Endoscopic Effects onPeristaltic Flow of a Nanofluid

In the present investigation we have studied the peristaltic flow of a nanofluid in an endoscope. The flow is investigated in a wave frame of reference moving with velocity of the wavec. Analytical solutions have been calculated using Homotopy perturbation method (HPM) for temperature and nanoparticle equation while exact solutions have been calculated for velocity and pressure gradient. Numerical integration have been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated for five different peristaltic waves.
Streamlines have been plotted at the end of the article.     

Mathematical Analysis for Peristaltic Flow of Two Phase Nanofluid in a Curved Channel

This paper describes the theoretical analysis for peristaltic motion of water base nanofluid containing distinct types of the nanoparticles like Cu, TiO₂, and Al₂O₃. Equations of nano fluid are modelled and simplified by constructing the suppositions of low Reynolds number as well as long wave length. The reduced equations are solved exactly. Solutions are represented through graphs. Outcomes for the velocity, temperature, pressure rise and stream lines are analyzed graphically. The work presented here is based on the fictitious values, however some other values can be tested experimentally.     

The Mathematical Analysis for Peristaltic Flow of Hyperbolic Tangent Fluid in a Curved Channel

In the present paper, we have investigated the peristaltic flow of hyperbolic tangent fluid in a curved channel. The governing equations of hyperbolic tangent fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation,long wave length and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method (HPM). The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise and stream functions.     

Mixed Convective Viscoelastic Nanofluid Flow Past a Porous Media with Soret-Dufour Effects

The present study is carried out to see the thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the mixed convection boundary layer flow of viscoelastic nanofluid flow over a vertical stretching surface in a porous medium. Optimal homotopy analysis method (OHAM) is best candidate to handle highly nonlinear system of differ-ential equations obtained from boundary layer partial differential equations via appropriate transformations. Graphical illustrations depicting different physical arising parameters against velocity, temperature and concentration distributions with required discussion have also been added. Numerically calculated values of skin friction coefficient, local Nusselt and Sherwood numbers are given in the form of table and well argued. It is found that nanofluid velocity increases with increase in mixed convective and viscoelastic parameters but it decreases with the increasing values of porosity parameter. Also, it is observed that Dufour number has opposite behavior on temperature and concentration profiles.     

Peristaltic Flow of Couple Stress Fluid in a Non-Uniform Rectangular Duct Having Compliant Walls

The present study investigates the peristaltic flow of couple stress fluid in a non-uniform rectangular duct with compliant walls.Mathematical modeling is based upon the laws of mass and linear momentum.Analytic solutions are carried out by the eigen function expansion method under long-wavelength and low-Reynolds number approximations.The features of the flow characteristics are analyzed by plotting the graphs of various values of physical parameters of interest.Trapping bolus scheme is also presented through streamlines.     

Numerical Study of Mixed Convective Peristaltic Flow through Vertical Tube with Heat Generation for Moderate Reynolds and Wave Numbers

The current study focuses on the numerical investigation of the mixed convective peristaltic mechanism through a vertical tube for non-zero Reynolds and wave number. In the set of constitutional equations, energy equation contains the term representing heat generation parameter. The problem is formulated by dropping the assumption of lubrication theory that turns the model mathematically into a system of the nonlinear partial differential equations. The results of the long wavelength in a creeping flow are deduced from the present analysis. Thus, the current study explores the neglected features of peristaltic heat flow in the mixed convective model by considering moderate values of Reynolds and wave numbers. The finite element based on Galerkin's weighted residual scheme is applied to solve the governing equations. The computed solution is presented in the form of contours of streamlines and isothermal lines, velocity and temperature profiles for variation of different involved parameters. The investigation shows that the strength of circulation for stream function increases by increasing the wave number and Reynolds number. Symmetric isotherms are reported for small values of time-mean flow. Linear behavior of pressure is noticed by vanishing inertial forces while the increase in pressure is observed by amplifying the Reynolds number.     

Magnetohydrodynamic Stagnation Point Flow of a Maxwell Nanofluid with Variable Conductivity

This article reports the simultaneous properties of variable conductivity and chemical reaction in stagnation point flow of magneto Maxwell nanofluid.The Buongiorno's theory has been established to picture the inducement of Brownian and thermophrotic diffusions effects.Additionally,the aspect of heat sink/source is reported.The homotopic analysis method(HAM) has been worked out for the solution of nonlinear ODEs.The behavior of inferential variables on the velocity,temperature,concentration and local Nusselt number for Maxwell nanofluid are sketched and discussed.The attained outcomes specify that both the temperature and concentration of Maxwell fluid display analogous behavior,while the depiction of Brownian motion is quite conflicting on both temperature and concentration fields.It is further noted that the influence of variable thermal conductivity on temperature field is similar to that of Brownian motion parameter.Moreover,for the confirmation of our study comparison tables are reported.     

Numerical Simulation of MHD Peristaltic Flow with Variable Electrical Conductivity and Joule Dissipation Using Generalized Differential Quadrature Method

In this paper, the MHD peristaltic flow inside wavy walls of an asymmetric channel is investigated, where the walls of the channel are moving with peristaltic wave velocity along the channel length. During this investigation,the electrical conductivity both in Lorentz force and Joule heating is taken to be temperature dependent. Also, the long wavelength and low Reynolds number assumptions are utilized to reduce the governing partial differential equations into a set of coupled nonlinear ordinary differential equations. The new set of obtained equations is then numerically solved using the generalized differential quadrature method(GDQM). This is the first attempt to solve the nonlinear equations arising in the peristaltic flows using this method in combination with the Newton-Raphson technique. Moreover, in order to check the accuracy of the proposed numerical method, our results are compared with the results of built-in Mathematica command NDSolve. Taking Joule heating and viscous dissipation into account, the effects of various parameters appearing in the problem are used to discuss the fluid flow characteristics and heat transfer in the electrically conducting fluids graphically. In presence of variable electrical conductivity, velocity and temperature profiles are highly decreasing in nature when the intensity of the electrical conductivity parameter is strengthened.     

Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate

In this Letter, the problem of forced convection over a horizontal flat plate is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.     

利用格子Boltzmann方法模拟矩形腔内纳米流体Raleigh-Benard对流

利用格 子 Boltzmann方法模拟矩形腔内纳米流体Rayleigh-Benard对流, 得到温度场和流线分布, 比较分析不同Ra数、体积分数、粒径下纳米流体对流换热的变化情况. 结果表明: 在相同的Ra 数和体积分数下, 纳米流体的对流换热随着粒径的增大而减弱; 在相同的Ra数和粒径下, 纳米流体的对流换热随着体积分数增大而增强. 关键词： 纳米流体 Raleigh-Benard 多相流 格子Boltzmann方法     

Mathematical Analysis for Peristaltic Flow of Two Phase Nanofluid in a Curved Channel

This paper describes the theoretical analysis for peristaltic motion of water base nanoBuid containing distinct types of the nanoparticles like Cu,TiO_2,and Al_2O_3.Equations of nano Quid are modelled and simplified by constructing the suppositions of low Reynolds number as well as long wave length.The reduced equations are solved exactly.Solutions are represented through graphs.Outcomes for the velocity,temperature,pressure rise and stream lines are analyzed graphically.The work presented here is based on the fictitious values,however some other values can be tested experimentally.     

纳米流体多相流动的多尺度模拟方法

针对纳米流体多相流动的微观特征,提出一种基于格子Boltzmann的多尺度耦合方法,在速度和悬浮纳米粒子分布变化比较剧烈的区域采用细网格多相模型,在其它区域视纳米流体为均匀混合的单相流体,使用粗网格单相模型.为保证不同尺度区域之间的物理信息(参数)的准确传递,运用质量和动量守恒原理,建立跨区域的边界耦合模型.几个算例表明,该方法既可以反映纳米流体流动的微观特征,又能提高计算效率,与单纯使用多相模型相比,节省大量时间.     

Approximate solution of the flow over a nonlinear magneto-hydrodynamic stretching sheet

The approximate solution of the magneto-hydrodynamic(MHD) boundary layer flow over a nonlinear stretching sheet is obtained by combining the Lie symmetry method with the homotopy perturbation method.The approximate solution is tabulated,plotted for the values of various parameters and compared with the known solutions.It is found that the approximate solution agrees very well with the known numerical solutions,showing the reliability and validity of the present work.     

Convective Heat Transfer of a Cu/Water Nanofluid Flowing Through a Circular Tube

Abstract

Fluids in which nanometer-sized solid particles are suspended are called nanofluids. These fluids can be employed to increase the heat transfer rate in various applications. In this study, the convective heat transfer for Cu/water nanofluid through a circular tube was experimentally investigated. The flow was laminar, and constant wall temperature was used as thermal boundary condition. The Nusselt number of nanofluids for different nanoparticle concentrations, as well as various Peclet numbers, was obtained. Also, the rheological properties of the nanofluid for different volume fractions of nanoparticles were measured and compared with theoretical models. The results show that the heat transfer coefficient is enhanced by increasing the nanoparticle concentrations as well as the Peclet number.     

Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions.     

Effects of Thermal Radiation and Slip Mechanism on Mixed Convection Flow of Williamson Nanofluid Over an Inclined Stretching Cylinder

The current investigation highlights the mixed convection slip flow and radiative heat transport of uniformly electrically conducting Williamson nanofluid yield by an inclined circular cylinder in the presence of Brownian motion and thermophoresis parameter.A Lorentzian magnetic body force model is employed and magnetic induction effects are neglected.The governing equations are reduced to a system of nonlinear ordinary differential equations with associated boundary conditions by applying scaling group transformations.The reduced nonlinear ordinary differential equations are then solved numerically by Runge-Kutta-Fehlberg fifth-order method with shooting technique.The effects of magnetic field,Prandtl number,mixed convection parameter,buoyancy ratio parameter,Brownian motion parameter,thermophoresis parameter,heat generation/absorption parameter,mass transfer parameter,radiation parameter and Schmidt number on the skin friction coefficient and local Nusselt are analyzed and discussed.It is found that the velocity of the fluid decreases with decrease in curvature parameter,whereas it increases with mixed convection parameter.Further,the local Nusselt number decreases with an increase in the radiation parameter.The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.     

Transverse Transport of Polymeric Nanofluid under Pure Internal Heating: Keller Box Algorithm

The present work aims to investigate transverse Oldroyd-B nanofluid flow on a stretched panel with consideration of internal heat generation. Buongiorno model is utilized to study influence of thermophoresis and Brownian motion effects. A numerical procedure known as Keller box algorithm is used to solve the governed physical model. Graphically velocity, temperature and concentration of nanoparticles are expressed. Also, concerned physical measures such as heat and mass transfer are investigated numerically. The simulations performed revealed that fluid parameters play a significant role in heat transfer under Brownian motion and thermophoresis effects. Local heat flux is elevated while local mass flux is suppressed with enhancing Brownian motion parameter. Streamlines pattern exhibits that flow is more inclined in the presence of Deborah number effects. To the best of our knowledge, transverse flow of an Oldroyd-B type fluid which incorporates the thermal relaxation effects has never been reported before in the presence of Brownian motion and internal heating phenomenon. Therefore we intend to discuss these features in detail. The obtained results are a novel contribution, which can be benchmark for further relevant academic research related to polymer industry.