Investigations of heat transfer and pressure drop between parallel channels with pseudoplastic and dilatant fluids

Central to the problem of heat exchangers design is the prediction of pressure drop and heat transfer in the noncircular exchanger duct passages such as parallel channels. Numerical solutions for laminar fully developed flow are presented for the pressure drop (friction factor times Reynolds number) and heat transfer (Nusselt numbers) with thermal boundary conditions [constant heat flux (CHF) and constant wall temperature (CWT) ] for a pseudoplastic and dilatant non‐Newtonian fluid flowing between infinite parallel channels. A shear rate parameter could be used for the prediction of the shear rate range for a specified set of operating conditions that has Newtonian behavior at low shear rates, power law behavior at high shear rates, and a transition region in between. Numerical results of the Nusselt number [constant heat flux (CHF) and constant wall temperature (CWT) ] and the product of the friction factor and Reynolds number for the Newtonian region were compared with the literature values showing agreement within 0.36% in the Newtonian region. For pseudoplastic and dilatant non‐Newtonian fluids, the modified power law model is recommended to use because the fluid properties have big discrepancies between the power law model and the actual values in low and medium range of shear rates. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3601–3608, 2003     

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.     

Gas Holdup and Solid‐Liquid Mass Transfer in Newtonian and non‐Newtonian Fluids in Bubble Columns

Gas holdup and surface‐liquid mass transfer rate in a bubble column have been experimentally investigated. De‐mineralized water, 0.5 and 1.0% aqueous solutions of carboxy methyl cellulose (CMC), and 60% aqueous propylene glycol have been used as the test liquids. Effects of column diameter, liquid height to column diameter ratio, superficial gas velocity and liquid phase viscosity on gas holdup and mass transfer rate are studied. Generalized correlations for the average gas holdup and wall to liquid heat and mass transfer coefficients are proposed. These are valid for both Newtonian and pseudoplastic non‐Newtonian fluids.     

Shear rate dependence of thermal conductivity and its effect on heat transfer in a Non-Newtonian flow system

The purpose of this research was to investigate the extent to which the thermal conductivity of non-Newtonian fluids is affected by fluid motion, and then the effect of this shear-rate-dependent thermal conductivity, measured in Lee [1995], on the heat transfer for a typical convective system. Such information would have important implications in the design and analysis of non-Newtonian thermal systems such as are found in food processing operations, polymer processing, paint manufacturing, biological systems and many others. A simple parallel plate flow model with temperature-independent properties gave increases in heat transfer on the order of 30–80 % compared to the heat transfer with shear-rate-independent thermal conductivity in Newtonian fluid flow over the entire temperature range (20–50 °C) of CMC solutions depending on the inlet average velocity due to the effect of the shear-rate-dependent thermal conductivity.     

Coupled Mass and Heat Transfer between a Cone and a Power‐Law Fluid

Coupled mass and heat transfer between a cone and a non‐Newtonian fluid was studied when the concentration level of the solute in the solvent is finite (finite dilution of solute approximation). Convective heat and mass transfer between a laminar flow and a stationary cone and between a rotating cone and a quiescent fluid is investigated. Solutions of both problems are found in the form of the dependencies of Sherwood number vs. Reynolds and Schmidt numbers. Coupled thermal effects during dissolution and solute concentration level effect on the rate of mass transfer are investigated. It is found that the rate of mass transfer between a cone and a non‐Newtonian fluid increases with the increase of the solute concentration level. The suggested approach is valid for high Peclet and Schmidt numbers. Isothermal and nonisothermal cases of dissolution are considered whereby the latter is described by the coupled equations of mass and heat transfer. It is shown that for positive dimensionless heat of dissolution, K > 0, thermal effects cause the increase of the mass transfer rate in comparison with the isothermal case. On the contrary, for K < 0 thermal effects cause the decrease of the mass transfer rate in comparison with the isothermal case. The latter effect becomes more pronounced with the increase of the concentration level of the solute in a solvent.     

Pressure drop and mixing behaviour of non‐Newtonian fluids in a static mixing unit

Static or motionless mixers have received wide application in chemical and allied industries due to their low cost and high efficiency. The pressure drop and mixing behaviour of such mixers have been widely studied. However, the available information for non‐Newtonian fluids is scanty. The results of pressure drop and mixing studies conducted with a locally made motionless mixer (MALAVIYA mixer) and four non‐Newtonian fluids—aq. CMC, PVA, and PEG solutions are reported in this article. The new mixer causes less pressure drop compared to some of the commercial mixers. Mixing behaviour of the unit is more closer to plug flow and a two‐parameter model correlates the dispersion data.     

