A comparative analysis of unsteady and steady Buongiorno’s Williamson nanoliquid flow over a wedge with slip effects

Comparison between unsteady and steady MHD Buongiorno’s model Williamson nanoliquid flow through a wedge with slip effects,chemical reaction and radiation is made in this analysis.Thermophoresis and Brownian motion are also considered in this study.Appropriate similarity variables are presented to transmute the governing PDEs into the set of non-linear ODEs.The most widely authenticated finite element method is implemented to analyze these set of ODEs numerically.The behavior of concentration,temperature and velocity sketches for varied values of relevant parameters is numerically calculated and the outcomes are plotted through graphs.The numerical values of dimensionless rates of mass transfer,heat and velocity are also evaluated and depicted through tables.It is noted that with upsurging values of angle of wedge parameter,the distributions of temperature of the liquid intensify in both steady and unsteady cases.

Nanoparticle aggregation effects on radiative heat transport of nanoliquid over a vertical cylinder with sensitivity analysis

A sensitivity analysis is performed to analyze the effects of the nanoparticle(NP)aggregation and thermal radiation on heat transport of the nanoliquids(titania based on ethylene glycol)over a vertical cylinder.The optimization of heat transfer rate and friction factor is performed for NP volume fraction(1%≤φ≤3%),radiation parameter(1≤R_(t)≤3),and mixed convection parameter(1.5≤λ≤2.5)via the facecentered central composite design(CCD)and the response surface methodology(RSM).The modified Krieger and Dougherty model(MKDM)for dynamic viscosity and the Bruggeman model(BM)for thermal conductivity are utilized to simulate nanoliquids with the NP aggregation aspect.The complicated nonlinear problem is treated numerically.It is found that the temperature of nanoliquid is enhanced due to the aggregation of NPs.The friction factor is more sensitive to the volume fraction of NPs than the thermal radiation and the mixed convection parameter.Furthermore,the heat transport rate is more sensitive to the effect of radiative heat compared with the NP volume fraction and mixed convection parameter.

Darcy-Forchheimer mangetized flow based on differential type nanoliquid capturing Ohmic dissipation effects

Hydromagnetic nanoliquid establish an extraordinary category of nanoliquids that unveil both liquid and magnetic attributes.The interest in the utilization of hydromagnetic nanoliquids as a heat transporting medium stem from a likelihood of regulating its flow along with heat transportation process subjected to an externally imposed magnetic field.This analysis reports the hydromagnetic nanoliquid impact on differential type(second-grade)liquid from a convectively heated extending surface.The well-known Darcy-Forchheimer aspect capturing porosity characteristics is introduced for nonlinear analysis.Robin conditions elaborating heat-mass transportation effect are considered.In addition,Ohmic dissipation and suction/injection aspects are also a part of this research.Mathematical analysis is done by implementing the basic relations of fluid mechanics.The modeled physical problem is simplified through order analysis.The resulting systems(partial differential expressions)are rendered to the ordinary ones by utilizing the apposite variables.Convergent solutions are constructed employing homotopy algorithm.Pictorial and numeric result are addressed comprehensively to elaborate the nature of sundry parameters against physical quantities.The velocity profile is suppressed with increasing Hartmann number(magnetic parameter)whereas it is enhanced with increment in material parameter(second-grade).With the elevation in thermophoresis parameter,temperature and concentration of nanoparticles are accelerated.

Thermal management of nanoliquid forced convective flow over heated blocks in channel by using double elliptic porous objects

Effects of using nanoliquid and double porous elliptic objects on the flow separation and convective heat transfer control for flow over multiple heated blocks in channel are numerically investigated by using finite element method.Spherical,brick,blade and cylindrical shaped alumina particles are used in water up to solid volume fraction of 2%.Impacts of Reynolds number(50≤Re≤500),permeability of the porous ellipses(10^(-5)≤D_(a1)≤5×10^(-2) and 10^(-5)≤D_(a2)≤5×10^(-2)),aspect ratio of the ellipses(0.25≤AR_(1)≤1.5,0.25≤AR_(2)≤1.5),distance between the ellipses(0.2H≤sx≤1.6H)and distance of the first ellipse from inlet(-H≤mx≤H)on the hydro-thermal performance are explored.The highest performance improvement is obtained by using the cylindrical shaped particles in the base heat transfer fluid at the highest solid volume fraction and the amount of heat transfer enhancement are 33%and 40.5%for hot blocks while negligible pressure drop is observed.Varying the aspect ratio of the ellipses in the perpendicular direction to the flow,up to 25%and 30%heat transfer increment are obtained for hot block with slight rise of pressure coefficient.However,when varying the horizontal location of the porous ellipses in the channel and permeability of them,there is considerable rise of pressure drop.Variation of the average heat transfer from the hot blocks with varying permeability of the ellipses are obtained as 32%and 25%.Successful hydro-thermal performance estimation results are achieved by using artificial neural networks with feed-forward network architecture of 1 hidden layer and 17 neurons.

