Numerical simulation of self-similar thermal convection from a spinning cone in anisotropic porous medium

Self-similar steady natural convection thermal boundary layer flow from a rotating vertical cone to anisotropic Darcian porous medium is investigated theoretically and numerically. The transformed non-dimensional two-point boundary value problem is reduced to a system of coupled, highly nonlinear ordinary differential equations, which are solved subject to robust surface and free stream boundary conditions with the MAPLE 17 numerical quadrature software. Validation with earlier non-rotating studies is included, and also further verification of rotating solutions is achieved with a variational finite element method(FEM). The rotational(spin) parameter emerges as an inverse function of the Grashof number. The influence of this parameter, primary Darcy number, secondary Darcy number and Prandtl number on tangential velocity and swirl velocity, temperature and heat transfer rate are studied in detail. It is found that the dimensionless tangential velocity increases whilst the dimensionless swirl velocity and temperature decrease with the swirl Darcy number, tangential Darcy number and the rotational parameters. The model finds applications in chemical engineering filtration processing, liquid coating and spinning cone distillation columns.     

FLOW AND HEAT TRANSFER OF OLDROYD-B FLUIDS IN A ROTATING CURVED PIPE

The flow and convected heat transfer of the Oldroyd-B fluids in a rotating curved pipe with circular cross-section were investigated by employing a perturbation method. A perturbation solution up to the second order was obtained for a small curvature ratio, κ. The variations of axial velocity distribution and secondary flow structure with F, Re and We were discussed in detail in order to investigate the combined effects of the three parameters on flow structure. The combined effects of the Coriolis force, inertia force and elastic force on the temperature distribution were also analyzed, which are greater than the adding independent effects of the three forces. The variations of the flow rate and Nusselt number with the rotation, inertia and elasticity were examined as well. The results show the characteristics of the heat and mass transfer of the Oldroyd-B fluids in a rotating curved pipe.     

Analytical approach to entropy generation and heat transfer in CNT-nanofluid dynamics through a ciliated porous medium

The transportation of biological and industrial nanofluids by natural propulsion like cilia movement and self-generated contraction-relaxation of flexible walls has significant applications in numerous emerging technologies. Inspired by multi-disciplinary progress and innovation in this direction, a thermo-fluid mechanical model is proposed to study the entropy generation and convective heat transfer of nanofluids fabricated by the dispersion of single-wall carbon nanotubes(SWCNT) nanoparticles in water as the base fluid. The regime studied comprises heat transfer and steady, viscous, incompressible flow, induced by metachronal wave propulsion due to beating cilia, through a cylindrical tube containing a sparse(i.e., high permeability) homogenous porous medium. The flow is of the creeping type and is restricted under the low Reynolds number and long wavelength approximations. Slip effects at the wall are incorporated and the generalized Darcy drag-force model is utilized to mimic porous media effects. Cilia boundary conditions for velocity components are employed to determine analytical solutions to the resulting non-dimensionalized boundary value problem. The influence of pertinent physical parameters on temperature, axial velocity, pressure rise and pressure gradient, entropy generation function, Bejan number and stream-line distributions are computed numerically. A comparative study between SWCNT-nanofluids and pure water is also computed. The computations demonstrate that axial flow is accelerated with increasing slip parameter and Darcy number and is greater for SWCNT-nanofluids than for pure water. Furthermore the size of the bolus for SWCNT-nanofluids is larger than that of the pure water. The study is applicable in designing and fabricating nanoscale and microfluidics devices, artificial cilia and biomimetic micro-pumps.     

