Numerical study of thermodiffusion effects on boundary layer flow of nanofluids over a power law stretching sheet

This paper deals with the triple-diffusive boundary layer flow of nanofluid over a nonlinear stretching sheet. In this model, where binary nanofluid is used, the Brownian motion, thermophoresis, and cross-diffusion are classified as the main mechanisms, which are responsible for the enhancement of the convection features of the nanofluid. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of group theory transformations, which is introduced by Blasius (The boundary layers in fluids with little friction, 1950). The variational finite element method is used to solve these ordinary differential equations. We have examined the effects of different controlling parameters, namely the Brownian motion parameter, the thermophoresis parameter, modified Dufour number, nonlinear stretching parameter, Prandtl number, regular Lewis number, Dufour Lewis number, and nanofluid Lewis number on the flow field and heat transfer characteristics. The physics of the problem is well explored for the embedded material parameters through tables and graphs. The present study has many applications in coating and suspensions, movement of biological fluids, cooling of metallic plate, melt-spinning, heat exchangers technology, and oceanography.     

Transient flow and heat transfer mechanism for Williamson-nanomaterials caused by a stretching cylinder with variable thermal conductivity

The utilization of nanometre-sized solid particles in working fluids has been seriously recommended due to their enhanced thermal characteristics. This suspension of solid particles in base fluids can significantly enhance the physical properties, such as, viscosity and thermal conductivity. They are widely used in several engineering processes, like, heat exchangers, cooling of electronic equipment, etc. In this exploration, we attempt to deliver a numerical study to simulate the nanofluids flow past a circular cylinder with convective heat transfer in the framework of Buongiorno’s model. A non-Newtonian Williamson rheological model is used to describe the behavior of nanofluid with variable properties (i.e., temperature dependent thermal conductivity). The leading flow equations for nanofluid transport are mathematical modelled with the assistance of Boussinesq approximation. Numerical simulation for the system of leading non-linear differential equations has been performed by employing versatile, extensively validated, Runge–Kutta Fehlberg scheme with Cash–Karp coefficients. Impacts of active physical parameters on fluid velocity, temperature and nanoparticle concentration is studied and displayed graphically. It is worth to mention that the temperature of non-Newtonian nanofluids is significantly enhanced by higher variable thermal conductivity parameter. One major outcome of this study is that the nanoparticle concentration is raised considerably by an increasing values of thermophoresis parameter.

     

Peristaltic pumping with double diffusive natural convective nanofluid in a lopsided channel with accounting thermophoresis and Brownian moment

In the current study, double-diffusive natural convective peristaltic flow of a nanofluid with induced magnetic field in an asymmetric porous channel is discussed. The five coupled equations are solved analytically using with new analytical techniques detail of which is given in solution section. The analytical solutions for pressure gradient and pressure rise, velocity profile, temperature, solutal concentration, and nanoparticle fraction are evaluated and presented through graphs.

     

Thermal radiation and slip effects on MHD stagnation point flow of non-Newtonian nanofluid over a convective stretching surface

The present analysis examines the combine effects of thermal radiation and velocity slip along a convectively nonlinear stretching surface. Moreover, MHD effects are also considered near the stagnation point flow of Casson nanofluid. Slipped effects are considered with the porous medium to reduce the drag reduction at the surface of the sheet. Main structure of the system is based upon the system of partial differential equations attained in the form of momentum, energy, and concentration equations. To determine the similar solution system of PDEs is rehabilitated into the set of nonlinear ordinary differential equations (ODEs) by employing compatible similarity transformation. Important physical parameters are acquired through obtained differential equations. To determine the influence of emerging parameters, resulting set of ODE’s in term of unknown function of velocity, temperature, and concentration are successfully solved via Keller’s box-scheme. All the obtained unknown functions are discussed in detail after plotting the results against each physical parameter. To analyze the behavior at the surface: skin friction, local Nusselt and Sherwood numbers are also illustrated against the velocity ratio parameter A, Brownian motion Nb, thermophoresis Nt, and thermal radiation parameters R. Results obtained from the set of equations described that skin friction is decreasing function of A, and local Nusselt and Sherwood number demonstrate the significant influenced by Brownian motion Nb, thermophoresis Nt, and radiation parameters R.

