Forced convection in cross flow of power law fluids over a tube bank

The forced convective heat transfer characteristics for incompressible power-law fluids past a bundle of circular cylinders have been investigated numerically. The cylinder-to-cylinder hydrodynamic interactions have been approximated via a simple cell model. The momentum and energy equations have been solved using a finite difference based numerical method for a range of physical and kinematic conditions. The role of the two commonly used thermal boundary conditions, namely, constant temperature or constant heat flux, on heat transfer characteristics has also been studied. Extensive numerical results elucidating the effect of shear-thinning viscosity on the values of Nusselt number have been obtained for Peclet numbers ranging from 1 to 5000, Reynolds number in the range 1-500, flow behaviour index 1?n?0.5 and three values of voidages, namely, 0.4, 0.5 and 0.6, typical of tubular heat exchangers and tube banks. Under all conditions, varying levels of enhancement in Nusselt number are observed due to shear-thinning behaviour. The surface averaged Nusselt number shows strong dependence on the values of voidage, power-law index, Reynolds and Peclet numbers. The paper is concluded by presenting comparisons with the scant experimental results available in the literature.     

Drag on chains and agglomerates of spheres in viscous newtonian and power law fluids

New experimental data on the free settling velocity of straight chains (up to twenty spheres) and planar clusters of touching spheres in Newionian and power law media are reported. The results embrace the following ranges of conditions: 0.65 ≤ n ≤ 1; Re < - 2.5 and 1.22 < m < 48.87 Pa·sⁿ. The straight chain drag measurements are in line with theoretical predictions for Newtonian fluids. The present results in power law fluids seem to suggest that it is possible to express the drag on a straight chain of spheres in terms of that on a single sphere of equal volume. Limited results with planar clusters are satisfactorily correlated using a volume equivalent sphere diameter.     

Effect of blockage on drag and heat transfer from a single sphere and an in-line array of three spheres

The effect of blockage ratio on the steady flow and heat transfer characteristics of incompressible fluid over a sphere and an in-line array of three spheres placed at the axis of a tube has been investigated numerically. The Navier-Stokes and thermal energy equations have been solved numerically using FLUENT for the following ranges of parameters: for a single sphere, 2 ≤ β ≤ 10; 1 ≤ Re ≤ 100; for the three-sphere system, for two values of sphere-to-sphere distance, namely s = 2 and 4. All computations were carried out for two values of the Prandtl number, i.e., 0.74 and 7, corresponding to the flow of air and water respectively. Extensive results on streamline patterns, wake characteristics (angle of separation and recirculation length), drag coefficient and Nusselt number are presented to elucidate the interplay between the blockage and the Reynolds number and their influence on drag and Nusselt number.     

Effect of blockage on heat transfer from a cylinder to power law liquids

The influence of planar confining walls on the steady forced convection heat transfer from a cylinder to power-law fluids has been investigated numerically by solving the field equations using FLUENT (version 6.2). Extensive results highlighting the effects of the Reynolds number (1?Re?40), power-law index (0.2?n?1.8), Prandtl number (1?Pr?100) and the blockage ratio (β=4 and 1.6) on the average Nusselt number have been presented. For a fixed value of the blockage ratio, the heat transfer is enhanced with the increasing degree of shear-thinning behaviour of the fluid, while an opposite trend was observed in shear-thickening fluids. Due to the modifications of the flow and temperature fields close to the cylinder, the closely placed walls (i.e., decreasing value of the blockage ratio) further enhance the rate of heat transfer as the fluid behaviour changes from Newtonian to shear-thickening fluids (n>1), the opposite influence is seen with the decreasing value of the flow behaviour index (n) in shear-thinning (n<1) fluids. Finally, the functional dependence of the present numerical results on the relevant dimensionless parameters has been presented in the form of closure relationships for their easy use in a new application.     