同轴套管间涡旋流动及强化传热数值模拟

相对旋转两同轴套管间的涡旋流动,能够带来二次流强化传热传质作用,在航空、水处理、生态保护、生物工程和膜分离等领域都具有广泛的应用价值。本文使用Fluent软件,对同轴套管间涡旋流动及传热特性进行数值模拟,考察了内管转速、内外管壁面温差等操作参数变化对同轴套管间流体传热性能的影响,分析了涡旋流动与传热效率之间的关联关系。模拟结果表明:内管转速增加在流场中形成泰勒涡,涡流扰动增大了高温壁面与流体间的热流密度,增强了流体传热效率。增大内外管壁面温差,也可加强流体传热性能,但其强化作用不及内管转速的强化作用显著。受流场中泰勒涡影响,流体速度、温度及热流密度沿轴向的分布都呈正弦状周期性波动,在相邻两涡交界面处,流体传热性能最好,在涡中心处的传热性能最差。     

Numerical solution of thermo-solutal mixed convective slip flow from a radiative plate with convective boundary condition

A mathematical model for mixed convective slip flow with heat and mass transfer in the presence of thermal radiation is presented. A convective boundary condition is included and slip is simulated via the hydrodynamic slip parameter. Heat generation and absorption effects are also incorporated. The Rosseland diffusion flux model is employed. The governing partial differential conservation equations are reduced to a system of coupled, ordinary differential equations via Lie group theory method. The resulting coupled equations are solved using shooting method. The influences of the emerging parameters on dimensionless velocity, temperature and concentration distributions are investigated. Increasing radiative-conductive parameter accelerates the boundary layer flow and increases temperature whereas it depresses concentration. An elevation in convection-conduction parameter also accelerates the flow and temperatures whereas it reduces concentrations. Velocity near the wall is considerably boosted with increasing momentum slip parameter although both temperature and concentration boundary layer thicknesses are decreased. The presence of a heat source is found to increase momentum and thermal boundary layer thicknesses but reduces concentration boundary layer thickness. Excellent correlation of the numerical solutions with previous non-slip studies is demonstrated. The current study has applications in bioreactor diffusion flows and high-temperature chemical materials processing systems.     

Numerical investigation of flow and heat transfer performances of horizontal spiral-coil pipes

The flow and heat transfer performances of horizontal spiral-coil pipes of circular and elliptical cross-sections are studied.The numerical results are compared with the experimental data,to verify the numerical method.The effects of the inlet water mass flow rate,the structural parameters,the helical pitch and the radius ratio on the heat transfer performances are investigated.Performances of the secondary fluid flow with different radius ratios are also investigated.Numerical results demonstrate that the heat transfer coefficient and the Nusselt number increase with the increase of the water mass flow rate or the helical pitch.The maximum heat transfer coefficient and the maximum Nusselt number are obtained when the radius ratio is equal to 1.00.In addition,the fluid particle moves spirally along the pipe and the velocity changes periodically.The particle flow intensity and the spiral movement frequency decrease significantly with the increase of the radius ratio.Besides,the secondary flow profile in the horizontal spiral-coil pipe contains two oppositely rotating eddies,and the eddy intensity decreases significantly along the pipe owing to the change of curvature.The decreasing tendency of the eddy intensity along the pipe increases with the increase of the radius ratio.     

The effect of variable viscosity on the flow and heat transfer of a viscous Agwater and Cu-water nanofluids

A numerical study is carried out to study the effects of the temperature dependent viscosity on the flow and heat transfer of a nanofluid over a flat surface in the presence of viscous dissipation. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, and are solved numerically by the Keller-box method. The numerical results indicate that the effect of nanoparticle volume fraction is to increase the heat transfer and hence enhance the thermal boundary layer thickness. This is true even in the presence of variable viscosity and the viscous dissipation. Furthermore, the results obtained for heat transfer characteristics with nanoparticles reveal many interesting behaviors that warrant further study on the effects of the "nano-solid-particles".     

Effects of Navier slip on unsteady flow of a reactive variable viscosity non-Newtonian fluid through a porous saturated medium with asymmetric convective boundary conditions

A study on the effects of Navier slip, in conjunction with other flow parameters, on unsteady flow of reactive variable viscosity third-grade fluid through a porous saturated medium with asymmetric convective boundary conditions is presented. The channel walls are assumed to be subjected to asymmetric convective heat exchange with the ambient, and exothermic chemical reactions take place within the flow system. The heat exchange with the ambient obeys Newton's law of cooling. The coupled equations, arising from the law of conservation of momentum and the first law of thermodynamics, then the derived system are nondimensionalised and solved using a semi-implicit finite difference scheme. The lower wall slip parameter is observed to increase the fluid velocity profiles, whereas the upper wall slip parameter retards them because of backflow at the upper channel wall. Heat production in the fluid is seen to increase with the slip parameters. The wall shear stress increases with the slip parameters while the wall heat transfer rate is largely unaltered by the lower wall slip parameter but marginally increased by the upper wall slip parameter.     

