Slip flow and heat transfer in rectangular and circular microchannels using hybrid FE/FV method

Rarefied gas flows typically encountered in MEMS systems are numerically investigated in this study. Fluid flow and heat transfer in rectangular and circular microchannels within the slip flow regime are studied in detail by our recently developed implicit, incompressible, hybrid (finite element/finite volume) flow solver. The hybrid flow solver methodology is based on the pressure correction or projection method, which involves a fractional step approach to obtain an intermediate velocity field by solving the original momentum equations with the matrix‐free, implicit, cell‐centered finite volume method. The Poisson equation resulting from the fractional step approach is then solved by node based Galerkin finite element method for an auxiliary variable, which is closely related to pressure and is used to update the velocity field and pressure field. The hybrid flow solver has been extended for applications in MEMS by incorporating first order slip flow boundary conditions. Extended inlet boundary conditions are used for rectangular microchannels, whereas classical inlet boundary conditions are used for circular microchannels to emphasize on the entrance region singularity. In this study, rarefaction effects characterized by Knudsen number (Kn) in the range of 0 ⩽ Kn ⩽ 0.1 are numerically investigated for rectangular and circular microchannels with constant wall temperature. Extensive validations of our hybrid code are performed with available analytical solutions and experimental data for fully developed velocity profiles, friction factors, and Nusselt numbers. The influence of rarefaction on rectangular microchannels with aspect ratios between 0 and 1 is thoroughly investigated. Friction coefficients are found to be decreasing with increasing Knudsen number for both rectangular and circular microchannels. The reduction in the friction coefficients is more pronounced for rectangular microchannels with smaller aspect ratios. Effects of rarefaction and gas‐wall surface interaction parameter on heat transfer are analyzed for rectangular and circular microchannels. For most engineering applications, heat transfer is decreased with rarefaction. However, for fluids with very large Prandtl numbers, velocity slip dominates the temperature jump resulting in an increase in heat transfer with rarefaction. Depending on the gas‐wall surface interaction properties, extreme reductions in the Nusselt number can occur. Present results confirm the existence of a transition point below and above wherein heat transfer enhancement and reduction can occur. Copyright © 2011 John Wiley & Sons, Ltd.     

竖直矩形通道内不凝性气体对凝结换热特性的影响

本文以去离子水为工质,实验研究了竖直矩形窄通道内少量残余不凝性气体对蒸汽凝结换热特性的影响。采用热阻分离法得到凝结侧换热表面传热系数,分析了不凝性气体的含量、冷却水质量流速、进口温度和热流密度对蒸汽凝结侧表面传热系数的影响。结果表明:当热流密度为1.668 kW/m~2,即蒸汽质量流速较小时,2%体积分数的不凝性气体使凝结侧表面传热系数下降了33%,但当热流密度为3.887 kW/m~2,蒸汽质量流速较大时,2%体积分数的不凝性气体仅使凝结侧表面传热系数降低了14%,此外,凝结换热表面传热系数随冷水质量流速和不凝性气体分数的增加而变小,随冷水进口温度和热流密度的增加而变大。     

Natural convection heat transfer of cold water in an eccentric horizontal cylindrical annulus — a numerical study

A numerical study of the natural convection heat transfer of cold water, having the density inversion between two isothermal eccentric horizontal cylinders is studied. A general code is developed for the body fitted coordinate system. This procedure transforms an arbitrarily shaped physical domain into a rectangular (square) domain. The governing equations in this computational domain are solved by the upwind finite difference scheme. The numerical solutions are obtained for a Rayleigh number (Ra) ranging between a Prandtl number (Pr) 12.0 and inversion parameter (γ) 0,−1 and −2. The affect of the radius ratio (R) on the flow patterns and heat transfer coefficients is studied by taking the Radius ratio as 1.5 and 2. The eccentricity affect is studied by moving the center of the inner cylinder horizontally and vertically (both positive and negative directions) with respect to the center of the outer cylinder. For the cases considered in the present study, it is again for the minimum heat transfer is observed like in the case of concentric annulus.     

Transient free convection flow past an impulsively started isothermal vertical cylinder with mass flux

This paper concern with the laminar flows, which arise in fluids due to the interaction of the force of gravity and density differences, caused by temperature differences and material or phase constitution for both air and water. A solution of laminar boundary layer equations has been obtained for the transient free convective flow past an impulsively started semi-infinite isothermal vertical cylinder with uniform mass flux. The solutions of the dimensionless, unsteady, coupled and non-linear governing partial differential equations are obtained by a more accurate, unconditionally stable and fast converging implicit finite difference scheme. The results show many interesting effects on velocity, temperature and concentration profiles and local as well as average shear stress, rate of heat and mass transfer. It is observed that there is a rise in the velocity due to the presence of mass diffusion.     

