow, heat, and mass transfer characteristics. The simulations are relevant to the diffusion of nano‐drugs in magnet‐targeted treatment of stenosed arterial disease.     

Gyrotactic microorganisms bioconvection in combined convective magnetohydrodynamic Casson nanofluid flow over a vertically surfaced saturated porous media with variable viscosity

The current article focuses on mass and thermal transfer analysis of a two-dimensional immovable combined convective nanofluid flow including motile microorganisms with temperature-dependent viscosity on top of a vertical plate through a porous medium, and a model has been developed to visualize the velocity slip impacts on a nonlinear partial symbiotic flow. The governed equations include all of the above physical conditions, and suitable nondimensional transfigurations are utilized to transfer the governed conservative equations to a nonlinear system of differential equations and obtain numerical solutions by using the Shooting method. Numerical studies have been focusing on the effects of intricate dimensionless parameters, namely, the Casson fluid parameter, Brownian motion parameter, thermophoresis parameter, Peclet number, bioconvection parameter, and Rayleigh number, which have all been studied on various profiles such as momentum, thermal, concentration, and density of microorganisms. The concentration boundary layer thickness and density of microorganisms increased as the Casson fluid parameter, Brownian and thermophoresis parameters increased, whereas the bioconvection parameter, Peclet number, and Rayleigh number increased. The thermal boundary layer thickness, concentration boundary layer thickness, and density of microorganisms all decreased. The velocity distribution decreases as the Peclet number, bioconvection, and thermophoresis parameters rise but rises as the Rayleigh number, Brownian motion parameter, and Casson fluid parameter rise. These are graphed via plots along with divergent fluid parameters.     

Passive control nanoparticles in double‐diffusive free convection nanofluid flow over an inclined permeable plate

The present study has been conducted to acquire the solutions for the flow problem of an incompressible nanofluid past a permeable inclined plate implanted in a porous medium. In this study, double‐diffusivity, Brownian motion, and thermophoresis as well as passive control nanoparticles have been studied. We employ Lie group transformation on the ruling equations to extract nonlinear ordinary differential equations and solve them numerically using the fourth‐order Runge‐Kutta method and shooting approach. The supremacy of affined parameters on temperature and velocity distributions has been exposed by means of tables and graphs. This investigation suggests that both fluid velocity and nanoparticle concentration are enhanced by the modified Dufour parameter and the thermophoresis parameter. The assistance of the Lewis number intensifies the heat transport for suction.     

Magnetized impacts of Brownian motion and thermophoresis on unsteady squeezing flow of nanofluid between two parallel plates with chemical reaction and Joule heating

Present research article investigate the heat and mass transfer characteristics of unsteady magnetohydrodynamic Casson nanofluid flow between two parallel plates under the influence of viscous dissipation and first order homogeneous chemical reaction effects. The impacts of thermophoresis and Brownian motion are accounted in the nanofluid model to disclose the salient features of heat and mass transport phenomena. The present physical problem is examined under the presence of Lorentz forces to investigate the effects of magnetic field. Further, the viscous and Joule dissipation effects are considered to describe the heat transfer process. The non‐Newtonian behaviour of Casson nanofluid is distinguished from those of Newtonian fluids by considering the well‐established rheological Casson fluid model. The two‐dimensional partial differential equations governing the unsteady squeezing flow of Casson nanofluid are coupled and highly nonlinear in nature. Thus, similarity transformations are imposed on the conservation laws to obtain the nonlinear ordinary differential equations. Runge‐Kutta fourth order integration scheme with shooting method and bvp4c techniques have been used to solve the resulting nonlinear flow equations. Numerical results have been obtained and presented in the form of graphs and tables for various values of physical parameters. It is noticed from present investigation that, the concentration field is a decreasing function of thermophoresis parameter. Also, concentration profile enhances with raising Brownian motion parameter. Further, the present numerical results are compared with the analytical and semianalytical results and found to be in good agreement.     