Forced convection heat transfer in tube banks in cross flow

The forced convection heat transfer characteristics for an incompressible, steady and Newtonian fluid flow over a bundle of circular cylinders has been investigated numerically. The inter-cylinder hydrodynamic interactions have been approximated by employing a simple cell model. The momentum and energy equations have been solved by using a finite difference based numerical solution procedure for a range of physical and kinematic conditions. Furthermore, the role of the type of thermal boundary condition, namely, a constant temperature or a constant heat flux, imposed on the surface of the cylinder has also been elucidated. Extensive results on the temperature fields, and on the variation of the Nusselt number on the surface of a typical cylinder in the assemblage have been obtained for two values of the Prandtl number (corresponding to air and water). The Reynolds number of flow was varied in the range 1-500 and the voidage of the assemblage ranged from 0.4 to 0.99 thereby covering the entire range of interest as encountered in tubular heat exchangers and in fibrous beds. The paper is concluded by presenting extensive comparisons with the limited analytical/numerical and/or experimental results available in the literature for the case of a single cylinder as well as that for tube bundles.     

Convective heat transfer coefficient for the side-wall in a fixed bed

Fixed beds are widely used in the chemical and process industry due to their relatively simple yet effective performance. Determining the radial heat transfer at the wall in a fixed bed is crucial to predict the performance of columns. Heat transfer parameters often need to be obtained experimentally. Various Nusselt ${\mathrm{Nu}}_w$ versus Reynolds ${Re}_p$ correlations in literature show considerable scatter and discrepancies. The tube-to-particle diameter ratio $\frac{D_{\mathrm{t}}}{D_{\mathrm{p}}}$ and boundary conditions on the particle surface have been understood to affect heat transfer near the wall by virtue of influence on the near-wall porosity and mixing. In this work, a fixed bed consisting of mono-disperse particles is generated via gravity-forced sedimentation modelling utilizing the discrete element method for a $\frac{D_{\mathrm{t}}}{D_{\mathrm{p}}}$ ratio of 3.3. The system is meshed and imported in a computational fluid dynamics (CFD) solver. Fluid inlet velocity is varied to get ${Re}_p\in \left[1,1500\right]$ corresponding to the laminar and turbulent flow regimes. The particles are treated as boundaries with Dirichlet, Neumann, and Robin boundary conditions applied for the closure of energy balance. Another set of simulations is run with particles modelled as solids with varying thermal conductivities ($k_s/k_f$). The heat flux and volume-averaged fluid temperature calculated during post-processing are used to determine the wall heat transfer coefficient and, subsequently, the wall Nu number. Fifteen ${\mathrm{Nu}}_w$ versus ${Re}_p$ correlations are compiled and analyzed. A new semi-empirical correlation for the wall Nusselt number has been developed for a fixed bed packed with monodisperse spheres for $\frac{D_t}{D_p}=3.3$ and results compared with data published in literature. Additionally, the impact of buoyancy effect on the wall Nusselt number has been studied.     

Laminar natural convection characteristics in an enclosure with heated hexagonal block for non-Newtonian power law fluids

This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.     

Surface-to-bed heat transfer in fluidised beds of fine particles

This work reports experimental results on the heat transfer between a fluidised bed of fine particles and a submerged surface. Experiments have been carried out using different bed materials (polymers, ballotini, corundum, carborundum and quartz sand) with Archimedes number between 2 and 50. Dry air at ambient pressure and temperature has been used as fluidising gas. Three different exchange surfaces, namely a sphere and two cylinders with different base diameter and same height, have been used.Experimental results show that the heat transfer coefficient increases with particle Archimedes number and is almost independent from particle thermal conductivity for K_p/K_g > 30. Finally, the comparison of heat transfer coefficient for the different surfaces shows that the effect of the surface geometry may account for a 30% variation in the heat transfer coefficient, with higher differences occurring for coarser particles.     

Convective instability in packed beds with internal heat sources and throughflow

This article focuses on convective instabilities of throughflow in packed beds with internal heat sources. When a packed bed is heated with internal heat sources, the effects of throughflow on the onset conditions of convection have been examined numerically under the linear stability theory. The resulting conditions show that stationary instabilities occur at higher values of Darcy-Rayleigh number than the critical values as the amount of throughflow increases. The effects of free and rigid boundaries on the onset condition are also obtained for the Brinkman porous media with throughflow.     

