Heat transfer in laminar flow of non-Newtonian fluids

The main objective of this work is the consideration of local heat transfer coefficients for non-Newtonian power-law pseudoplastic liquid in laminar flow in circular conduits. The wall boundary conditions chosen are cases involving uniformly constant heat flux and step change in heat flux.Analytical solutions are developed for the wall temperature profile and compared with experimental data. Additionally, the experimental data have been correlated for comparison with existing relationships, hitherto not verified adequately. The limits of experimental data are:

     

Wall effect in laminar flow of non-Newtonian fluid through a packed bed

Experiments were conducted on laminar flow of non-Newtonian fluid through a packed bed of low column to packing particle diameter ratio (3.8) to elucidate the wall effect on pressure drop and mass flux. Carboxy methyl cellulose (CMC) at different concentrations was passed through the packed bed and the pressure drop was measured at different CMC concentrations and flow rates. It was found that the pressure drop increases with the increase in CMC flow rate. The pressure drop also increases with the increase in CMC concentration for a given flow rate. The friction factor is plotted against Reynolds number and the data for different CMC concentration are found to be scattered around a line expressed as f=1.03/Re^0.87. The tri-regional model of Cohen and Metzner [1] predicted correctly the mass flux in the packed bed at different pressure drop values and CMC concentrations with parameters K₀ (related to pore geometry) value of 1.5 and L_e/L (related to effective path length) value of 1.2, respectively.     

Numerical nonisothermal flow analysis of non-Newtonian fluid in a nonintermeshing counter-rotating twin screw extruder

A simulation technique for nonisothermal flow analysis of non-Newtonian fluid in a nonintermeshing counter-rotating twin screw extruder was developed by modifying the flow analysis network (FAN) method. The local shear viscosity in the flow field was calculated by an iteration method combing the three types of mean shear rate functions. The modified Cross model and an Arrhenius-type function for temperature dependence were also introduced. Streamlines in the flow field are represented by computing the movements of fluid particles based on the flux fields. The computed residence time from the streamlines led us to solve the energy equation by replacing the coordinate system. The profiles of pressure, shear rate, shear viscosity, temperature, and residence time were simulated. The influence of operating and geometrical parameters on the screw characteristics are discussed. Further, residence time distribution (RTD), strain distribution function (SDF), and interfacial area growth are predicted from the computation of streamlines to analyze the mixing capabilities of the extruder.     

Isothermal and nonisothermal crystallization of polyethylene

Differential scanning calorimetry is employed to study the crystallization kinetics of two commercial injection-molding high-density polyethylene resins. Also, polarized light microscopy has been used to elucidate the morphological structures formed at various crystallization conditions. Corrections and operating procedures are recommended in order to correct for temperature lag in scanning, transient response during isothermal crystallization and for thermal gradients within the polymer sample. As a result of these studies, a modified Avrami equation has been proposed in order to obtain a more extensive and reliable characterization of isothermal crystallization kinetics. Moreover, a procedure is recommended and employed to predict nonisothermal crystallization behavior on the basis of isothermal crystallization kinetics.     

Isothermal and nonisothermal crystallization kinetics of nylon-11

Analysis of the isothermal, and nonisothermal crystallization kinetics of Nylon-11 is carried out using differential scanning calorimetry. The Avrami equation and that modified by Jeziorny can describe the primary stage of isothermal and nonisothermal crystallization of Nylon-11. In the isothermal crystallization process, the mechanism of spherulitic nucleation and growth are discussed; the lateral and folding surface free energies determined from the Lauritzen–Hoffman equation are ς = 10.68 erg/cm² and ς_e = 110.62 erg/cm²; and the work of chain folding q = 7.61 Kcal/mol. In the nonisothermal crystallization process, Ozawa analysis failed to describe the crystallization behavior of Nylon-11. Combining the Avrami and Ozawa equations, we obtain a new and convenient method to analyze the nonisothermal crystallization kinetics of Nylon-11; in the meantime, the activation energies are determined to be −394.56 and 328.37 KJ/mol in isothermal and nonisothermal crystallization process from the Arrhonius form and the Kissinger method. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 70: 2371–2380, 1998     

Analysis of the flow pattern in apparatuses with laminar flows of non-Newtonian fluids

The distribution of residence times of flow elements in tubular and film apparatuses with laminar flows of non-Newtonian fluids is analyzed. The effect of the characteristics of non-Newtonian fluids on the flow pattern is quantitatively evaluated.     