Transient cryogenic chill down process in horizontal and inclined pipes

Experimental results are presented that describe the parametric effects of inclination of transfer line and mass flux on cryogenic chill down process. Experiments were performed in a pressurized liquid nitrogen transfer line made of stainless steel. Fluid and wall temperatures were measured at various axial locations of the test section to monitor the chill down process. The local heat transfer coefficient and heat flux were predicted for the transient chill down period using an inverse heat transfer technique. The results show that the chill down period is characterized by three distinct flow regimes at all mass flux rates. However the variation in chill down time is more predominant at low mass fluxes. Heat transfer coefficient and heat flux calculated using the inverse heat transfer technique further confirmed this and showed that peak heat flux increases with increase of mass flux. It is found that the inclination of the chilling line displayed similar temperature profile but accompanied with variation in chill down time. Results suggest the existence of an optimum upward line inclination minimizing the chill down time.     

Condensation of refrigerants in a multiport tube with rectangular minichannels

This study investigated the condensation heat transfer and pressure drop characteristics of refrigerants R134a, R32, R1234ze(E), and R410A in a horizontal multiport tube with rectangular minichannels, in the mass velocity range of 100–400 kg m⁻² s⁻¹ and saturation temperature set at 40 and 60 °C. The effect of mass velocity, vapor quality, saturation temperature, refrigerant properties, and hydraulic diameter of rectangular channels on condensation characteristics is clarified. A new correlation is proposed for predicting the frictional pressure drop for condensation flow in minichannels. A heat transfer model for condensation heat transfer in rectangular minichannels is developed considering the flow patterns and effects of vapor shear stress and surface tension. Then, based on this model, a new heat transfer correlation is proposed. The proposed correlations successfully predict the experimental frictional pressure drop and heat transfer coefficients of the test refrigerants in horizontal rectangular minichannels.     

Natural convection in a non-rectangular porous enclosure

This paper describes a numerical solution procedure to study heat transfer process by two dimensional natural convection phenomena in a non-rectangular enclosure of arbitrary geometry. Momentum transfer in the system is described by an elliptic partial differential equation, which governs the behaviour of the stream function. An algebraic grid generation technique is used to transform the governing equations into a body fitted rectangular co-ordinate system that allows coincidence of all boundary lines with the co-ordinate lines. Numerical solutions of the resulting equations in the computational domain are obtained using an alternating directional implicit method by adding false transient terms. Results from the numerical experiments in the case of a non-rectangular enclosure are obtained that show the magnitude and directions of convection currents and contours of the temperature. The effect of increase in the inclination of the upper boundary is to increase the average Nusselt number.     

Natural convection in a non-rectangular porous enclosure

This paper describes a numerical solution procedure to study heat transfer process by two dimensional natural convection phenomena in a non-rectangular enclosure of arbitrary geometry. Momentum transfer in the system is described by an elliptic partial differential equation, which governs the behaviour of the stream function. An algebraic grid generation technique is used to transform the governing equations into a body fitted rectangular co-ordinate system that allows coincidence of all boundary lines with the co-ordinate lines. Numerical solutions of the resulting equations in the computational domain are obtained using an alternating directional implicit method by adding false transient terms. Results from the numerical experiments in the case of a non-rectangular enclosure are obtained that show the magnitude and directions of convection currents and contours of the temperature. The effect of increase in the inclination of the upper boundary is to increase the average Nusselt number.     

Thermal boundary layers over a shrinking sheet: an analytical solution

In this paper, the heat transfer over a shrinking sheet with mass transfer is studied. The flow is induced by a sheet shrinking with a linear velocity distribution from the slot. The fluid flow solution given by previous researchers is an exact solution of the whole Navier–Stokes equations. By ignoring the viscous dissipation terms, exact analytical solutions of the boundary layer energy equation were obtained for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions were expressed by Kummer’s function. Closed-form solutions were found and presented for some special parameters. The effects of the Prandtl number, the wall mass transfer parameter, the power index on the wall heat flux, the wall temperature, and the temperature distribution in the fluids were investigated. The heat transfer problem for the algebraically decaying flow over a shrinking sheet was also studied and compared with the exponentially decaying flow profiles. It was found that the heat transfer over a shrinking sheet was significantly different from that of a stretching surface. Interesting and complicated heat transfer characteristics were observed for a positive power index value for both power-law wall temperature and power-law wall heat flux cases. Some solutions involving negative temperature values were observed and these solutions may not physically exist in a real word.     

