Solidification of a low peclet number fluid flow in a round pipe with the boundary condition of the third kind

This paper presents a theoretical investigation on the solidification of a low Peclet number fluid flow in the thermal entrance region of a round pipe. The velocity is assumed laminar and fully developed throughout the pipe and the fluid temperature is taken to be uniform at X = ?∞. The pipe wall is adiabatic at X ≤ 0 and is cooled convectively at X ≥ 0. The exact solution in the liquid and solid phase are obtained by using the method of separation of variables and constructing two sets of orthonormal functions from the nonorthogonal eigenfunctious at X = ± 0. The solutions including temperature distributions, liquid-solid interfaces and Nusselt numbers for the parameters, Bi = 20, 4, 0.4, 0.04, Pe = 1, 3, 5, 10, 20, 30, ∞ and the superheat ratios, ξ = (1 ? θ_f)/θ_f, θ_f= 0.1, 0.2, …, 0.9 are presented in this paper. The length of ice-free zone x_f corresponding to Pe = ∞ are in excellent agreement with the existing solution.     

Thermal analyses of poly(3-hydroxybutyrate), poly(3-hydroxybutyrate-co-3-hydroxyvalerate), and poly(3-hydroxybutyrate-co-3-hydroxyhexanoate)

Thermal analyses of poly(3-hydroxybutyrate) (PHB), poly(3-hydroxybutyrate-co-3-hydroxyvalerate) [P(HB–HV)], and poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) [P(HB–HHx)] were made with thermogravimetry and differential scanning calorimetry (DSC). In the thermal degradation of PHB, the onset of weight loss occurred at the temperature (°C) given by T_o = 0.75B + 311, where B represents the heating rate (°C/min). The temperature at which the weight-loss rate was at a maximum was T_p = 0.91B + 320, and the temperature at which degradation was completed was T_f = 1.00B + 325. In the thermal degradation of P(HB–HV) (70:30), T_o = 0.96B + 308, T_p = 0.99B + 320, and T_f = 1.09B + 325. In the thermal degradation of P(HB–HHx) (85:15), T_o = 1.11B + 305, T_p = 1.10B + 319, and T_f = 1.16B + 325. The derivative thermogravimetry curves of PHB, P(HB–HV), and P(HB–HHx) confirmed only one weight-loss step change. The incorporation of 30 mol % 3-hydroxyvalerate (HV) and 15 mol % 3-hydroxyhexanoate (HHx) components into the polyester increased the various thermal temperatures T_o, T_p, and T_f relative to those of PHB by 3–12°C (measured at B = 40°C/min). DSC measurements showed that the incorporation of HV and HHx decreased the melting temperature relative to that of PHB by 70°C. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 90–98, 2001     

Thermogravimetric analysis of poly(3‐hydroxybutyrate) and poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate)

The thermal degradation of poly(3‐hydroxybutyrate) (PHB) and poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate) [P(HB‐HV)] was studied using thermogravimetry (TG). In the thermal degradation of PHB, the temperature at the onset of weight loss (T_o) was derived by T_o = 0.97B + 259, where B represents the heating rate (°C/min). The temperature at which the weight loss rate was maximum (T_p) was T_p = 1.07B + 273, and the final temperature (T_f) at which degradation was completed was T_f = 1.10B + 280. The percentage of the weight loss at temperature T_p (C_p) was 69 ± 1% whereas the percentage of the weight loss at temperature T_f (C_f) was 96 ± 1%. In the thermal degradation of P(HB‐HV) (7:3), T_o = 0.98B + 262, T_p = 1.00B + 278, and T_f = 1.12B + 285. The values of C_p and C_f were 62 ± 7 and 93 ± 1%, respectively. The derivative thermogravimetric (DTG) curves of PHB confirmed only one weight loss step change because the polymer mainly consisted of the HB monomer only. The DTG curves of P(HB‐HV), however, suggested multiple weight loss step changes; this was probably due to the different evaporation rates of the two monomers. The incorporation of 10 and 30 mol % of the HV component into the polyester increased the various thermal temperatures (T_o, T_p, andT_f) by 7–12°C (measured at B = 20°C/min). © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 2237–2244, 2001     

