Non-isothermal laminar pipe flow — I. Theoretical

The Graetz-problem — heat transfer to a fluid flowing laminarly in a circular tube with constant temperature — has been extended to the case of a variable viscosity. Calculations are performed on the heat transfer to and the hydrodynamics of non-isothermal, rectilinear, laminar flow of incompressible, power-law fluids in round tubes. The consistency-index is assumed to vary exponentially with temperature.The results are presented as logarithmic mean Nusselt-numbers and dimensionless velocity distributions and pressure drops as a function of the dimensionless axial length in the tube and as function of a quantity Q which measures the deviation of “isoviscous” fluid behaviour. It turns out that the heat transfer rate is a unique function of the velocity gradient at the wall.All results are summarized in a few practical approximations.     

气体在任意截面形状微尺度槽道中的滑移流动

利用正交函数法对气体在具有任意截面形状的微尺度槽道内的充分发展层流滑移流动特性进行了理论分析,获得了任意截面形状微槽道内的速度分布和流动阻力特性的分析解,并以矩形微槽为例分析了微槽截面上的速度分布和阻力特性.结果表明：随Kn数的增加,由于壁面处滑移流动的影响,气体流经微槽的流动阻力常数小于大尺度理论预测值;理论分析解的结果与实验结果吻合较好,表明在一定的Kn数范围内Navier-Stokes方程在考虑了速度滑移后可以描述微通道内的气体流动过程;正交函数法在微槽内滑移流动的分析中是可行的.     

有序涡旋对三角槽道脉动流强化传热的影响

以水为工质对三角槽道内单相液体充分发展层流脉动传热特性进行了研究。应用粒子图像测速技术（PIV）测得流场内涡的变化规律,从“涡及涡运动”的角度揭示了“有序”的涡生长及迁移过程对脉动流强化传热的影响。此外,应用“场协同”理论,通过数值模拟深入分析了流场特性与传热之间的关系。研究发现,“有序”的涡生长及迁移过程,破坏了流体边界层,促进了近壁区热流场与速度场的协同,同时,强化了三角槽道内流体与主流区流体的掺混,热量输运能力提升;存在最佳的Strouhal数（St）,使得涡旋既能充分发展又能在较短时间脱落进入主流,实现最大效率的壁面换热;有序涡旋对速度场、温度梯度场以及压力梯度场三者协同性的改善是换热性能提升的关键。     

Effect of Shear Work on the Heat Transfer Characteristics of Gaseous Flows in Microchannels

The effect of shear work at solid boundaries for parallel plates and a micropipe is considered to analyze the heat transfer characteristics in the slip flow region for gaseous flow. The fluid flow is assumed to be laminar, incompressible, steady, and hydrodynamically and thermally fully developed. The effects of second‐order velocity slip, temperature jump, shear work at the solid surface, and viscous dissipation are considered. The constant heat flux boundary condition is used at the surface of the parallel plates and of the micropipe. Closed‐form expressions are obtained for the temperature distribution and Nusselt number as a function of various modeling parameters for both geometries. The results show that neglecting the shear work underpredicts the Nusselt number.     

LAMINAR FLOW HEAT TRANSFER WITH INLINE MIXERS INSERTS

Heat transfer coefficients were measured for heat transfer to a Newtonian fluid flowing in laminar flow through a tube with inline mixer inserts. Kenics “Static” mixer and Ross LPD mixer inserts were studied as heat transfer augmentation devices. The mixer inserts were in the inner tube of a concentric tube heat exchanger. Steam was condensed in the annulus of the exchanger. Significant heat transfer enhancement was obtained with both inserts at the expense of even greater pressure drop increases. The use of the Ross mixer insert gave greater augmentation than did the use of the kenics insert. An analysis using the analogy between momentum and heat transfer allowed the prediction of heat transfer coefficients from pressure drop measurements. The predicted coefficients were in good agreement with experimentally measured heat transfer coefficients for laminar flow.     