An Unsteady Oscillatory Flow of Generalized Casson Fluid with Heat and Mass Transfer: A Comparative Fractional Model

It is of high interest to study laminar flow with mass and heat transfer phenomena that occur in a viscoelastic fluid taken over a vertical plate due to its importance in many technological processes and its increased industrial applications. Because of its wide range of applications, this study aims at evaluating the solutions corresponding to Casson fluids’ oscillating flow using fractional-derivatives. As it has a combined mass-heat transfer effect, we considered the fluid flow upon an oscillatory infinite vertical-plate. Furthermore, we used two new fractional approaches of fractional derivatives, named AB (Atangana–Baleanu) and CF (Caputo–Fabrizio), on dimensionless governing equations and then we compared their results. The Laplace transformation technique is used to get the most accurate solutions of oscillating motion of any generalized Casson fluid because of the Cosine oscillation passed over the infinite vertical-plate. We obtained and analyzed the distribution of concentration, expressions for the velocity-field and the temperature graphically, using various parameters of interest. We also analyzed the Nusselt number and the skin friction due to their important engineering usage.     

Numerical analysis of two-dimensional lagging thermal behavior under short-pulse-laser heating on surface

In this work, the dual-phase-lag (DPL) model of heat conduction is introduced in treating the transient heat conduction problems in finite rigid mediums under short-pulse-laser heating. Two-dimensional numerical solutions in a rectangular and an axially symmetric system are given by finite difference method. Calculations are performed to exhibit various two-dimensional lagging thermal behavior of conduction heat transfer, such as wavy, wavelike, and diffusive behavior.     

Unsteady compressible boundary layer flow on the stagnation line of an infinite swept cylinder

Summary Numerical solutions of flow and heat transfer process on the unsteady flow of a compressible viscous fluid with variable gas properties in the vicinity of the stagnation line of an infinite swept cylinder are presented. Results are given for the case where the unsteady temperature field is produced by (i) a sudden change in the wall temperature (enthalpy) as the impulsive motion is started and (ii) a sudden change in the free-stream velocity. Solutions for the simultaneous development of the thermal and momentum boundary layers are obtained by using quasilinearization technique with an implicit finite difference scheme. Attention is given to the transient phenomenon from the initial flow to the final steady-state distribution. Results are presented for the skin friction and heat transfer coefficients as well as for the velocity and enthalpy profiles. The effects of wall enthalpy parameter, sweep parameter, fluid properties and transpiration cooling on the heat transfer and skin friction are considered.     

Viscous flow due to an exponentially shrinking permeable sheet in nanofluid in presence of slip

Classical problem of steady boundary layer flow of nanofluid over an exponentially permeable shrinking sheet in presence of slip is investigated. The model used for nanofluid includes Brownian motion and thermophoresis effects. The governing equations for momentum, energy, and nanofluid solid volume fraction are transformed to ordinary differential equations with the help of similarity transformations and then solved numerically using fourth order Runge–Kutta method with shooting technique. It is found that the governing parameters, viz. the suction/blowing parameter, velocity slip, thermal and mass slip parameters, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number significantly affect the flow field, heat, and mass transfer. The results obtained indicate that the dual solutions exist for certain values of the mass suction parameter. Velocity increases whereas the temperature and nanoparticle volume fraction decrease due to suction through the porous sheet. It is noted that with the increase in velocity slip fluid velocity increases whereas temperature and concentration decrease. Due to increase in thermal slip and mass slip both temperature and concentration decrease.     

Experimental investigation of heat transfer enhancement in helical coil heat exchangers using water based CuO nanofluid

The present work deals with the study of heat transfer enhancement using water based CuO nanofluids in the helical coil heat exchanger. Nanofluids were prepared using two-step method by using wet chemical method. Nanofluids with various volume percentage between 0 and 0.5 of CuO nanoparticles and their flow rate between 30 and 80 LPH (Reynolds number ranging from 812 to 1895, Laminar flow regime) were considered in the present study. The setup consists of a test section (helical coil), cooler, reservoir, pump, flow meter, thermocouples and flow controlling system. The temperature measurements were carried out with the help of thermocouples. The investigation was carried out to study the effect of particle loading and flow rate on heat transfer coefficient and Nusselt number. It has been found that the increase in the loading of CuO nanoparticles in base fluid shows a significant enhancement in the heat transfer coefficient of nanofluid. In the present study, at 0.1 vol% concentration of CuO nanoparticles in nanofluid, enhancement in heat transfer coefficient was 37.3% as compared to base fluid while at 0.5 vol%, it is as high as 77.7%. Also with the increase in the flow rate of the CuO nanofluid, significant increase in heat transfer coefficient was observed.     