     

Double-diffusive convection with variable viscosity from a vertical truncated cone in porous media in the presence of magnetic field and radiation effects

This work is focused on the study of combined heat and mass transfer or double-diffusive convection near a vertical truncated cone embedded in a fluid-saturated porous medium in the presence of thermal radiation, magnetic field and variable viscosity effects. The viscosity of the fluid is assumed to be an inverse linear function of the fluid temperature. A boundary-layer analysis is employed to derive the non-dimensional governing equations. The governing equations for this investigation are transformed into a set of non-similar equations and solved numerically using the fourth-order Runge–Kutta integration scheme with the Newton–Raphson shooting technique. Comparisons with previously published work on special cases of the problem are performed and the results are found to be in excellent agreement. A parametric study illustrating the influence of the radiation parameter, magnetic field parameter, viscosity-variation parameter, buoyancy ratio and the Lewis number on the fluid velocity, temperature and solute concentration profiles as well as the Nusselt number and Sherwood number is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.     

Spectral and Haar wavelet collocation method for the solution of heat generation and viscous dissipation in micro-polar nanofluid for MHD stagnation point flow

The aim and significance of paper presents, the semi-numerical investigation of magnetohydrodynamic flow of micropolar nanofluid with stagnation point is carried out under the influence of viscous dissipation and heat generation. The micropolar nanofluids are electrically conducting non-Newtonian fluids. The important applications of these fluids are observed in many research areas viz. bioengineering, biofuels and biomedical sectors etc. The appropriate similarity transformations are used to transform the governing equations into system of coupled nonlinear ordinary differential equations and are solved by using shifted Chebyshev collocation method and Haar wavelet collocation method. The variations in velocity, angular velocity, temperature and concentration profiles under the impact of various physical parameters, characterizing the flow field are discussed and are presented via graphs and tables. Temperature enhancement occurs with increment in each parameter except for Prandtl number. The concentration near the surface decreases with increment in the values of parameters and gradually it increases, except for Prandtl number and Schmidt number. The reverse trend of heat transfer occurs​ near a surface, when the dominance of stream velocity over stretching velocity is observed.     

MHD flow of radiative micropolar nanofluid in a porous channel: optimal and numerical solutions

The flow of a radiative and electrically conducting micropolar nanofluid inside a porous channel is investigated. After implementing the similarity transformations, the partial differential equations representing the radiative flow are reduced to a system of ordinary differential equations. The subsequent equations are solved by making use of a well-known analytical method called homotopy analysis method (HAM). The expressions concerning the velocity, microrotation, temperature, and nanoparticle concentration profiles are obtained. The radiation tends to drop the temperature profile for the fluid. The formulation for local Nusselt and Sherwood numbers is also presented. Tabular and graphical results highlighting the effects of different physical parameters are presented. Rate of heat transfer at the lower wall is seen to be increasing with higher values of the radiation parameter while a drop in heat transfer rate at the upper wall is observed. Same problem has been solved by implementing the numerical procedure called the Runge–Kutta method. A comparison between the HAM, numerical and already existing results has also been made.

     

Nanofluid flow over a shrinking sheet with surface slip

In the present study, the effects of partial slip on mixed convection stagnation point flow and heat transfer of nanofluid impinging normally toward a shrinking sheet are investigated numerically. In particular, focus is on Cu–water and Al₂O₃–water nanofluids. Similarity transformation technique is adopted to obtain the self-similar ordinary differential equations and then solved numerically using Runge–Kutta–Fehlberg method with shooting technique. A parametric study is performed to explore the effects of various governing parameters on the fluid flow and heat transfer characteristics. Both the cases of assisting and opposing flows are considered. The physical aspects of the problem are highlighted and discussed.     