Equilibrium facilitated mass transfer in plate type reactive membrane separation devices

The introduction of mobile carrier species which react reversibly with the solute species in liquid membrane mass transfer separation devices can give enhanced mass transfer rate. For one-dimensional laminar boundary layer flow of a Newtonian fluid past a single-membrane separator with equilibrium facilitated transport inside the membrane, the mass transfer rate in the separator was analyzed numerically. For a Damköhler number equal to infinity, the effect of maximum facilitation factor, dimensionless equilibrium constant, dimensionless velocity and similarity transformation parameter on the performance of separators was investigated. The dependence of the membrane-fluid interfacial concentration and equilibrium facilitation factor on dimensionless velocity and similarity transformation parameter was discussed.     

Heat and mass transfer in non-newtonian fluid flow with power function velocity profiles

Heat and mass transfer in laminar and turbulent non-Newtonian fluids is investigated in this work using the power function velocity profiles. Analytical solutions are presented for cases of mass transfer in laminar non-Newtonian fluid flows, namely for a flat velocity profile (plug flow), for the case of a constant velocity gradient at the solid boundary (Couette flow), and for the velocity distribution within a laminar boundary layer on a flat plate, and these are illustrated by rotating disks and cylinders in laminar Ostwald-de Waele fluids. Further, turbulent mass transfer processes (tubular flow, rotating disk, and rotating cylinder) in non-Newtonian fluids (Ostwald-de Waele fluid and drag-reducing fluid) at low and large Schmidt numbers are also discussed using the solutions of mass transfer in flows with power function velocity profiles. Reasonable agreement is found between the predictions of this work and the available experimental data and correlations.     

竖直窄矩形通道内环状流的流动传热特性

为了研究竖直窄矩形通道内环状流的流动传热特性,建立了窄矩形通道内环状流的数学物理模型,并进行了实验验证。通过数值求解环状流的数学物理模型得到了环状流区域的压降梯度、沸腾传热系数和液膜内的速度分布。结果表明窄矩形通道内的环状流模型能够很好地预测环状流区域的压降梯度和沸腾传热系数,而且环状流液膜内速度在法向的分布是非线性的,在层流边界层区速度梯度较大。热通量和窄矩形通道的尺寸对液膜的流速有很大影响,随热通量的增加和窄矩形通道尺寸的减小液膜的流速逐渐增加,然而质量流速对液膜流速的影响较小,而且随质量流速的增加液膜的速度逐渐减小。     

Low-Reynolds number heat transfer enhancement in sinusoidal channels

Fully developed laminar flow and heat transfer in three-dimensional, streamwise-periodic sinusoidal channels with circular and semi-circular cross-sections are considered. Computational fluid dynamics (CFD) is used to investigate the effect of Reynolds number (5?Re?200) and amplitude to half wavelength ratio (0.222?A/L?0.667) on heat transfer enhancement and pressure drop for steady, incompressible, constant property, water (Pr=6.13) flows in geometries with L/d=4.5 for the constant wall heat flux (H2) and constant wall temperature (T) boundary conditions.The flow field in the sinusoidal geometries is increasingly dominated by secondary flow structures (Dean vortices) with increasing Reynolds number and A/L. These vortices act to promote convective heat transfer enhancement, resulting in high rates of heat transfer and low pressure loss relative to fully developed flow in a straight pipe. Heat transfer enhancement exceeds the relative pressure-drop penalty by factors as large as 1.5 and 1.8 for the circular and semi-circular cross-sections, respectively.     

Conduction and dissipation in the shearing flow of granular materials modeled as non-Newtonian fluids

After providing a brief review of the constitutive modeling of the stress tensor for granular materials using non-Newtonian fluid models, we study the flow between two horizontal flat plates. It is assumed that the granular media behaves as a non-Newtonian fluid (of the Reiner-Rivlin type); we use the constitutive relation derived by Rajagopal and Massoudi [Rajagopal, K. R. and M. Massoudi, “A Method for measuring material moduli of granular materials: flow in an orthogonal rheometer,” Topical Report, DOE/PETC/TR-90/3, 1990] which can predict the normal stress differences. The lower plate is fixed and heated, and the upper plate (which is at a lower temperature than the lower plate) is set into motion with a constant velocity. The steady fully developed flow and the heat transfer equations are made dimensionless and are solved numerically; the effects of different dimensionless numbers and viscous dissipation are discussed.     