Influence of wall properties on the peristaltic flow of a nanofluid: Analytic and numerical solutions

This study is concerned with the peristaltic transport of nanofluid in a channel with complaint walls. Transport equations involve the combined effects of Brownian motion and thermophoretic diffusion of nanoparticles. Mathematical modeling is carried out by utilizing long wavelength and low Reynolds number assumptions. The coupled nonlinear boundary value problem (BVP) has been solved numerically by using shooting technique through software Mathematica. The analytic solutions are computed by a robust analytical tool namely the homotopy analysis method (HAM). Attention has been focused on the behaviors of Brownian motion parameter (Nb), thermophoresis parameter (Nt), Prandtl number (Pr) and Eckert number (Ec). The results indicate an appreciable increase in the temperature and nanoparticles concentration with the increase in the strength of Brownian motion effects. Further heat transfer coefficient is a decreasing function of Nb and Nt.     

Effect of Newtonian Heating and Thermal Radiation on Heat and Mass Transfer of Nanofluids over a Stretching Sheet in Porous Media

Laminar boundary layer slip flow from a stretching surface in a nanofluid‐saturated homogenous, isotropic porous medium is studied numerically. A Newtonian heating boundary condition in the presence of thermal radiation is incorporated and a Darcy model utilized for the porous medium. The model used for the nanofluids include the effects of Brownian motion and thermophoresis. A group theoretical analysis is conducted to generate similarity transformations. The governing transport equations are nondimensionalized and rendered into a set of coupled similarity ordinary differential equations using similarity transformations. The transformed equations are then solved using the Runge–Kutta–Fehlberg fourth‐fifth order numerical method with shooting technique. It is shown that the physical quantities of interest depend on a number of parameters. The results are presented in tabular and graphical forms. Comparison of the present numerical solutions with published work shows very good agreement. The study finds applications in high‐temperature nanotechnological materials processing.     

Radiative flow of micropolar nanofluid accounting thermophoresis and Brownian moment

This article describes the Brownian motion and thermophoresis aspects in nonlinear flow of micropolar nanoliquid. Stretching surface with linear velocity creates the flow. Energy expression is modeled subject to consideration of thermal radiation phenomenon. Effect of Newtonian heating is considered. The utilization of transformation procedure yields nonlinear differential systems which are computed through homotopic approach. The important features of several variables like material parameter, conjugate parameter, Prandtl number, Brownian motion parameter, radiation parameter, thermophoresis parameter and Lewis number on velocity, micro-rotation velocity, temperature, nanoparticles concentration, surface drag force and heat and mass transfer rates are discussed through graphs and tables. The presented analysis reveals that the heat and mass transfer rates are enhanced for higher values of radiation and Brownian motion parameters. Present computations are consistent with those of existing studies in limiting sense.     

Heat and Mass Transfer Flow of a Nanofluid over an Inclined Plate under Enhanced Boundary Conditions with Magnetic Field and Thermal Radiation

This article presents the magnetohydrodynamic boundary layer flow, heat and mass transfer characteristics of a nanofluid over an inclined porous vertical plate with thermal radiation and chemical reaction. The new enhanced concentration boundary condition on the surface of the wall is considered in this analysis. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using the similarity variables and are solved numerically using the finite element method. The effect of key parameters such as magnetic parameter (M), buoyancy ratio (Nr), Prandtl number (Pr), thermal radiation (R), Brownian motion (Nb), thermophoresis (Nt), Lewis number (Le), and chemical reaction parameter (Cr) on velocity, temperature, and concentration distributions is discussed in detail and the results are shown graphically. Furthermore, the impact of these parameters on skin‐friction coefficient, Nusselt number, and Sherwood number is also investigated and the results are shown in tabular form. The developed algorithm is validated with works published previously and was found to be in good agreement. The thermal boundary layer thickness is elevated, whereas the solutal boundary layer thickness retards with the improving values of the Brownian motion parameter (Nb). The rates of nondimensional temperature and concentration both decelerate with higher values of the thermophoresis parameter (Nt).     