Galerkin finite element analysis of magneto-hydrodynamic natural convection of Cu-water nanoliquid in a baffled U-shaped enclosure

In this paper,single-phase homogeneous nanofluid model is proposed to investigate the natural convection of magneto-hydrodynamic(MIID)flow of Newtonian Cu—H20 nanoli­quid in a baffled U-shaped enclosure.The Brinkman model and Wasp model are considered to measure the effective dynamic viscosity and effective thermal conductivity of the nanoliquid coreespondingly.Nanoliquid's effective properties such as specific heat,density and thermal expansion coefficient are modeled using mixture theory.The complicated PDS(partial differ­ential system)is treated for numeric solutions via the Galerkin finite element method.The perti­nent parameters Hartmann number(1≤Ha≤60),Rayleigh number(10^(3)≤Ra≤10^(6))and nanoparticles volume fraction (0% ≤Ф≤4%) are taken for the parametric analysis, and it is conducted via streamlines and isotherms. Excellent agreement between numerical results and open literature. It is ascertained that heat transfer rate enhances with Rayleigh number Ra and volume fraction 0, however it is diminished for laiger Hartmann number Ha.

Hydromagnetic Carreau Nanoliquid in Frames of Dissipation and Activation Energy

The novel characteristics of magnetic field and entropy generation in mixed convective flow of Carreau fluid towards a stretched surface are investigated.Buongiornio nanoliquid model consists of thermophoresis and Brownian movement aspects is opted for analysis.Energy expression is modeled subject to thermal radiation and viscous dissipation phenomenon.Concentration by zero mass flux condition is implemented.Consideration of chemical reaction and activation energy characterizes the mass transfer mechanism.Total entropy generation rate and Bejan number is formulated.The utilization of transformation variables reduces the PDEs into non-linear ODEs.The obtained nonlinear complex problems are computed numerically through Shooting scheme.The impact of involved variables like local Weissenberg number,magnetic parameter,thermal radiation parameter,Brownian motion parameter,thermophoresis parameter,buoyancy ratio parameter,mixed convection parameter,Prandtl parameter,Eckert number,Schmidt number,non-dimensional activation energy parameter,chemical reaction parameter,Brinkman number,dimensionless concentration ratio variable,diffusive variable and dimensionless temperature ratio variable on velocity,temperature,nanoparticles concentration,entropy generation,Bejan number,surface drag force and heat transfer rate are examined through graphs and tables.

化学反应对粗糙边界和被动控制微极性纳米流体热稳定性的影响:神经网络

本文在无通量和粗糙边界的情况下演示了化学反应对微极性纳米流体中热对流初始状态的影响。本研究应用Saffman界面条件求解粗糙边界。考虑在许多工业应用中具有重要作用的微极性非牛顿纳米流体。对于线性稳定性,利用正态模态技术(NMT)将控制系统的偏微分方程(PDE)转化为特征值问题(EVP),并采用基于有限差分的三阶段LobattoⅢa方法进行数值求解。发现对流的主要模式是静止模式。增加纳米流体中热流通量与自旋霍尔效应的耦合系数(δ)、自旋霍尔效应与涡度的耦合系数(K)、粗糙度参数(λ_(1),λ_(2))、化学反应参数(Cr)、修正扩散比(NA)和微极性参数(A)的取值,可以降低对流,从而稳定系统。然后,在81个数据点的基础上,利用嵌入多人感知的人工神经网络(ANN)确定四个控制参数与Rayleigh临界数之间的关系。

Hybrid nanomaterial flow and heat transport in a stretchable convergent/divergent channel:a Darcy-Forchheimer model

The flow behavior in non-parallel walls is an important factor of any physical model including cavity flow and canals, which is applicable for diverging/converging channel. The present communication explains that the flow of the hybrid nanomaterial subjected to the convergent/divergent channel has non-parallel walls. It is assumed that the hybrid nanomaterial movement is in the porous region. A Darcy-Forchheimer medium of porosity is considered to interpret the porosity features. A useful similarity function is adopted to get the strong ordinary coupled equations. Numerical solutions are achieved through the Runge-Kutta-Fehlberg(RKF) fourth-fifth order method, and they are validated with the existing results. Physical nature of the involving constraints is reported with the help of plots. It is explored that the velocity of divergent channel decreases, and convergent channel enhances for the higher solid volume faction. Further, the presence of inertia coefficient and porosity parameter amplifies the velocity at the wall.