CFD方法与间接蒸发冷却换热器的三维数值模拟

本文采用计算流体力学(CFD)和数值传热学方法,对间接蒸发冷却器内流体流动与热质交换过程进行简化和假设,建立了换热器内三维层流流动与传热的数学物理模型.采用交错网格离散化非线性控制方程组,编制了三维simple算法程序.对间接蒸发冷却器内的流场、温度场及浓度场进行数值模拟研究,得到换热器内的流体流动状态和热流分布,并分析了通道宽度变化对换热器内流体流动与换热的影响.     

埋地热含蜡原油管道的非稳态传热问题

我国生产的原油大多为含蜡原油，加热输送是含蜡原油的主要输送方式。埋地热含蜡原油管道的运行中涉及若干复杂的非稳态传热问题。从管内原油传热（内部传热）和管道与外部环境的传热（外部传热）两方面，分析和总结了含蜡原油管道非稳态传热问题的研究现状，介绍了管道在土壤中传热的影响因素，比较了其各种解析和数值解法，阐述了管道停输状态下管内含蜡原油相变传热的规律及研究方法，讨论了非稳定流动状态下管内油流的水力—热力耦合问题及求解方法，指出了埋地热含蜡原油管道的非稳态传热方面需进一步研究的问题。     

Interfacial mass transfer and mass transfer coefficient in aqua ammonia packed bed absorberTransfert de masse à l'interface et coéfficient de transfert de masse dans un absorbeur à matelas dispersant eau–ammoniac

A mathematical model was given to predict the mass transfer between flow of a mixture of ammonia vapor and water vapor and a flow of aqua ammonia solution at any interface within a packed bed absorber (PBA). The model used the molal mass and heat transfer coefficients in both the liquid and gas phases, the interface molal solution concentration, interface molal vapor mixture concentration, interface temperature, and the heat transfer coefficients in the liquid and gas phases in both sides of the interface. The heat transfer coefficient was corrected to account for the mass transfer. The model was also used to derive a convenient mass transfer coefficient which was based on the bulk mass concentration, not on the molal concentration, and not directly dependent on the concentration at the interface. To complete the model, mathematical correlations were derived for several thermodynamic and physical properties of aqua ammonia solution and vapor mixture. A computer program was developed to demonstrate the use of the model to predict the rate of absorption of ammonia vapor at an interface within the packed bed at various operating conditions.     

地热对井系统裂隙岩体三维渗流传热耦合的等效模拟方法

研究地热对井系统中的裂隙岩体渗流传热问题对于开采深层地热能和发展可再生清洁能源利用技术具有重要价值。基于渗流传热耦合理论和离散裂隙网络模型,提出了裂隙岩体三维热流耦合的等效模拟方法：考虑由岩块基质及复杂离散裂隙网络组成的双重介质,采用无厚度单元模拟裂隙、线单元模拟对井,通过裂隙、对井和岩块三者之间的流量和热量交换实现渗流和传热过程耦合分析。通过与解析方法和精细模拟方法相比较,验证了等效模拟方法的有效性;并将其应用于含大规模裂隙岩体地热对井系统热采过程的数值模拟,获取了储层内温度场的分布规律,评价了裂隙开度对储层平均温度和整体开采率的影响。结果表明：该文方法能够对裂隙及井筒中的渗流传热行为进行细致模拟,在保证精度的前提下,可大幅减小计算量和计算时长;裂隙网络的非均匀及各向异性分布导致岩体温度场分布呈现高度不均匀性,反映了热流耦合的早期热突破和长尾效应等特点;裂隙内水的对流传热作用明显,冷锋面沿储层内的主要贯通裂隙网络移动,裂隙开度是影响岩体温度场分布的重要因素。     

Free convection heat and mass transfer along a vertical surface in a porous medium

Summary This study deals with free convection heat and mass transfer from a vertical plate embedded in a fluid saturated porous medium with constant wall temperature and concentration. The temperature and concentration variations across the boundary layer produce a buoyancy effect which gives rise to flow field. Integral method of Von-Karman type is applied to obtain the analytical solution of this fundamental problem.     

Forced convection of low temperature nitrogen gas in rectangular channels with small aspect ratio

Forced convection of low temperature (80-150 K) nitrogen gas flowing through rectangular channels with hydraulic diameters of 0.513-1.814 mm and aspect ratios of 0.013-0.048 has been investigated experimentally. Close attention was focused on the effects of channel depth and heat addition on the heat transfer and flow characteristics, the transition from laminar to turbulent flow and the existence of an optimum channel depth. A dimensionless heating number was adopted to characterize the heating effect. The experimental correlation developed for the Nusselt number shows that the heat addition is the most important effect, followed by the channel aspect ratio, Reynolds number and Prandtl number.