Thermal properties of hexadecane encapsulated in poly(divinylbenzene) particles

The thermal properties of n‐hexadecane (HD) encapsulated in crosslinked capsule particles containing a water and/or air domain were studied from the viewpoint of heat‐storage applications. The capsule particles were prepared by the microsuspension polymerization of divinylbenzene at 70°C with the self‐assembling of phase‐separated polymer method that we developed. In the differential scanning calorimetric thermograms, pure HD had a single solidification temperature (T_s) peak at 15°C, whereas the encapsulated HD containing a water domain had two peaks at 6 and 1°C. That is, the encapsulated HD containing the water domain required a longer time and lower temperature to complete the solidification than pure HD, which was negative for heat‐storage applications. However, once the particles were dried and the water domain was replaced with air, the problem with the partially lowered T_s improved. The air domain was also found in the encapsulated HD core after solidification because of the shrinkage of HD. The presence of the air domain did not affect the thermal stability of the encapsulated HD. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

On the spectral density of a class of chaotic time series

The purpose of this paper is to show explicitly the spectral density function of the stationary stochastic process determined by a certain class of two-dimensional maps F_α defined below (α is a parameter in (0, 1)), the random variable φ(x, y) = x and the invariant probability described below. We first define the transformation T_α: [0, 1]←[0, 1] given by T _α(x) = {x/α if 0 ≤x < α and (α(x?α)/1 ?α) if α≤x≤ 1 where α∈ (0, 1) is a constant. The map T_α describes a model for a particle (or the probability of a certain kind of element in a given population) that moves around, in discrete time, in the interval [0, 1]. The results presented here can be stated either for T_α or for F_α but we prefer the latter. The results for T_α can be obtained from the more general setting described by F_α. The map F_α is defined from K = ([0, 1]× (0, α)) ∨ ([0, α]×[α, 1]) ?;R;² to itself and is given by F_α(x, y) = (T_α(x), G_α(x, y)) for (x, y) ∈K, where G _α(x, y) = {αy if 0 ≤x < α and α + ((1 ?α)/α)y if α≤x < 1. The spectral density function of the stationary process with probability ν (invariant for F_α and absolutely continuous with respect to the Lebesgue measure) Z_t = X_t + ξ_t = φ{F^t_α(X₀, Y₀)} + ξ_t for t∈Z where (X₀, Y₀) ∈R² and ξ_t}_t∈Z is a white noise process, is given explicitly (Theorem 1) by f _Z (λ) = f_X(λ) + (σ²_ξ/2π) = (1/2πvar(X_t))[γ{exp(iλ)}?C(0)] + (σ²/2π) for all λ∈[0, 2π), where var(X_t) = (α²?α + 1)(α²? 5α + 5){12(2 ?α)²}^?1, γ is given by Equation (2.10) of Proposition 5 and C(0) = (1 + α²?α³){3(2 ?α)}^?1. We also estimate the parameter α based on a time series.     

Some thermodynamic properties of tetrafluoroethene-hexafluoropropene copolymers

Copolymers of tetrafluoroethene (TFE) with hexafluoropropene (HFP) have been prepared in the 0-14mol% HFP composition range. Their melting temperatures (T_m), enthalpies (ΔH_f) and entropies (ΔS_f) of first and second fusion, and crystallinities (X) according to x-ray diffraction(x.r.d.) and differential scanning calorimetry (d.s.c.) have been determined. The results indicate that ΔH_f/X_x.r.d of the polymer crystals decreases with higher HFP content.     

Time–temperature dependent brittle fracture of viscoelastic solids

The Griffith formulation is used to study fracture behavior of poly(methyl methacrylate) (PMMA) as a function of strain rate and temperature over the range 4.4 × 10^?5 ≤ ε ≤ 4.4 × 10^?2 in./in./sec and 25°C ≤ T ≤ T_g, T_g being the glass transition temperature. It is found that the transition from brittle to ductile failure occurs abruptly at a temperature T_f which is dependent on strain rate and is approximately the same as the glass transition temperature of the material. The Griffith brittle fracture criterion is found to apply below T_f for all strain rates. The brittle fracture behavior is shown to obey the time–temperature equivalence principle in the same way as the material's other viscoelastic properties, having the same shift function.     