Isothermal and nonisothermal crystallization kinetics of bio-sourced nylon 69☆

Bio-sourced nylon 69,one of promising engineering plastics,has a great potential in developing sustainable technology and various commercial applications.Isothermal and nonisothermal crystallization kinetics of nylon 69 is a base to optimize the process conditions and establish the structure–property correlations for nylon 69,and it is also highly bene ficial for successful applications of nylon products in industry.Isothermal and nonisothermal crystallization kinetics has been investigated by differential scanning calorimetry for nylon 69,bio-sourced even–odd nylon.The isothermal crystallization kinetics has been analyzed by the Avrami equation,the calculated Avrami exponent at various crystallization temperatures falls into the range of 2.28 and 2.86.In addition,the Avrami equation modi fied by Jeziorny and the equation suggested by Mo have been adopted to study the nonisothermal crystallization.The activation energies for isothermal and nonisothermal crystallization have also been determined.The study demonstrates that the crystallization model of nylon 69 might be a twodimensional(circular)growth at both isothermal and nonisothermal crystallization conditions.Furthermore,the value of the crystallization rate parameter(K)decreases signi ficantly but the crystallization half-time(t1/2)increases with the increase of the isothermal crystallization temperature.To nonisothermal crystallization,the crystallization rate increases as the cooling rate increases according to the analysis of Jeziorny's theory.The results of Mo's theory suggest that a faster cooling rate is required to reach a higher relative degree of crystallinity in a unit of time,and crystallization rate decreases when the relative degree of crystallinity increases at nonisothermal crystallization conditions.     

Isothermal and nonisothermal crystallization kinetics of nylon 10 12

This article studied the crystallization behaviors of a newly industrialized polyamide, Nylon 10 12, under isothermal and nonisothermal conditions from the melt. A differential scanning calorimeter (DSC) was used to monitor the energetics of the crystallization process. During isothermal crystallization, relative crystallinity develops in accordance with the time dependence described by the Avrami equation with the exponent n=2.0. For nonisothermal studies, several different analysis methods were used to describe the crystallization process. The experimental results show that the Ozawa approach cannot adequately describe the nonisothermal crystallization kinetics. However, Avrami treatment for nonisothermal crystallization is able to describe the system very well. The calculated activation energy is 264.4 KJ/mol for isothermal crystallization by Arrhenius form and 235.5 KJ/mol for nonisothermal crystallization by Kissinger method.     

Modeling pressure losses for Newtonian and non-Newtonian laminar and turbulent flow in long square edged orifices

A lack of experimental data and predictive models prompted the determination of loss characteristics of four sharp square-edged orifices for laminar to turbulent flow regime (1 ≤ Re ≤ 100,000). Novel experimental data for β ratios of 0.36, 0.4, 0.5 and 0.7 obtained with Newtonian and non-Newtonian fluids and an empirical correlation for predicting pressure losses through long square edged orifice plates is presented. For turbulent flow, new experimental results compared well with existing predictive models, thus validating the experimental results. Comparison of existing correlations as well as the new correlation shows that, although with some shortcomings, good progress is made toward a design correlation that spans a wide range of laminar to turbulent flow conditions for long orifices.     

On non-Newtonian flow past a sphere

The approximate solutions for flow of and Ostwald-de Waele fluid past a sphere at R_e·0 = 60 and 1 ? n ? 0·8 are obtained by the use of an extended method of moments. As n decreases, (1) friction drag decreases, (2) pressure drag increases for flow past a blunt body, (3) total drag increases for flow past a sphere, (4) wake length increases for flow past a sphere, (5) separation point moves forward for flow past a sphere.     

Isothermal and nonisothermal melt‐crystallization kinetics of syndiotactic polystyrene

Analyses of the isothermal and nonisothermal melt kinetics for syndiotactic polystyrene have been performed with differential scanning calorimetry, and several kinetic analyses have been used to describe the crystallization process. The regime II→III transition, at a crystallization temperature of 239°, is found. The values of the nucleation parameter K_g for regimes II and III are estimated. The lateral‐surface free energy, σ = 3.24 erg cm^?2, the fold‐surface free energy, σ_e = 52.3 ± 4.2 erg cm^?2, and the average work of chain folding, q = 4.49 ± 0.38 kcal/mol, are determined with the (040) plane assumed to be the growth plane. The observed crystallization characteristics of syndiotactic polystyrene are compared with those of isotactic polystyrene. The activation energies of isothermal and nonisothermal melt crystallization are determined to be ΔE = ?830.7 kJ/mol and ΔE = ?315.9 kJ/mol, respectively. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 2528–2538, 2002     

Isothermal and nonisothermal crystallization kinetics of partially melting nylon 10 12

Nylon 10 12, a newly industrialized engineering plastic, shows a double‐melting phenomenon during melting. Partial melts were obtained when the sample was heated to the temperature between the two melting peaks. A differential scanning calorimeter was used to monitor the energies of the isothermal and nonisothermal crystallization from the partially melted samples. During isothermal crystallization, relative crystallinity develops with a time dependence described by the Avrami equation, with the exponent n = 1.0. For nonisothermal studies, kinetics treatments based on the Avrami and Ozawa equations are presented to describe the crystallization process. It was found that the two treatments can describe the nonisothermal crystallization from the partially melted samples. The derived Avrami and Ozawa exponents are all about 1.0, which means that the partially melted samples crystallize by one‐dimensional growth, which may cause thickening of the lamellae. We calculated the crystallization activation energies for isothermal and nonisothermal crystallization from the partially melted samples. It was found that the activation energy determined by the Kissinger method was not rational, which may be attributed to the free‐nucleation process for nonisothermal crystallization from partially melted samples. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1311–1319, 2003     