Heat transport of hybrid nanomaterial in an annulus with quadratic Boussinesq approximation

The convective heat transfer of hybrid nanoliquids within a concentric annulus has wide engineering applications such as chemical industries, solar collectors, gas turbines, heat exchangers, nuclear reactors, and electronic component cooling due to their high heat transport rate. Hence, in this study, the characteristics of the heat transport mechanism in an annulus filled with the Ag-MgO/H_2O hybrid nanoliquid under the influence of quadratic thermal radiation and quadratic convection are analyzed. The nonuniform heat source/sink and induced magnetic field mechanisms are used to govern the basic equations concerning the transport of the composite nanoliquid. The dependency of the Nusselt number on the effective parameters(thermal radiation, nonlinear convection,and temperature-dependent heat source/sink parameter) is examined through sensitivity analyses based on the response surface methodology(RSM) and the face-centered central composite design(CCD). The heat transport of the composite nanoliquid for the spacerelated heat source/sink is observed to be higher than that for the temperature-related heat source/sink. The mechanisms of quadratic convection and quadratic thermal radiation are favorable for the momentum of the nanoliquid. The heat transport rate is more sensitive towards quadratic thermal radiation.

Quadratic convective flow of radiated nano-Jeffrey liquid subject to multiple convective conditions and Cattaneo-Christov double diffusion

A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiation, magnetohydrodynamic(MHD), and convective conditions are accounted. The conversion of governing equations into ordinary differential equations is prepared via stretching transformations. The consequent equations are solved using the Runge-Kutta-Fehlberg(RKF) method. Impacts of physical constraints on the liquid velocity, the temperature, and the nanoparticle volume fraction are analyzed through graphical illustrations. It is established that the velocity of the liquid and its associated boundary layer width increase with the mixed convection parameter and the Deborah number.

Flow of colloidal suspension and irreversibility analysis with aggregation kinematics of nanoparticles in a microchannel

The current exploration focuses on the ethylene glycol(EG)based nanoliquid flow in a microchannel.The effectiveness of the internal heat source and linear radiation is reflected in the present investigation.The estimation of suitable thermal conductivity model has affirmative impact on the convective heat transfer phenomenon.The examination is conceded with the nanoparticle aggregation demonstrated by the Maxwell-Bruggeman and Krieger-Dougherty models which tackle the formation of nanolayer.These models effectively describe the thermal conductivity and viscosity correspondingly.The dimensionless mathematical expressions are solved numerically by the Runge Kutta Fehlberg approach.A higher thermal field is attained for the Bruggeman model due to the formation of thermal bridge.A second law analysis is carried out to predict the sources of irreversibility associated with the thermal system.It is remarked that lesser entropy generation is obtained for the aggregation model.The entropy generation rate declines with the slip flow and the thermal heat flux.A notable enhancement in the Bejan number is attained by increasing the Biot number.It is established that the nanoparticle aggragation model exhibits a higher Bejan number in comparision with the usual flow model.

谱松弛法研究时变Darcy-Forchheimer流体的Navier滑动条件（英文）

在金属和聚合物薄片的工业应用中,流动情况非常不稳定,并且薄片温度由设定的表面温度和热通量共同决定。此外,合理选择冷却液对实验结果也十分重要。本研究中,结合了各种效应(如布朗效应、热泳效应、Navier 滑动条件和对流边界条件),对流过不稳定拉伸片表面的 Darcy-Forchheimer流体进行了数值分析。为了求解控制方程,使用了适当的相似变换,导出了非线性常微分方程,并使用谱松弛法对得到的耦合动量和能量方程进行了数值求解。通过系统的数值求解,分析了现有模型中的重要物理参数。发现不稳定参数的存在对速度、温度和浓度场以及相关的热量和质量传输速率具有显着影响。同时,增大惯性系数和孔隙率可加快边界处的速度。

纳米沟道中离子扩散系数

提出了一种测量纳米沟道中离子扩散系数的新方法。该方法的原理是:首先测出纳米沟道两端之间溶液电阻的变化,推算出两端离子浓度的变化,然后运用有限扩散理论,计算出纳沟道中离子扩散系数。根据本文的扩散系数测试系统,成功测得一定浓度的KC l溶液在纳沟道中扩散系数。结果表明离子在纳沟道中的扩散系数小于在宏观沟道中的扩散系数的现象。并分析了双电层效应和尺寸效应对纳沟道中离子扩散的影响。

Modeling Chemically Reactive Flow of Sutterby Nanofluid by a Rotating Disk in Presence of Heat Generation/Absorption

In this article we investigate the flow of Sutterby liquid due to rotating stretchable disk. Mass and heat transport are analyzed through Brownian diffusion and thermophoresis. Further the effects of magnetic field, chemical reaction and heat source are also accounted. We employ transformation procedure to obtain a system of nonlinear ODE's. This system is numerically solved by Built-in-Shooting method. Impacts of different involved parameter on velocity, temperature and concentration are described. Velocity, concentration and temperature gradients are numerically computed. Obtained results show that velocity is reduced through material parameter. Temperature and concentration are enhanced with thermophoresis parameter.