Effect of bismaleimide reactive extrusion on the crystallinity and mechanical performance of poly(lactic acid) green composites

Poly(D ‐,L ‐lactic acid) (PDLA) and PDLA‐wood pulp fiber injection molded composites were modified with very small amounts (< 1 wt %) of N′‐(o‐phenylene)dimalemide and 2,2′‐dithiobis(benzothiazole) by reactive extrusion and their resulting mechanical and thermal properties characterized. The modification produced an increase in the percent crystallinity (X_c), heat deflection temperature (HDT), impact energy, tensile strength, and modulus in PDLA. A significant reduction in the melting temperature (T_m) and an increase in the thermal resistance (T_max) were also found. Fourier‐Transform infrared spectroscopy (FTIR) suggests the creation of hydrogen bonds, a thiol ester and/or ester bond during the modification. Reactive extrusion of commercially available poly(lactic acid) (PLA) by means of N′‐(o‐phenylene)dimalemide and 2,2′‐dithiobis(benzothiazole) provides a low cost and simple processing method for the enhancement of the properties of this biopolymer. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Some aspects of nonisothermal crystallization of polymers. III. Crystallization during melt spinning

Crystallization during melt spinning is studied as an example of the nonisothermal crystallization of polymers. The following equation is derived, taking the temperature distribution within a filament into consideration: where T = temperature, X = crystallinity, κ = thermal diffusivity, V = velocity, ΔH = heat of crystallization, and C_p = specific heat at constant pressure. The assumptions and the procedure for a numerical calculation of crystallinity and temperature within a running filament are described, and some results of calculation are illustrated. The results are compared with those obtained by a simpler calculation in which the radial temperature distribution is neglected. The simpler method proved useful in connection with x-ray measurements.     

Ion-Induced Nucleation in Nanoparticle Synthesis by Ionization Chemical Vapor Deposition

Particle formation mechanisms in nanoparticle synthesis by ionization chemical vapor deposition (CVD), in which source gases are ionized before being fed into the reactor, were investigated experimentally. First, nonagglomerated nanoparticles were formed from a tetraethylorthosilicate (TEOS)/O ₂ mixture ionized with a sonic-jet ionizer at various furnace temperatures, T _f, and TEOS concentrations, N _TEOS. Then, the electrical mobility of the nanoparticles and ions were measured using a differential mobility analyzer combined with a Faraday cup electrometer, and the particle number concentration by a condensation nucleus counter. Measurements at 293 ≤ T _f ≤ 1173 K and 0 ≤ N _TEOS ≤ 1.38 × 10 ^?5 mol/l showed that (a) negative TEOS and TEOS cluster ions were formed at T _f = 293 K, (b) gas-phase intermediates forming nanoparticles were formed at T _f ≥ 673 K, (c) for T _f = 873 K condensation of the intermediates onto ions (i.e., ion-induced nucleation) started at N _TEOS ≥ 4.48 × 10 ^?7 mol/l, and (d) the growth from ions to nanoparticles was discontinuous for this change in N _TEOS.     

Liquid (melt) heat capacities and heats of vaporization of oligomers of poly(hexamethylene sebacate)

The liquid heat capacities and heats of vaporization of three linear esters of poly(hexamethylene sebacate) with hexylcapped end groups (M(mol. wt.) = 370, 655, and 939) have been determined. The heats of vaporization of the oligomers measured at a mean temperature were corrected to 323.15 to 523.15°K by use of the experimental liquid (melt) heat capacities and the calculated gas heat capacities. The corrected heats of vaporization were fitted to the equation ΔH_v = S(T)M^α + I(T), where the temperature dependence of the slope and intercept are represented, respectively, as S(T) = ClnT + K_o and I(T) = a T + b_o, and α is an exponent. The results indicate (at corresponding molecular weights and constant temperature) that the ratio of the liquid heat capacities of the oligomer ester and the n-alkane, and similarly the ratio of the heats of vaporization, depend on the number of carboxyl groups in the oligomer ester chain.     

Differential scanning calorimetric analysis of edible oils: Comparison of thermal properties and chemical composition

The thermal profiles of 17 edible oil samples from different plant origins were examined by differential scanning calorimetry (DSC). Two other confirmatory analytical techniques, namely gas-liquid chromatography (GLC) and high-performance liquid chromatography (HPLC), were used to determine fatty acid (FA) and triacylglycerol (TAG) compositions. The FA and TAG compositions were used to complement the DSC data. Iodine value (IV) analysis was carried out to measure the degree of unsaturation in these oil samples. The DSC melting and crystallization curves of the oil samples are reported. The contrasting DSC thermal curves provide a way of distinguishing among these oil samples. Generally, the oil samples with a high degree of saturation (IV<65) showed DSC melting and crystallization profiles at higher temperature regions than the oil samples with high degree of unsaturation (IV>65). Each thermal curve was used to determine three DSC parameters, namely, onset temperature (T _o ), offset temperature (T _f ) and temperature range (difference between T _o and T _f ). Reproducibility of DSC curves was evaluated based on these parameters. Satisfactory reproducibility was achieved for quantitation of these DSC parameters. The results show that T _o of the crystallization curve and T _f of the melting curve differed significantly (P<0.01) in all oil samples. Our observations strengthen the premise that DSC is an efficient and accurate method for characterizing edible oils.     