Heat transfer of evaporating droplet flow in low pressure systems

Convective heat transfer of laminar droplet flow is analyzed for a low pressure system, where latent heat of evaporation and ratio of liquid density to vapor density is high (for example, water at l atm). The droplet size is considered to be approximately constant but the vapor velocity is considered increasing along the tube. The heat transfer effect of droplets in the vapor stream is treated as distributed heat sink. Results are presented in non-dimensional form for circular tubes, with constant wall heat flux or constant wall temperature boundary conditions. Distinct heat transfer behavior of droplet flow is revealed.     

对流传热过程强化与能耗分析

为了强化对流传热,工程上普遍采用提高流体流速和改变管路流体力学特性的方法,但在强化传热的同时,增加了能耗.通过实验分析了流体流速对光滑直管和螺旋槽管传热效果的影响,得到了滞流区和湍流区的传热关系式和阻力与流速的函数关系式.通过对比相同流速下光滑直管和螺旋槽管强化比与阻力的情况,得到了两种流型下强化比以及阻力与流速的关系式,为工程设计和生产操作提供了理论参考.     

双波纹流道中的流体流动特性及LDV实验

开发了一种双波纹流道结构,基于正交实验方法设计了9组不同结构参数的双波纹流道,采用计算流体力学（CFD）方法,研究了一定Reynolds数范围内（25≤Re≤200）,9组双波纹流道内的流体充分发展层流流动和传热性能。研究结果表明,流道的波纹波幅对于流体流动和传热性能的影响较大。设计制作了流体在双波纹流道中流动的冷模实验装置,采用激光多普勒测速仪（LDV）对于流道内特殊位置点的速度进行测量,将实验测量结果与数值模拟计算结果进行对比。结果表明,实验测量结果与数值模拟计算结果变化趋势一致且吻合较好,主流速度的最大相对误差为28.7%,由此验证了数值模拟计算的可靠性和准确度。     

A numerical study on unsteady natural convection of air with variable viscosity over an isothermal vertical cylinder

The present study deals with the boundary layer flow and heat transfer of unsteady laminar free convection flow past a semi-infinite isothermal vertical cylinder immersed in air. The fluid viscosity is assumed to vary with the temperature. An implicit finite-difference method has been employed to solve the governing non-dimensional boundary layer equations. A parametric study is performed to illustrate the influence of variable viscosity on the velocity and temperature profiles. The numerical results reveal that the viscosity has significant influences on the transient velocity and temperature profiles, average skin-friction coefficient and the average heat transfer rate. The results indicate that as the viscosity parameter increases, the temperature and the skin-friction coefficient increase, while the velocity near the wall and the Nusselt number decrease.     

三维槽道的周期性层流流动与传热

应用数值模拟方法分析了以周期性方式布置不同节距比(PR=L/H)、倾角为45°挡板槽道的流动特性与传热特性。挡板在槽道上下壁面对齐布置高度比(BR=b/H)为0.2,以便在槽道内部形成一对沿流向的反向旋涡。数值模拟计算Reynolds数范围为100~1000,流体介质为空气。计算结果表明:布置斜置挡板后,在槽道内诱导产生了沿流向的旋涡流,且在测试段中旋涡流冲击槽道上下壁面和槽道一侧壁面,结果使得传热效率提高;分析了范围内平均Nusselt数比Nu/Nu₀、摩擦系数比f/f₀及传热增强系数η随节距比PR和Reynolds数的变化关系,并建立了相应的准则关系式;当挡板间节距比为0.5时,传热增强系数可达最大值3.0。     