THREE-DIMENSIONAL NUMERICAL SIMULATION OF THERMAL-HYDRAULIC PERFORMANCE OF A CIRCULAR TUBE WITH EDGEFOLD-TWISTED-TAPE INSERTS

Three-dimensional numerical simulations and experiments were carried out to study the heat transfer characteristics and the pressure drop of air flow in a circular tube with Edgefold-Twisted Tape (ETT) inserts and with classic Spiral-Twisted-Tape (STT) inserts of the same twist ratio. The RNG turbulence model for mildly swirling flows, the enhanced wall treatment for low Reynolds numbers, and the SIMPLE pressure-velocity method were adopted to simulate the flow and heat transfer characteristics. Within the range of Reynolds number from 2 500 to 9 500 and the twist ratio y from 5.4 to 11.4, the Nusselt number of the tube with ETT inserts is found to be 3.9% ? 9.2% higher than that with STT inserts, and the friction factor of the tube with ETT inserts is 8.7% ? 74% higher than that of STT inserts. The heat enhancement is due to higher tangential velocity and asymmetrical velocity profile with the increase and decrease of the periodic velocity within an edgefold length. It is found that main factors affecting the heat transfer of ETT inserts are the twist angle and the gap width between the tube and inserts. A larger twist angle leads to a higher tangential velocity, and larger Nusselt number and friction factor. The thermal-hydraulic performance slowly decreases as the twist angle increases. The gap width between tube and inserts has a significant influence on the heat transfer, while little influence on pressure drops. The thermal-hydraulic performance increases in average by 124% and 140% when the gap width reduces from 1.5 mm to 1.0 mm and 0.5 mm. The larger the gap width, the higher velocity through the gap will be, which would reduce the main flow velocity and tangential velocity. So a small gap is desirable. Comparing experimental and numerical results at variable air flow and tube wall temperature, the numerical results are found to be in a reasonable agreement with the experiment results, with difference of the Nusselt number in a range of 1.6% ? 3.6%, and that of the friction factor in a range of 8.2% ? 13.6%.     

表面活性剂减阻流体热边界层温度脉动及传热特性实验研究

该文针对在水中添加阳离子表面活性剂产生的减阻作用同时降低传热性能的现象,应用相位多普勒激光测量系统和热电偶温度测量系统对二维流道内表面活性剂减阻流体热边界层内的湍流温度脉动以及传热特性进行了实验研究.研究表明,表面活性剂减阻流体平均温度梯度在流动缓冲层很大,热扩散率较低,而水的热阻主要发生在近壁区域的高扩散层.表面活性剂减阻流体温度脉动强度与速度脉动强度有相似的分布趋势,其峰值都向外层移动.在近壁处的高扩散层温度脉动频率很小,而在平均温度梯度很大的低扩散层,减阻流体的温度脉动频率有所增强.而水的温度脉动频率比表面活性剂溶液高且在整个断面上几乎没有变化.对于表面活性剂热流体,湍流温度脉动对轴向热流量的贡献更大,使得轴向热流量的最大值出现在靠近温度脉动强度最大值所在的位置.表面活性剂减阻流体法向湍流热流量分布与雷诺应力分布有相似的趋势.     

Natural convective heat transfer and nanofluid flow in a cavity with top wavy wall and corner heater

A numerical analysis of natural convection of nanofluid in a wavy-walled enclosure with an isothermal corner heater has been carried out. The cavity is heated from the left bottom corner and cooled from the top wavy wall while the rest walls are adiabatic. Mathematical model has been formulated using the single-phase nanofluid approach. Main efforts have been focused on the effects of the dimensionless time, Rayleigh number, undulation number, nanoparticle volume fraction and length of corner heaters on the fluid flow and heat transfer inside the cavity. Numerical results have been presented in the form of streamlines, isotherms, velocity and temperature profiles, local and average Nusselt numbers. It has been found that nanoparticle volume fraction essentially affects both fluid flow and heat transfer while undulation number changes significantly only the heat transfer rate.     