Nonlinear magnetohydrodynamic flow of nanofluids across a porous matrix over an extending sheet with mass transpiration and bioconvection

The consequences of the nonlinear magnetic field and radiative thermal energy are evaluated for bioconvective viscous flow across a porous matrix over a nonlinearly stretching sheet. The rationale of the study is to attain enhanced thermal transportation. The dilute dispersion of nanoentities and bioconvection of swimming microorganisms are taken into consideration. The coupled partial differential system of field equations is transformed into ordinary differential form. Finally, the numeric solution is obtained by utilizing the fourth-order Runge–Kutta method shooting technique, and results are validated through an acceptable accord with existing studies. The variation of influential parameters such as combined magnetic parameter, mass transpiration parameter, thermophoresis, Brownian motion, bioconvection Lewis numbers made notable impacts on fluid velocity, temperature, concentration of nanoentities, and distribution of microorganisms.     

Variable viscosity and thermophoresis for Soret and Dufour's effects on MHD generation in a non‐Daracian porosity fluid

The effect of thermophoresis on a magnetic field generation in a non‐Daracian porous medium flow with the variation of the viscosity fluid in the presence of Soret and Dufour, thermal reaction and diffusion effects over a stretching surface is investigated in the present analysis. The governing equations of continuity, momentum, energy, and concentration are transformed into nonlinear ordinary differential equations, using similarity transformations and then solved numerically. The influence of various physical parameters on velocity, temperature, and concentration profiles are illustrated graphically, and the physical aspects are discussed in detail. Finally, the effects of related physical parameters on the skin friction, the rate of heat and mass transfer are also studied.     

Hydromagnetic non‐Newtonian nanofluid transport phenomena from an isothermal vertical cone with partial slip: Aerospace nanomaterial enrobing simulation

In this article, the combined magneto‐hydrodynamic heat, momentum, and mass (species) transfer in external boundary layer flow of Casson nanofluid from a vertical cone surface with convective conditions under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multidegree, nonsimilar PDEs consisting of the momentum, energy, and concentration equations via appropriate nonsimilarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second‐order, accurate finite difference method of the implicit type. The influences of the emerging parameters, that is, magnetic parameter (M), Casson fluid parameter (β), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr), velocity slip (S_f) and thermal slip (S_T) on velocity, temperature, and nanoparticle concentration distributions is illustrated graphically and interpreted at length. Validation of solutions with a Nakamura tridiagonal method has been included. The study is relevant to enrobing processes for electrically conductive nanomaterials, of potential use in aerospace and other industries.     

Impact of the magnetic dipole on stagnation point flow of ferromagnetic Walters-B liquid: A passive control approach with Buongiorno's model

The properties of ferromagnetic fluids make them suitable for a wide range of applications, including loudspeakers, magnetic resonance imaging, computer hard drives, magnetic drug delivery, and magnetic hyperthermia. Owing to all such potential applications, the present research work is established to explain the stagnation point flow, heat, and mass transfer of Walters-B liquid in the presence of magnetic dipole, Brownian diffusion, and thermophoresis. To control the nanoparticles concentration at the surface, a passive control condition is employed. Using suitable similarity transformations, the governing equations are converted into nonlinear ordinary differential equations. Noticeable behavior of significant parameters on flow fields is studied graphically. The significant outcomes of the present study are that the increased values of viscoelastic parameter decline the velocity but an inverse trend is seen in heat transfer. The increased values of the Brownian motion parameter decline the heat transfer but a contrary trend is seen for augmented values of the thermophoresis parameter. The heat transfer rate is increased for rising values of radiation parameter and Biot number. The upward values of the thermophoresis parameter decline the rate of mass transfer. The escalating values of ferromagnetic interaction and velocity ratio parameters improve the skin friction.     