Viscoelastic Liquids in Stirred Vessels – Part I: Power Consumption in Unaerated Vessels

Different shear‐thinning and elastic fluids (STE fluids) have been stirred under unaerated conditions, in vessels equipped with Rushton disc turbines. Their power consumption has been evaluated over a wide range of stirring rates and their Metzner‐Otto constant (k_s) has been measured. A correlation has then been proposed to predict k_s values for a Rushton turbine operating in non‐Newtonian solutions. Power curves of STE fluids have been drawn and compared with reference curves (Newtonian, shear‐thinning inelastic and elastic with constant shear viscosity fluids). The STE fluids have thus been divided into two categories. The STE fluids of the first category (STE I fluids), which are concentrated viscous solutions of polymers (guar, CMC) reducing the power consumption at the beginning of the transitional region and connecting with the Newtonian reference at higher Reynolds numbers. In contrast, STE solutions of the second category (STE II fluids), which are solutions of drag reducing polymers (PAA), are less viscous and more elastic. They reduce the power consumption at the end of the transitional region and do not connect with the Newtonian reference, at least until Re = 6000. A general correlation has finally been proposed to model the power curve of STE fluids stirred by a Rushton turbine from the laminar to the turbulent regions, as a function of their elasticity.     

Experimental and numerical analysis of heat transfer including viscous dissipation in a scraped surface heat exchanger

Viscous dissipation plays an important role in the dynamics of fluids with strongly temperature-dependent viscosity because of the coupling between the energy and momentum equations. The heat generated by viscous friction causes a local temperature increase in the high shearing zone with a consequent decrease of the viscosity which may dramatically change the temperature and velocity distribution. These processes are mainly controlled by the Brinkman number, the rotating velocity and the thermal boundary conditions. This work analyses forced convection heat transfer including the viscous dissipation in a scraped surface heat exchanger (SSHE). In this study the increase of the temperature due to the viscous dissipation is analysed both experimentally and numerically for Newtonian and non-Newtonian fluids. Heat transfer simulations including viscous dissipation were carried out by means of the CFD code of the software Fluent, version 6.3, with solving momentum and energy equations. Two thermal boundary conditions were considered: pseudo-adiabatic wall and constant temperature on the stator wall exchange. In the case of Newtonian fluid (pure HV45), for both considered thermal boundary conditions, an important increase of the temperature was obtained. In the case of non-Newtonian shear thinning fluid (2 wt% CMC solution), viscous dissipation is neglected. The developed numerical model agrees well with experimental results. The validated numerical model was then used to study the effect of index and consistency behaviour of shear thinning fluid using power-law rheological behaviour on the viscous dissipation, and correlation using dimensionless analysis expressed with different dimensionless process numbers is proposed for Newtonian and non-Newtonian shear thinning fluid.     

Hydrodynamics in an Internal Loop Airlift Reactor with a Convergence‐Divergence Draft Tube

Gas holdup and liquid circulation of one conventional draft tube and three different convergence‐divergence draft tubes in an internal loop airlift reactor were investigated. Experiments were carried out in two‐phase systems with air‐water and air‐CMC (carboxyl methyl cellulose) solution and three‐phase system with air‐water‐resin particles. The two‐phase drift‐flux model was used to estimate gas holdup for three‐phase Newtonian and two‐phase non‐Newtonian systems. It is shown that gas holdup in convergence‐divergence draft tubes is higher than that in a conventional draft tube and increases with superficial gas velocity. Variation of the structural parameters of convergence‐divergence draft tubes has little effect on gas holdup in the two‐phase and three‐phase system. The mathematical model, which is based on a drift‐flux model, was developed to describe the liquid circulation velocity in the reactor satisfactorily.     