Precipitation phenomenon of nanoparticles in power-law fluids over a rotating disk

The steady flow and mass transfer of nanofluids with power-law type base fluids over a free-rotating disk are investigated. Previously, we have modeled the volume fraction of nanoparticles and verified the experimental conclusion through the numerical simulation of particle distribution in nanofluid in a Petri dish under the influence of movement using a power-law model of mass diffusivity. We further this study by a similar model of the mass diffusivity following a power-law type to consider the laminar non-Newtonian power-law flow in a rotating infinite disk with angular velocity about the z-axis. The coupled governing equations are transformed into ODEs. Homotopy analysis method (HAM) is applied to solve the ODEs while special attention is paid to deal with the nonlinear items in the ODEs. In the last section, we provide images of nanoparticles suspended in power-law fluids in a rotating disk as obtained using the laser speckle method. When they are compared with the analytical results gained by the HAM, they qualitatively matched the solutions of the concentration equation of nanofluids.     

A mathematical model of MHD nanofluid flow having gyrotactic microorganisms with thermal radiation and chemical reaction effects

In this article, we have examined three-dimensional unsteady MHD boundary layer flow of viscous nanofluid having gyrotactic microorganisms through a stretching porous cylinder. Simultaneous effects of nonlinear thermal radiation and chemical reaction are taken into account. Moreover, the effects of velocity slip and thermal slip are also considered. The governing flow problem is modelled by means of similarity transformation variables with their relevant boundary conditions. The obtained reduced highly nonlinear coupled ordinary differential equations are solved numerically by means of nonlinear shooting technique. The effects of all the governing parameters are discussed for velocity profile, temperature profile, nanoparticle concentration profile and motile microorganisms’ density function presented with the help of tables and graphs. The numerical comparison is also presented with the existing published results as a special case of our study. It is found that velocity of the fluid diminishes for large values of magnetic parameter and porosity parameter. Radiation effects show an increment in the temperature profile, whereas thermal slip parameter shows converse effect. Furthermore, it is also observed that chemical reaction parameter significantly enhances the nanoparticle concentration profile. The present study is also applicable in bio-nano-polymer process and in different industrial process.

     

Impacts of gold nanoparticles on MHD mixed convection Poiseuille flow of nanofluid passing through a porous medium in the presence of thermal radiation,thermal diffusion and chemical reaction

Impacts of gold nanoparticles on MHD Poiseuille flow of nanofluid in a porous medium are studied. Mixed convection is induced due to external pressure gradient and buoyancy force. Additional effects of thermal radiation, chemical reaction and thermal diffusion are also considered. Gold nanoparticles of cylindrical shape are considered in kerosene oil taken as conventional base fluid. However, for comparison, four other types of nanoparticles (silver, copper, alumina and magnetite) are also considered. The problem is modeled in terms of partial differential equations with suitable boundary conditions and then computed by perturbation technique. Exact expressions for velocity and temperature are obtained. Graphical results are mapped in order to tackle the physics of the embedded parameters. This study mainly focuses on gold nanoparticles; however, for the sake of comparison, four other types of nanoparticles namely silver, copper, alumina and magnetite are analyzed for the heat transfer rate. The obtained results show that metals have higher rate of heat transfer than metal oxides. Gold nanoparticles have the highest rate of heat transfer followed by alumina and magnetite. Porosity and magnetic field have opposite effects on velocity.