Chemical conversion of wood to thermoplastic material

A chemically modified wood meal (CE-wood) was prepared by cyanoethylation in the presence of alkaline salts. The temperature T_f at which the wood could flow was measured by a simple mechanical flow tester. The CE-wood demonstrated thermal flow at around 250°C. The T_f value decreased with increasing cyanoethyl content of the wood. Treatment of the wood meal before cyanoethylation with sodium periodate or sodium chlorite lowered T_f. The flow temperature was also decreased by blending the CE-wood with appropriate synthetic polymers or plasticizers. Treatment of CE-wood with chlorine solution was found to be the most effective method of lowering T_f. The T_f value of the slightly chlorinated CE-wood (Cl content=2%) was about 100°C lower than that of the original CE-wood. The lowering of T_f for CE-wood by treatment with chlorine may be interpreted in terms of the plasticizing effect of chlorination on the lignin moiety in the wood.     

Polymerization of acrylic bone cement investigated by differential scanning calorimetry: Effects of heating rate and TCP content

The polymerization reaction of a bone cement (standard Surgical Simplex-P Radiopaque) upon heating has been investigated by differential scanning calorimetry (DSC). The effects of the addition of tricalcium phosphate (TCP) on the rate and the heat of polymerization during DSC heating were evaluated. The rate and polymerization heat (ΔH) were characterized by the initial curing temperature (T_i), peak temperature (T_p), completing curing temperature (T_f), the curing range (ΔT = T_f ? T_i) and the area of the DSC exotherm. It was found that T_i, T_p, T_f, ΔT, and ΔH all increase with increasing heating rate. Increasing TCP content also induced increases in T_i, T_p, T_f, ΔT, and ΔH. From the kinetic analysis, the polymerization of acrylic bone cement was found to be a first order reaction. The effects of heating rate and TCP contents on the rate and the heat of polymerization could be explained based on the frequency factor and the activation energy extracted from the kinetic analysis. Increases in both heating rate and TCP content depressed the frequency factor and the activation energy.     

Effect of two stage, tray and heat pump assisted-dehumidified drying on drying characteristics and qualities of dried ginger

Desorption isotherms for sliced gingers have been measured. A non-linear regression programme was used to fit four moisture sorption isotherm models to the experimental data. The Modified Halsey and Modified Oswin models gave the best fit for X_e = f(RH_e, T) and RH_e = f(X_e, T), respectively. Tray and heat pump dehumidified drying incorporated by single and two stage drying were conducted. It was found that the modified Page model was the most effective. The drying constant was fitted to drying air temperature using the Arrhenius model. Effective moisture diffusivities were determined using the drying data. The heat pump dehumidified drying incorporated by the two stage drying could reduce the drying time at 40 °C by 59.32% and increase 6-gingerol content by 6%. Quality evaluation by 6-gingerol content, rehydration ratio and ΔE* showed the best quality for dried sliced gingers in the heat pump dehumidified drying incorporated by the two stage drying at 40 °C.     

The effects of curing temperature on fracture energy and cohesive parameters for the adhesive Araldite 2015

This paper attempts to investigate the effects of curing temperature on the fracture energy, the glass transition temperature (T_g) and cohesive parameters for the adhesive Araldite 2015. Relationship between curing temperature and the glass transition temperature was taken into account. Tensile tests were performed on the dogbone-shaped bulk specimens to evaluate the effect of curing temperature on the mechanical properties of the adhesive. DCB test results were used to obtain the cohesive laws of the adhesive Araldite 2015. The exponential and PPR cohesive zone models were used to obtain some of the fracture properties. Inverse analyses were also performed, if the experimental softening curves are incompatible with the numerical ones. It was seen that softening behavior of the adhesive can be easily controlled by the shape parameters available in the PPR cohesive zone model. It is seen from the DCB test results that curing the adhesive about the temperature at which the T_g∞ is obtained caused the adhesive to have more ductility, higher load-carrying capacity and higher fracture energy than curing it below or above the temperature at which T_g∞ is attained. Here, the T_g∞ is the T_g of the fully cured network. Experimental and numerical R curves were obtained to account for deviations between experiments and simulations. A good agreement between the numerical and experimental load-displacement curves was achieved showing the adequacy of the cohesive model used.     