Heat Transfer Phenomena of Power Law Fluids in Double‐Pass Heat Exchangers with Isoflux Conditions

A new design of conjugated heat transfer in double‐pass parallel‐plate laminar countercurrent operations of power law fluids under wall isoflux was investigated experimentally and theoretically. The analytical solutions were obtained with a superposition model by introducing an eigenfunction expansion in terms of a power series for the homogeneous part and an asymptotic solution for the inhomogeneous part. The influence of the power law index on the average Nusselt numbers with the various design and operating parameters is also delineated. The theoretical predictions of the experimental results are represented graphically. The heat transfer performance was considerably improved when compared with a single‐pass parallel‐plate heat exchanger (without inserting a solid separator sheet). Suitable adjustments of the solid separator sheet position can effectively enhance the heat transfer efficiencies for such a recycling double‐pass device, as compared with the efficiencies of single‐ and double‐pass devices.     

Effect of Operating Parameters on Gas‐Solid Hydrodynamics and Heat Transfer in a Spouted Bed

Through a combined computational fluid dynamics and discrete element method approach, the effect of the operating parameters on the hydrodynamics and heat‐transfer properties of gas‐solid two‐phase flows in a spouted bed are extensively investigated. Considering the high velocity in the fountain region, gas turbulence is resolved by employing the large‐eddy simulation. The rolling friction model is adopted for more precise predictions of solid behavior near the wall. Subsequently, the gas‐solid flow patterns, gas‐solid velocities, and temperature evolution are investigated. Moreover, different operating conditions and geometry configurations are evaluated with respect to heat‐transfer performance. The results provide a fundamental understanding of heat‐transfer mechanisms in spouted beds.     

Some Characteristics of Stirred Vessel Flows of Dilute Polymer Solutions Powered by a Hyperboloid Impeller

Measurements of the power consumption and mean and turbulent velocities in the wall jet of a stirred vessel flow, powered by a hyperboloid impeller, were carried out. The fluids were aqueous solutions of tylose, CMC and xanthan gum (XG), at weight concentrations ranging from 0.1% to 0.6%, which exhibited varying degrees of shear‐thinning and viscoelasticity. The hyperboloid impeller parameter k of Metzner and Otto (1957) was found to be equal to 27.2 ±4. In the Reynolds number range of 10³ to 3 × 10⁴ the mixing power was reduced for all non‐Newtonian fluids, but never by more than 13%. The flows of the 0.2% CMC and 0.2% XG solutions were found to be less turbulent than those of water, especially for the latter fluid where a reduction in axial rms in excess of 50% was found in the wall jet. This was attributed to elasticity effects and especially to the high zero shear viscosity of the latter fluid.     

Micellization of a di‐block copolymer in ethylene glycol and its utilization for suspension of carbonaceous nanostructures

Suspensions of carbonaceous nanoparticles (NPs) in ethylene glycol (EG) can be used as colloidal inks for additive manufacturing and nano‐fluids for heat‐transfer applications. While micellar solutions of surfactants are often used for suspension of the NPs in water, micellization of surfactants in EG is suppressed as compared to aqueous solutions and a well‐defined critical micellization concentration (CMC) is often not observed. Unlike the surfactants, a di‐block copolymer comprising a poly(ethylene glycol) monomethylether methacrylate (PEGMA) segment, 2‐(diethylaminoethyl) methacrylate (DEAEMA) and butyl methacrylate (BMA), poly(O950)‐b‐(DEAEMA‐co‐BMA) was found to assemble into spherical micelles in EG. Surface tension measurements show a well‐defined CMC that depends on the volume fraction of EG. Cryogenic transmission electron microscopy and dynamic light scattering show the presence of spherical micelles with a diameter that reduces with the volume fraction of EG. The micellar solutions were further used for suspending carbonaceous NPs of different geometry and characteristic dimensions: C₆₀ fullerenes, multi‐walled carbon nanotubes, and nanodiamonds. The flow behavior of the suspensions exhibits a relatively low viscosity and mostly Newtonian behavior due to strong interaction between the NPs and the micelles. These suspensions may be used as colloidal inks for two‐dimensional and three‐dimensional printing. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46518.     