Computation of Darcy-Forchheimer flow of Sisko nanofluid over a stretching cylinder

This study investigates the Darcy-Forchheimer flow of Sisko nanofluid with viscous dissipation and convective thermal boundary conditions. The Buongiorno two-component nanoscale model is deployed for nanofluid characteristics, which take into account the physical phenomena responsible for the slip velocity between the base fluid and the nanoparticles such as thermophoresis and Brownian diffusion. The Darcy- Forchheimer model employed here includes the effects of boundary and inertial forces. The nonlinear coupled partial differential equations governing the fluid flow are converted into the nonlinear ordinary differential equations by choosing suitable similarity transformations. The nondimensionalized differential equations are then solved utilizing the finite difference based bvp-4c tool in MATLAB software. The numerical solutions are presented graphically to demonstrate the impact of involved physical parameters on temperature, velocity, and nanoparticle volume fraction. Moreover, the rate of heat transfer, mass transfer, and skin friction are physically interpreted. The present investigation reveals that the Darcy number enhances the velocity and depleted the temperature while the Forchheimer number depleted the velocity and enhances the temperature of the Sisko nanofluid. The thermophoresis, Brownian diffusion parameters, and the Forchheimer number contribute to the reduction in the heat transfer rate while the Darcy number enhances it. The skin friction at the wall can be controlled by controlling the values of Darcy number.     

Unsteady bioconvection Darcy-Forchheimer nanofluid flow through a horizontal channel with impact of magnetic field and thermal radiation

Unsteady bioconvection Darcy-Forchhiemer nanofluid flow is considered in the current investigation in the presence of micro-organisms. The flow is exposed to thermal radiation and a uniform magnetic field in a horizontal channel. The impacts of Brownian motion and thermophoresis are also considered for the flow problem. The unsteady governing equations are modeled and transformed into a nondimensional form by employing a suitable group of similar variables. The solution of the modeled equations is determined by the semianalytical method homotopy analysis method. The features of flow characteristics such as temperature, concentration, velocity, and the motile micro-organism distributions in response to the variations of the emerging parameters are simulated and examined in detail. Among the many results of the study, it is found that velocity upsurges with rising values of the unsteadiness parameter while declining with growth in the magnetic, inertial, and porosity parameters. Temperature augments with growing estimations of Brownian, unsteadiness, and radiation parameters and declines with enhancing values of Prandtl number. Amassed estimations of the Brownian factor reduce the concentration of nanoparticles while growing values of thermophoresis, unsteadiness parameters, and Schmidt number increase it. Moreover, the motile micro-organism profile is a reducing function of the bioconvection Lewis numbers, Peclet, and bioconvection concentration difference parameter.     

Heat transfer and buoyancy‐driven convective MHD flow of nanofluids impinging over a thin needle moving in a parallel stream influenced by Prandtl number

The current study focuses on investigating the influence of transverse magnetic field, variable viscosity, buoyancy, variable Prandtl number, viscous dissipation, Joulian dissipation, and heat generation on the flow of nanofluids over thin needle moving in parallel stream. The theory of nanofluids that includes the Buongiorno model featured by slip mechanism, such as Brownian motion and thermophoresis, has been implemented. Further, convective boundary condition and zero mass flux condition are considered. The nondimensionally developed boundary layer equations have been solved by Runge–Kutta–Fehlberg method with shooting technique for different values of parameters. The most relevant outcomes of the present study are that the augmented magnetic field strength, viscosity parameter, buoyancy ratio parameter, and the size of the needle undermine the flow velocity, establishing thicker velocity boundary layer while Richardson number and Brownian motion show opposite trend. Another most important outcome is that increase in the size of the needle, viscous dissipation, convective heating, and heat generation upsurges the fluid temperature, leading to improvement in thermal boundary layer. The effects of different natural parameters on wall shear stress and heat and mass transfer rates have been discussed.