Approximations for non-symmetric truncated sequential and repeated significance tests

Let X₁, X₂…X_N be a random sample from a N(μ, l) population. Using the B-value process {B(t); 0 ≤ t ≤ 1} introduced by Lan and Wittes (1988) one ran design a sequential test for H₀ : μ = μ₀ versus H₁ : μ > μ₀ for some functions γ1(t) > γ2(t): if B(t) > γ₁(t) stop and reject H₀ , if B(t) < γ2(t) stop and do not reject H₀ , otherwise take one more observation. When t = 1, stop anyway rejecting H₀ if B(1) > γ1(1). We suggest some approximations which are usually upper bounds for the significance level, power of the tests and lower bounds for the expected stopping time. Simulations show that the approximations get better as N → ∞ and/or μ → ∞. The exact values are difficult to obtain while the suggested approximations are very easy to compute in the case of linear and RST type boundaries and simulation results show that they are quite reasonable in several cases, even for moderate N.     

Structure/Enthalpy of Formation Relationships for Hydrocarbons Containing Benzene Rings

Simple protocols to convert molecular mechanics (MMX/PCMODEL), semiempirical PM3, and HF ab initio energies to accurate heats of formation for hydrocarbons with benzene rings are described. The data set consists of every hydrocarbon benzene derivative with an experimentally determined ΔH_f^o (g), and the ΔH_f^o (g)'s cover a range of -140 to +410 kJ/mol. The molecular structures are comprised of numerous structural types. Hierarchical sets of molecular structure parameters are defined to describe these molecules. The independent variables include atom types (level 1), group and ring terms (level 2), nonbonded atom interactions (level 3), and the calculated MMX, PM3 or ab initio HF energies, which contribute a final level 4 parameter for rectification of the ΔH_f^o (g) data. The additivity, level 1-3 parameters give an excellent correlation of the experimental ΔH_f^o (g)'s, average error = 3.4 kJ, and maximum error = 12.1 kJ. However, the correlations are further enhanced by addition of any level 4 parameter, with maximum improvement coming at the 6-31G*//STO-3G HF level of calculation.     

A BOUNDARY CROSSING PROBLEM WITH APPLICATION TO SEQUENTIAL ESTIMATION

Let X ₁, X ₂ … be independent and identically distributed random variables with density f(x) = αx ^α?1, 0 < x < 1 where α is a fixed positive number. Let N_c = inf{j ≥ m: M_j ≤ (j/c) ^β } where M_j = max(X ₁,…,X_j ) and m is a fixed positive integer. We study the properties of N_c as c → ∞. As an application, we consider the problem of estimating sequentially the range of the uniform distribution and study the second order properties of an appropriate estimate.     

Role of pretreatment with potassium permanganate and urea on mechanical and degradable properties of photocured coir (Cocos nucifera) fiber with 1,6‐hexanediol diacrylate

Coir fibers were modified with 1,6‐hexanediol diacrylate (HDDA) using ultraviolet (UV) radiation. Concentration of HDDA, soaking time, and radiation dose were optimized and found to be 30% HDDA in methanol along with photoinitiator Irgacure‐500 (2%) and 120 min of soaking time registered as the better performance (polymer loading (PL) 7%, tensile strength factor, T_f = 1.50). Urea of different concentrations (0.5–2%) were incorporated with 30% HDDA to monitor its effect on the properties and 1% urea produced the best results (PL = 25%, T_f = 1.82). For the improvement of the properties, the fibers were subjected to surface treatment with potassium permanganate (KMnO₄) of different concentrations at various treating times. Enhanced properties (PL = 86%. T_f = 4.42) of the fibers treated with KMnO₄ (0.05%) were obtained. The KMnO₄ treated fibers were again treated with HDDA (30%) solution along with urea (1%) and found to produce the best results (PL = 100%, T_f = 4.5). Water uptake and degradable properties of the treated and virgin fibers were obtained. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 4361–4368, 2006