MHD flow of a visco-elastic fluid through a porous medium between infinite parallel plates with time dependent suction

This work provides a comprehensive theoretical analysis of MHD unsteady free convection viscoelastic fluid flow through a porous medium. The medium is treated as incompressible and optically transparent. The flow of the fluid is initiated by shearing action of the moving wall with time dependent suction. Radiative heat flow is considered in temperature equation. The coupled nonlinear problem has been solved asymptotically. Approximate solutions have been obtained for the mean velocity, mean temperature using multi parameter perturbation technique. The originality of the present study is to investigate the effect of viscoelastic property of the fluid(Walters B? model) on the flow and heat transfer phenomena when the flow is permeated through a porous medium with uniform porous matrix subject to transverse magnetic field and time dependent fluctuative suction at the boundary surface. The case of viscous flow has been discussed as a particular case on comparison with the result reported earlier and it is in good agreement. Flow reversal is indicated incase of viscoelastic fluid with high heat capacity in the presence of magnetic field. The higher cooling of the plate in case of viscoelastic flow also causes a flow reversal.     

Numerical investigation of entropy generation and heat transfer of pulsating flow in a horizontal channel with an open cavity

In this study, the entropy generation and the heat transfer of pulsating air flow in a horizontal channel with an open cavity heated from below with uniform temperature distribution are numerically investigated. A numerical method based on finite volume method is used to discretize the governing equations. At the inlet of the channel, pulsating velocity is imposed for a range of Strouhal numbers St_p from 0 to 1 and amplitude A_p from 0 to 0.5. The effects of the governing parameters, such as frequency and amplitude of the pulsation, Richardson number, Ri, and aspect ratio of the cavity, L/H, on the flow field, temperature distribution, average Nusselt number and average entropy generation, are numerically analyzed. The results indicate that the heat transfer and entropy generation are strongly affected by the frequency and amplitude of the pulsation and this depends on the Richardson number and aspect ratio of the cavity. The pulsation is more effective with the aspect ratio of the cavity L/H= 1.5 in terms of heat transfer enhancement and entropy generation minimization.     

Entropy generation analysis for the peristaltic flow of Cu-water nanofluid in a tube with viscous dissipation

The purpose of the current investigation is to examine the influence of different physical parameters on the entropy generation. The entropy generation number due to heat transfer and fluid friction is formulated. The velocity and temperature distributions across the tube are presented along with pressure attributes. Exact analytical solution for velocity and temperature profile is obtained. It is found that the entropy generation number attains high values in the region close to the walls of the tube, while it falls to low values near the center of the tube.     

Kelvin-Helmholtz instability.with mass transfer through porous media： Effect of irrotational viscous pressure

This paper studies the effect of the irrotational viscous pressure on Kelvin-Helmholtz instability of the plane interface of two viscous and incompressible fluids in a fully saturated porous media with mass and heat transfers across the interface. In the earlier work, the instability of the plane interface of two viscous and streaming miscible fluids through porous media was studied by assuming that the motion and the pressure are irrotational and the viscosity enters the normal stress balance. This theory is called the viscous potential flow theory. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by considering viscous contributions of the irrotational pressure. The Darcy-Brinkman model is used in the investigation and the stability criterion is formulated in terms of a critical value of the relative velocity. It is observed that the heat and mass transfer has a destabilizing effect on the stability of the system while the irrotational shearing stresses stabilize the system.     