Isothermal and nonisothermal crystallization kinetics of syndiotactic polystyrene/clay nanocomposites

Differential scanning calorimeter (DSC) and X‐ray diffraction methods were used to investigate the isothermal and nonisothermal crystallization behavior and crystalline structure of syndiotactic polystyrene (sPS)/clay nanocomposites. The sPS/clay nanocomposites were prepared by mixing the sPS polymer solution with the organically modified montmorillonite. DSC isothermal results revealed that introducing 5 wt% of clay into the sPS structure causes strongly heterogeneous nucleation, inducing a change of the crystal growth process from mixed three‐dimensional and two‐dimensional crystal growth to two‐dimensional spherulitic growth. The activation energy of sPS drastically decreases with the presence of 0.5 wt% clay and then increases with increasing clay content. The result indicates that the addition of clay into sPS induces the heterogeneous nucleation (a lower ΔE) at lower clay content and then reduces the transportation ability of polymer chains during crystallization processes at higher clay content (a higher ΔE). We studied the non‐isothermal melt‐crystallization kinetics and melting behavior of sPS/clay nanocomposites at various cooling rates. The correlation among crystallization kinetics, melting behavior and crystalline structure of sPS/clay nanocomposites is discussed. Polym. Eng. Sci. 44:2288–2297, 2004. © 2004 Society of Plastics Engineers.     

Friction factor-Reynolds number relationship for laminar flow of non-Newtonian fluids in open channels of different cross-sectional shapes

The effect of channel shape on the friction factor-Reynolds number relationship for laminar, open channel flow of three non-Newtonian fluids was investigated. For each channel shape, the data can be described by a general relationship, f=K/Re where f is the Fanning friction factor and Re is the appropriate Haldenwang et al. (2002) Reynolds number corresponding to the flow curve model used to describe the non-Newtonian behaviour exhibited by the test fluid. The K values were found to be 14.6 for triangular channels with a vertex angle of 90°, 16.2 for semi-circular channels, 16.4 for rectangular channels and 17.6 for trapezoidal channels with 60° sides. These K values were found to be in line with those reported by Straub et al. (1958) and Chow (1959) for open channel flow of Newtonian fluids as opposed to the assumption made by Haldenwang et al., 2002, Haldenwang et al., 2004 of using a constant value of 16 based on the pipe flow paradigm for all channel shapes.     

Isothermal and nonisothermal crystallization kinetics of fully bio‐based polyamides

We studied the crystallization behaviors of bio‐based BDIS polyamides synthesized from the following biomass monomers: 1,4‐butanediamine (BD), 1,10‐decanediamine (DD), itaconic acid (IA), and sebacic acid (SA). Isothermal crystallization, melting behavior, and nonisothermal crystallization of BDIS polyamides were investigated by differential scanning calorimetry (DSC). The Avrami equation was used to describe the isothermal crystallization of BDIS polyamides. The modified Avrami equation, the Ozawa equation, the modified Ozawa equation, and an equation combining the Avrami and Ozawa equations were used to describe the nonisothermal crystallization. The equilibrium melting point temperature of BDIS polyamide was determined to be 163.0°C. The Avrami exponent n was found to be in the range of 2.21–2.79 for isothermal crystallization and 4.10–5.52 for nonisothermal crystallization. POLYM. ENG. SCI., 56:829–836, 2016. © 2016 Society of Plastics Engineers     

Isothermal and nonisothermal crystallization kinetics of a semicrystalline copolyterephthalamide based on poly(decamethylene terephthalamide)

The isothermal and nonisothermal crystallization kinetics of a semicrystalline copolyterephthalamide based on poly(decamethylene terephthalamide) (PA‐10T) was studied by differential scanning calorimetry. Several kinetic analyses were used to describe the crystallization process. The commonly used Avrami equation and the one modified by Jeziorny were used, respectively, to describe the primary stage of isothermal and nonisothermal crystallization. The Avrami exponent n was evaluated to be in the range of 2.36–2.67 for isothermal crystallization, and of 3.05–5.34 for nonisothermal crystallization. The Ozawa analysis failed to describe the nonisothermal crystallization behavior, whereas the Mo–Liu equation, a combination equation of Avrami and Ozawa formulas, successfully described the nonisothermal crystallization kinetics. In addition, the value of crystallization rate coefficient under nonisothermal crystallization conditions was calculated. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 819–826, 2004