微细铜丝在水中自然对流换热

采用实验与数值模拟相结合的方法分别研究了封闭空间内水平放置的直径为39.9、65.8、119.1 μm的微细铜丝（微丝）在水中的对流换热,分析了微丝表面自然对流换热特性及机理。实验通过焦耳加热的方法测量了不同直径微丝在水中自然对流的传热系数及Nusselt数。同时建立三维不可压数学模型对微丝在水中的自然对流进行数值模拟,并将计算结果与实验值进行了对比。研究表明,数值模拟结果与实验值基本吻合,微丝在水中自然对流的传热系数随直径减小而显著增大,Nu则明显减小,且Nu随热通量增加的变化率也随直径减小而明显降低;微丝表面边界层厚度随直径减小而变薄,但边界层厚度与微丝直径的比值则逐渐增大;另外,对比微丝与常规尺度圆管表面自然对流的流场、温度场以及边界层分布,发现相同温差下微丝表面自然对流换热的边界层与常规尺度下沿壁面由底部向上发展的形状不同,而是沿微细丝表面呈椭圆形包裹于其上,因此削弱了表面对流换热强度,导致温度场呈现出较明显的导热特征。     

Computation of wall to suspension heat transfer in vertical pipes

In this article, turbulent gas-solid flow in a vertical pipe is investigated for predicting the heat transfer from the heated wall to the suspension. The Eulerian-Eulerian model is used, incorporating a four-way coupling; i.e., considering inter-particle collisions as well as particle-wall collisions. Both the phases are simulated based on Reynolds averaged Navier-Stokes equations (RANS) with a two-equation k ? ? turbulence model for the gas phase and a granular temperature equation for the solid phase. The closure of the granular temperature (kinetic energy associated with the random motion of the particles) equation is done by the use of kinetic theory of granular flows. The main objective of the study is to investigate the variations of two-phase heat-transfer coefficient and Nusselt number with flow parameters like flow Reynolds number, particulate loading, and particle size. In comparison to single-phase flow, heat transfer is found to be significantly increased with the increase in Reynolds number and particulate loading. This happens because of the presence of the solid particles in a gas flow, which bring changes to the heat-transfer characteristics of the gas phase. Heat transfer increased by adding solid particles for particulate loading in the range of 1 to 20 and particle size in the range of 30 to 50 µm.     

Effect of Non‐Newtonian Characteristics on Convective Liquid‐Solid Heat Transfer in Packed and Fluidised Beds of Spherical Particles

In this work, the field (continuity, momentum and thermal energy) equations togetherwith a cell model have been solved numerically to elucidate the influence of non‐Newtonian (Power law rheology) liquid characteristics on liquid‐solid heat transfer in packed and fluidised beds of spherical particles. The results presented herein relate to wide ranges of conditions of bed voidage, power‐law index and Peclet number but are limited to low Reynolds number (≤1) flow conditions. Within the range of conditions, the effect of power‐law index is found to be small and this is also consistent with the available experimental results on liquid‐solid mass transfer in these systems.     

Particle scale study of heat transfer in packed and bubbling fluidized beds

The approach of combined discrete particle simulation (DPS) and computational fluid dynamics (CFD), which has been increasingly applied to the modeling of particle‐fluid flow, is extended to study particle‐particle and particle‐fluid heat transfer in packed and bubbling fluidized beds at an individual particle scale. The development of this model is described first, involving three heat transfer mechanisms: fluid‐particle convection, particle‐particle conduction and particle radiation. The model is then validated by comparing the predicted results with those measured in the literature in terms of bed effective thermal conductivity and individual particle heat transfer characteristics. The contribution of each of the three heat transfer mechanisms is quantified and analyzed. The results confirm that under certain conditions, individual particle heat transfer coefficient (HTC) can be constant in a fluidized bed, independent of gas superficial velocities. However, the relationship between HTC and gas superficial velocity varies with flow conditions and material properties such as thermal conductivities. The effectiveness and possible limitation of the hot sphere approach recently used in the experimental studies of heat transfer in fluidized beds are discussed. The results show that the proposed model offers an effective method to elucidate the mechanisms governing the heat transfer in packed and bubbling fluidized beds at a particle scale. The need for further development in this area is also discussed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