     

Fully developed thermal transport in combined pressure and electroosmotically driven flow of nanofluid in a microchannel under the effect of a magnetic field

This paper critically analyzes, for the first time, the effect of nanofluid on thermally fully developed magnetohydrodynamic flows through microchannel, by considering combined effects of externally applied pressure gradient and electroosmosis. The classical boundary condition of uniform wall heat flux is considered, and the effects of viscous dissipation as well as Joule heating have been taken into account. Closed-form analytical expressions for the pertinent velocity and temperature distributions and the Nusselt number variations are obtained, in order to examine the role of nanofluids in influencing the fully developed thermal transport in electroosmotic microflows under the effect of magnetic field. Fundamental considerations are invoked to ascertain the consequences of particle agglomeration on the thermophysical properties of the nanofluid. The present theoretical formalism addresses the details of the interparticle interaction kinetics in tune with the pertinent variations in the effective particulate dimensions, volume fractions of the nanoparticles, as well as the aggregate structure of the particulate system. It is revealed that the inclusion of nanofluid changes the transport characteristics and system irreversibility to a considerable extent and can have significant consequences in the design of electroosmotically actuated microfluidic systems.     

Identification and simulation of a spatial ecological model in a lake with fractal boundary

We propose a 2D ecological model of phytoplankton dynamics accounting for the distribution and the evolution of algae in a large basin located in the Amazonian region. The model is described by a set of reaction-drift-diffusion equations and is driven by several exogenous inputs, such as wind velocity and direction, water temperature and solar radiation. Due to the roughness of the domain, a preliminary boundary extraction with a curvelet algorithm is performed. Then, the model is simulated in an approximated domain, where the contour has been reconstructed by estimating a set of Recurrent Fractal Interpolation Functions, aimed at preserving its fractal structure. Simulations are combined with time and space chlorophyll-a data in order to estimate the parameters of the model. The proposed algorithm is based on an iterative two-step identification procedure, where reaction parameters are recovered first and then used for estimating diffusion and transport parameters. Comparison results at different accuracy approximations and before and after the algorithm implementation are presented and discussed.     

Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel

In this paper, heat transfer and flow analysis for a non-Newtonian third grade nanofluid flow in porous medium of a hollow vessel in presence of magnetic field are simulated analytically and numerically. Blood is considered as the base third grade non-Newtonian fluid and gold (Au) as nanoparticles are added to it. The viscosity of nanofluid is considered a function of temperature as Vogel's model. Least Square Method (LSM), Galerkin method (GM) and fourth-order Runge–Kutta numerical method (NUM) are used to solve the present problem. The influences of the some physical parameters such as Brownian motion and thermophoresis parameters on non-dimensional velocity and temperature profiles are considered. The results show that increasing the thermophoresis parameter (N_t) caused an increase in temperature values in whole domain and an increase in nanoparticles concentration just near the inner wall of vessel. Furthermore by increasing the MHD parameter, velocity profiles decreased due to magnetic field effect.     

Identification and simulation of a spatial ecological model in a lake with fractal boundary

We propose a 2D ecological model of phytoplankton dynamics accounting for the distribution and the evolution of algae in a large basin located in the Amazonian region. The model is described by a set of reaction-drift-diffusion equations and is driven by several exogenous inputs, such as wind velocity and direction, water temperature and solar radiation. Due to the roughness of the domain, a preliminary boundary extraction with a curvelet algorithm is performed. Then, the model is simulated in an approximated domain, where the contour has been reconstructed by estimating a set of Recurrent Fractal Interpolation Functions, aimed at preserving its fractal structure. Simulations are combined with time and space chlorophyll-a data in order to estimate the parameters of the model. The proposed algorithm is based on an iterative two-step identification procedure, where reaction parameters are recovered first and then used for estimating diffusion and transport parameters. Comparison results at different accuracy approximations and before and after the algorithm implementation are presented and discussed.     

Lie group analysis of stagnation-point flow of a nanofluid

This article concerns with a steady two-dimensional boundary layer flow of an electrically conducting incompressible nanofluid over a stretching sheet in a porous medium with internal heat generation/absorption. The transport model includes the effect of Brownian motion with thermophoresis in the presence of chemical reaction and magnetic field. Lie group analysis is applied to the governing equations. The transformed self similar non-linear ordinary differential equations along with the boundary conditions are solved numerically. The influences of various relevant parameters on the flow field, temperature and nanoparticle volume fraction as well as wall heat flux and wall mass flux are elucidated through graphs and tables.     

Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel

A numerical study is presented for the two-dimensional flow of a micropolar fluid in a porous channel. The channel walls are of different permeability. The fluid motion is superimposed by the large injection at the two walls and is assumed to be steady, laminar and incompressible. The micropolar model due to Eringen is used to describe the working fluid. The governing equations of motion are reduced to a set of non-linear coupled ordinary differential equations (ODEs) in dimensionless form by using an extension of Berman’s similarity transformations. A numerical algorithm based on finite difference discretization is employed to solve these ODEs. The results obtained are further improved by Richardson’s extrapolation for higher order accuracy. Comparisons with the previously published work are performed and are found to be in a good agreement. It has been observed that the velocity and microrotation profiles change from the most asymmetric shape to the symmetric shape across the channel as the parameter R or the permeability parameter A are varied between their extreme values. The results indicate that larger the injection velocity at a wall relative to the other is, smaller will be the shear stress at it than that at the other. The position of viscous layer has been found to be more sensitive to the permeability parameter A than to the parameter R. The micropolar fluids reduce shear stress and increase couple stress at the walls as compared to the Newtonian fluids.     

Effects of lubrication in the oblique stagnation-point flow of a nanofluid

This study investigates the oblique flow of a nanofluid near a stagnation point past a lubricated plate. A power-law fluid is utilized for lubrication. A suitable set of transformation is utilized to obtain system of dimensionless governing equations. A well-known numerical technique known as Keller-box method is employed to get the similar solution. Influence of emerging parameters on the flow characteristics has been discussed in the presence of lubrication through graphs and numerical data ranging from no slip (\(\beta \to \infty )\) to full slip (\(\beta \to 0)\). Impact of thermophoresis and Brownian motion is further investigated. A comparison in the special cases between the present and published data validates this work.     

有环境约束时完成一族跟踪任务的力控制

本文为工业机器人提出了一种极点配置控制法，这种控制方法的优点有：一是它的积分作用消除了机器人的微小扰动和稳态误差；二是能任意设置系统的极点，因此能保证闭环系统的稳定性和规定状态变量的暂态响应；三是加入了加速度反馈，抑制了由电枢电感所引起的机械手的振动，最后，给出了ＰＵＭＡ５６２机器人的计算机仿真和实验结果验证了此控制法的有效性。     

Physiological analysis of streamline topologies and their bifurcations for a peristaltic flow of nano fluid

In the present article, the techniques of dynamical systems are utilized to investigate the streamline patterns along their bifurcations for peristaltic flow under mixed convection effect. Here the peristaltic flow is discussed in a vertical channel. The flow is considered in a two-dimensional symmetric channel as well as an axisymmetric tube. We have evaluated the peristaltic flow of blood base nanofluid. The momentum equations are reduced by employing approximation of low Reynolds number and long wavelength. For the discourse of the path of particle in the wave frame, an arrangement of nonlinear independent differential equations are built up and the strategies for dynamical frameworks are utilized to examine the local bifurcations and their topological changes. Critical points classifications were made by scrutiny of the eigenvalues of the Jacobian matrix. This principle are utilized to divulge the local bifurcation of the critical points encountered for different flow situations. Flow situations marked as: backward flow, trapping or augmented flow. The analysis is disclosed that the number and size of trapped bolus increases in planner channel and decline in axisymmetric channel by increasing Grashof number. Moreover, the decreasing behaviour of temperature is depicted, which clarify the nanofluid as a cooling agent. Graphically, a wide range of topological changes of bifurcations are examined. At long last, to outline the bifurcation the diagram of global bifurcation is utilized.