Effects of variable fluid properties on the thin film flow of Ostwald-de Waele fluid over a stretching surface

We investigate, in this paper, the effects of thermo-physical properties on the flow and heat transfer in a thin film of a power-law liquid over a horizontal stretching surface in the presence of a viscous dissipation. The fluid properties, namely the fluid viscosity and the fluid thermal conductivity, are assumed to vary with temperature. Using a similarity transformation, the governing partial differential equations with a time dependent boundary are converted into coupled non-linear Ordinary Differential Equations (ODEs) with variable coefficients. Numerical solutions of the coupled ODEs are obtained by a finite difference scheme known as the Keller-box method. Results for the velocity and temperature distributions are presented graphically for different values of the pertinent parameters. The effects of unsteady parameter on the skin friction, the wall temperature gradient and the film thickness are presented and analyzed for zero and non-zero values of the temperature-dependent thermo-physical properties. The results obtained reveal many interesting features that warrant further study on the non-Newtonian thin film fluid flow phenomena, especially the shear-thinning phenomena.     

Flow,thermal criticality and transition of a reactive third-grade fluid in a pipe with Reynolds' model viscosity

Neglecting the consumption of the material, a steady incompressible flow of an exothermic reacting third-grade fluid with viscous heating in a circular cylindrical pipe is numerically studied for both cases of constant viscosity and Reynolds' viscosity model. The coupled ordinary differential equations governing the flow in cylindrical coordinates, are transformed into dimensionless forms using appropriate transformations, and then solved numerically. Solutions using Maple are presented in tabular form and given in terms of dimensionless central fluid velocity and temperature, skin friction and heat transfer rate for three parametric values in the Reynolds' case. The numerical results for the velocity and temperature fields are also presented through graphs. Bifurcations are discussed using shooting method. Comparisons are also made between the present results and those of previous work, and thus verify the validity of the provided numerical solutions. Important properties of thermal criticality are provided for variable viscosity parameter and reaction order. Further numerical results are presented in the form of tables and graphs for transition of physical parameters, while varying certain flow and fluid material parameters. Also, the flow behaviour of the reactive fluid of third-grade is compared with those of the Newtonian reactive fluid.     

水位变化对粗砂土内流动与传热的影响

该文以粗砂土为研究对象,对粗砂土在不同水位条件下流动与传热情况进行研究。建立粗砂土三维模型,采用有限体积法进行数值计算,并利用恒温实验平台进行验证。结果表明:在正常条件下粗砂土内以对流换热为主,其流线呈顺时针方向流动;粗砂土内水气交界面处存在温度场和流态的突变,出现了半涡形结构和高于壁面温度的现象;瑞利数对粗砂土对流换热影响显著,与Nu数呈指数关系;在实验中温度呈非线性变化,各测点温度值分布为4层2区;模拟值与实验值基本一致,三维模型具有更高的准确度。     

LAMINAR FLOW AND HEAT TRANSFER IN THE DEVELOPING REGION OF HELICAL SQUARE DUCTS

Simultaneous development of the laminar flow and heat transfer in helical square ducts was numerically studied. The governing equations were written in an orthogonal helical coordinate system and fully parabolized in the axial direction. Results were found out over a wide range of the governing parameters. Two axial velocity entries were taken into account. The development of secondary flow, axial velocity and temperature distribution for the large Dean number were examined in detail and the effects of different governing parameters on the friction factor and the Nusselt number were annlyzee. Many new and interesting conclusions were reached. The present results reveal the nature of fluid flow and heat transfer in the developing region of helical square ducts.     

NUMERICAL STUDY OF VORTEX SHEDDING FROM A SQUARE CYLINDER AND ITS EFFECTS ON HEAT TRANSFER OF MIXED CONVECTION

1 .　INTRODUCTIONForseveraldecades ,thenumericalandexperi mentalinvestigationofvortexsheddingfromaheated cooledbluntbodyinthemixednaturalandforcedconvectionregimeshasbeenasubjectofgreatinterestamongappliedmathematicians,fluiddynamicistsandheattransferanalysistowingtoitsnumerousengineeringapplicationssuchasthecoolingofelectroniccomponents ,thecoolingofhotwireanemometersandtheliftenhancementasattributedtotheMagnuseffects .Literatureonvortexsheddingfromcircularcylinderinthemixedconvectionregi…