加热功率对三角形微肋阵内流动与对流换热特性的影响

建立了三角形微肋阵对流换热性能测试系统, 以去离子水为工质对三角形微肋阵(d=247 μm, H=500 μm)的流动及对流换热特性进行了实验研究, 测试并得到了去离子水流经三角形微肋阵时压力降、阻力系数f及Nusselt数(Nu)等参数在不同Reynolds数(Re)及加热功率P下的变化规律, 分析了加热功率对于三角形微肋阵流动阻力及对流换热特性的影响机理。实验结果表明, Re为0~250范围内, 随加热功率增加三角形微肋阵阻力系数明显增大, 增加幅度最高可达200%以上;当Re>250时, 不同加热功率对阻力系数的影响显著减弱;而当Re>600时, 阻力系数几乎不再随加热功率增加而发生变化。当Re<250时, 随加热功率增加三角形微肋阵Nu逐渐增大, Nu增加幅度最高可达75%以上, 即加热功率增加可以强化对流换热;然而当Re>250时, 受三角形背风区旋涡演变的影响, Nu随加热功率增加而逐渐减小。     

The development of a mechanism for gas-particle heat transfer in shallow fluidised beds of large particles

A basic mechanism for gas-particle heat transfer in shallow fluidised beds of large particles has been developed on the basis of an experimental investigation of the fluidising behavior of such a system. The validity of the proposed mechanism was tested by comparison of experimentally measured outlet gas temperature fluctuations with those predicted by the mechanism. Whereas the predicted and measured fluctuations showed the same trends, the predicted fluctuation was usually a little higher than that measured. This is attributed to an over-simplification of the flow patterns within the bed.     

Oscillatory flow and axial dispersion in packed beds of spheres

The effect of oscillations in the bulk flow on the axial dispersion coefficient in packed beds of spherical particles has been studied using the imperfect pulse tracer method with two probes located within the bed. Three bed sizes with diameters in the range 25-47.3 mm have been used with oscillation frequencies and amplitudes in the range 0-2.4 Hz and 0-3.5 mm, respectively. In the absence of oscillations, the axial dispersion coefficient increases linearly with interstitial velocity. For a given bulk velocity and oscillation frequency, the axial dispersion coefficient-amplitude relationship shows a minimum. Over the ranges of conditions studied, the best reduction (up to 50%) in the axial dispersion coefficient from the non-oscillation base case occurred at the highest frequency studied and when the wall effect was the greatest, i.e. when the column-to-particle size was the smallest. The axial dispersion coefficient was fitted to a mathematical model, which takes into account the diameters of both the column and the packing, the fluid velocity, and the oscillation intensity (frequency and amplitude). The model was adapted from those developed by Göebel et al. (1986) and Mak et al. (1991) so as to need no a priori assumptions about the relationship between oscillation parameters and the axial dispersion coefficient. The model provides near-perfect fits to the experimental data for the higher frequencies studied.     

不同圆球复合无序堆积床内流动传热数值分析

圆球堆积床内孔隙分布影响其内部流场及温度场分布, 且小管径-球径比堆积床由于壁面限制, 内部孔隙率变化剧烈, 其内部流动和传热不均匀现象明显。针对D/d_p为3的圆球无序堆积床构建了3种非等直径圆球复合堆积结构:径向分层复合堆积、轴向分层复合堆积以及随机复合堆积结构, 并采用DEM-CFD方法建模计算, 从径向及整体角度分析比较不同复合堆积床内流动换热特性及其流场和温度场分布的均匀性。结果表明:孔隙率及孔隙大小分布共同影响堆积床内流场和温度场分布;相对于单一等直径圆球堆积, 采用复合堆积结构能使堆积床内部孔隙率分布更均匀, 其内部流场和温度场分布也更为均匀;对于D/d_p为3的堆积通道, 径向分层堆积结构对于提高整体流动换热性能及改善内部流动换热均匀性都有显著效果。