鼓泡反应器中幂律型流体流动与传质特性

很多废水处理装置涉及非牛顿型流体中的多相流动和传质问题,研究其中的气液传质过程有助于实现装置的优化设计和高效节能运行。以鼓泡反应器内清水和不同质量分数的羧甲基纤维素钠（CMC）水溶液为实验对象,分别研究气相表观气速和液相流变特性对气泡尺寸分布、全局气含率和体积氧传质系数的影响。实验结果表明,液相的流变特性对其传质特性参数均有较大影响。与清水相比,CMC水溶液中气泡平均直径和分布范围更大;清水和CMC水溶液的全局气含率均随表观气速的增加而增大;CMC水溶液的体积氧传质系数随CMC水溶液质量分数的增加而减小。基于实验研究,得出修正的体积氧传质系数公式和适用于幂律型非牛顿流体流动体系氧传递过程的无量纲关联式,可很好地实现非牛顿流体流动的废水处理装置中气液传质参数的计算。     

Heat transfer in bubble column and airlift bioreactors: Newtonian and non-Newtonian fermentation broths

A theoretical model has been developed for heat transfer in bubble column and airlift bioreactors, which is applicable for Newtonian and non-Newtonian fermentation media. The proposed model is based on a similarity between heat transfer in gas-sparged pneumatic reactors and turbulent natural convection. The applicability of the proposed model was discussed using a wide range of experimental data, and good agreement was obtained.     

Mixed convection flow of non‐Newtonian fluid from a slotted vertical surface with uniform surface heat flux

In the present paper, the combined convection flow of an Ostwald–de Waele type power‐law non‐Newtonian fluid past a vertical slotted surface has been investigated numerically. The boundary condition of uniform surface heat flux is considered. The equations governing the flow and the heat transfer are reduced to local non‐similarity form. The transformed boundary layer equations are solved numerically using implicit finite difference method. Solutions for the heat transfer rate obtained for the rigid surface compare well with those documented in the published literature. From the present analysis, it is observed that, an increase in χ leads to increase in skin friction as well as reduction in heat transfer at the surface. As the power‐law index n increases, the friction factor as well as heat transfer increase.     

Experimental Study of Heat Transfer Intensification under Vibration Condition

Experimental and theoretical models for enhancement of heat transfer from a tube with rings rotating on the external surface were investigated. The rings were rotated on acting vibration forces (hula‐hoop phenomenon). The working fluid flowing into the tube was water. The Reynolds number ranged from 800 to 2000. The amplitude range of the parameters of vibration was 0.1 mm to 1 mm, and the frequency range was 10 to 120 Hz. On the basis of a dimensionless analysis, a mathematical model for the heat‐transfer process was developed. It was shown that the mean heat transfer coefficient became higher as the velocity of vibration increased. The experimental results were in good agreement with the theoretical model.     

Conjugate thermal simulation for sheet extrusion die

The thermal effects on manifold temperature uniformity and output flow uniformity are important for polymer extrusion die design. Lin and Jaluria (Lin and Jaluria, Polym. Eng. Sci., 37, 1582 (1997)) has carried out a numerical study on conjugate heat transfer for extrusion polymer flow under the assumption that the die body surface is in uniform temperature or heat transfer coefficient. In this study, we have solved the non‐uniform body surface temperature as part of the simulation solutions based on heat flux boundary conditions (including radiation and convection heat transfer). The body temperature is computed in conjugated with the melt polymer flow with non‐linear viscous shear heating effect. The relative tough thermal conditions are set to test uniformity of the temperature distribution on the manifold wall. We also give the results of the heat transfer effect on the flow velocity distribution. POLYM. ENG. SCI., 54:682–694, 2014. © 2013 Society of Plastics Engineers     

固定床传热中的参数估值传热参数中的床高效应

本文试验测定了固定床的传热数据,计算和分析表明,床高效应反映了加热段进口热边界层对传热参数的影响,不能通过在传热 模型中引入轴向导热项或采用抛物线型进口边界条件获得补偿;轴向导热项对拟合传热参数以及模拟床层内的温度场均无意义,因此拟均相模型应该采用ＰＦ模型的形式。要想到可靠的传热参数,必须通过不同床高下的传热 数据来获得传热参数的渐近值。     

Dynamic Heat Transfer Characteristics Modeling of Microencapsulated Phase Change Material Slurries

Convective heat transfer characteristics of microencapsulated phase change material slurries (MPCSs) flowing in a circular tube under constant heat flux are studied and a feasible heat transfer model is presented. The heat transfer coefficient of MPCS and the wall temperature of the circular tube are simulated. The simulation results agree qualitatively with the experimental results. The effects of Stefan (Ste) number, mass concentration, phase change temperature range, and Reynolds (Re) number on heat transfer characteristics are discussed. The results indicate that the Ste‐number and mass fraction are the most important parameters influencing heat transfer properties compared to the phase change temperature range and Re‐number which less affect these characteristics.