AN ADVANCING FRONT MODEL OF TRANSPORT INTO PULSATING LAMINAR FLOW

The diffusion and transport of a gas species is analyzed for a slowly pulsating fluid in laminar tube flow. It is assumed that the fluid velocity is in phase with the pulsating pressure gradient. A reversible chemical reaction within the fluid is modeled using advancing front theory. The pulsation is assumed to affect only the diffusion boundary layer thickness, which may be out of phase with the flow pulsation. The solution is approximate for small perturbations of the boundary layer thickness. With these assumptions a closed form solution for the bulk transport is obtained. The results are expressed as differences in the bulk transport relative to a steady flow having the same average flow conditions. The pulsation effect is expressed as a function of the non-dimensional flow amplitude and frequency parameters for various average conditions. Comparison with experimental measurements of oxygen diffusing into water and hemoglobin solutions shows good agreement. For the range of parameters used for the measurements, there is no effect of the pulsation on time-averaged transfer rates.     

COMBINED FORCED AND FREE CONVECTION IN BOUNDARY LAYER FLOW OF NON-NEWTONIAN FLUID ON A HORIZONTAL PLATE

An analysis is presented to study the effects of buoyancy-induced streamwise pressure gradients on laminar forced convection heat transfer to non-Newtonian fluids from a horizontal plate. Numerical solution of the transformed boundary layer equations has been carried out for different values of the flow behavior index and the buoyancy parameter by means of the local nonsimilarity method. A discussion is provided for the effect of the buoyancy force on the friction factor, the dimensionless heat transfer rate and the details of the velocity as well as temperature fields.     

A Re‐Examination of heat transfer in laminar divergent flow between two parallel fixed discs

Upon a critical review of pertinent literature, new theoretical expressions for dimensionless heat transfer rates between two parallel fixed circular discs and a fluid in radial divergent laminar flow are established and compared to previously published theory and experimental data. Based on the logarithmic mean temperature difference, the new analytical relationships are shown to adequately predict dimensionless heat transfer rates, and it is recommended that they be used in preference to certain earlier expressions which are either erroneous or of strongly limited applicability.     

Scaling transformation for the effects of chemical reaction on free convective heat and mass transfer in the presence of variable stream conditions

Natural convective boundary layer flow and heat and mass transfer of a fluid with temperature-dependent fluid viscosity, chemical reaction and thermal radiation over a vertical stretching surface in the presence of suction is investigated by scaling transformation analysis. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie-group transformations viz. scaling group of transformations. An exact solution is obtained for translation symmetry and numerical solutions for scaling symmetry. Effects of temperature-dependent fluid viscosity, chemical reaction and thermal radiation on the dimensionless velocity, temperature and concentration profiles are shown graphically. Comparison with previously published work is performed and excellent agreement between the results is obtained. The conclusion is drawn that the flow field and temperature and concentration profiles are significantly influenced by these parameters.     

Influence of the meandering channel geometry on the thermo-hydraulic performances of an intensified heat exchanger/reactor

In the global context of process intensification, heat exchanger/reactors are promising apparatuses to implement exothermic chemical syntheses. However, unlike heat exchange processes, the implementation of chemical syntheses requires to control the residence time to complete the chemistry. A way to combine the laminar regime (i.e. enough residence time) with a plug flow and the intensification of both heat and mass transfers is the corrugation of the reaction path.In this work, the experimental set-up is based on plate heat exchanger/reactor technology. 7 milli-channel corrugated geometries varying the corrugation angle, the curvature radius, the developed length, the hydraulic diameter and the aspect ratio have been designed and experimentally characterized (heat transfer, mixing times, pressure drops, RTD). The objectives were to assess their respective performances to derive some correlations depending on the channel design.The results confirmed the benefits of the reaction channel corrugation. Heat and mass transfers have been intensified while maintaining a plug flow behaviour in the usually laminar flow regime. Moreover, whatever the meandering channel's curvature radius, the results highlighted the relevance of considering the Dean number as the scale-up parameter. This dimensionless number, more than the Reynolds number, seems to govern the flow in the wavy channels.