Sheet bowing in thermoforming

Sheets to be thermoformed are often heated unevenly, with a higher temperature above the sheet. This results in upward bowing of the sheet, and this is caused by thermal expansion. We combine the analytical solution for the temperature gradient in a slab heated by radiation with a relationship developed from the cylindrical geometry of the sheet as it bows. We thus derive a dimensionless equation for sheet bowing as an implicit function of time for both top and dual heating. We thus uncover a new dimensionless group which we call sheet bowability. We find good agreement between our theory and our new top‐heated sheet bowing measurements. We provide a worked example so that the engineer can see how to apply our results. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers     

Sag in commercial thermoforming

Our previous analytical solution gives sag advancing implicitly as , or for , sag advances with the cube root of time for a thin wide rectangular Newtonian isothermal sheet. This previous analytical work applies to sheets that are pinned along just two edges, and not all the way around. Corresponding sagometer experimental results confirmed this cube root relation. This work compares the prediction with measured commercial thermoforming behavior on rectangular sheets that are, of course, pinned all the way around. Then sag parallel superposition is used to extend for a sheet pinned all the way around. We evaluate sag parallel superposition using a finite element method (FEM) employing ANSYS Polyflow. The equation assumes sagging sheet cylindricity, and from our FEM we find that this assumption is reliable when . We compare sag measured in commercial thermoforming, using high‐impact polystyrene (HIPS) sheets that are pinned all the way around, by extending with parallel superposition. It is found that the time evolution of the commercial sag follows nearly exactly the same shape as the isothermal prediction. We measure sag runaway, and although the isothermal analysis , predicts the sag runaway time accurately, our isothermal theory overpredicts the amount of sag in the nonisothermal commercial operation by as much as a factor of 14. It is also shown how to use sheet sag measurements from commercial thermoforming to deduce the Newtonian viscosity of a thermoforming resin at a temperature that is above its softening point. © 2013 American Institute of Chemical Engineers AIChE J, 60: 1529–1535, 2014     

Mathematical Modeling of Flux in Ultrafiltration Membrane for Water Treatment

Abstract

Calculation of water flux in a spiral ultrafiltration element was conducted by the novel proposed method, in which all necessary parameters were determined solely from membrane sheet test. By comparing water flux of the commercial element with the data from membrane sheet measurement, this study found that the tendency of water flux variation with time in the membrane element was similar to that which occurred in the membrane sheet, including the consideration of scale‐up effect due to hydrodynamics influence. Therefore, it is possible to express the variation of water flux in the membrane element based on the results from membrane sheet measurement using a practical water source. Surface water and sea water were separately employed to carry out a pilot test with an 8‐inch spiral membrane element, made of polyvinylidene fluoride(PVDF) with a molecular weight cut‐off of 150 kDa, and water fluxes under various transmembrane pressures. Calculations were approximate agreement with that of the pilot test, which enables us believe that the proposal method is reliable for designing a practical ultrafiltration system.     

Experimental study on fire properties of interior materials used in low‐floor light‐rail trains

In this work, cone calorimeter tests were conducted to investigate fire properties of interior materials (floor covering [FC], aluminum plate covered with paint [APCP], light diffuser [LD], and gel coat [GC]) used in low‐floor light‐rail trains. Ignition time (t_ig) of each material decreases with the increase of radiative heat flux. The decreasing order of the four samples by ignition time under the same radiative heat flux is LD > APCP > FC > GC. The heat release rate (HRR), peak value of HRR (PHRR), time from ignition to PHRR (t_p), fire growth rate index (FIGRA), and fire growth index (FGI) rise with the increasing radiative heat flux. For the FC, LD, and GC, single HRR peak is observed in the HRR history while three peaks are observed for APCP. For PHRR, LD > FC > APCP > GC, while for t_p, GC < FC < APCP < LD. Under most conditions, the FIGRA and FGI of the FC is the highest among the four materials. Results of this work are beneficial to evaluate fire hazard of low‐floor light‐rail train and determine the emphasis of fire prevention.     

Thermal effects on the percolation behavior of polyvinylidene fluoride/nickel composites

Percolation theory predicts the ideal percolation threshold (P_C) for insulator/conductor composites (ICC) to be at 0.16 of the conductor volume fraction in the composite. In this article, we have investigated the percolation behavior in polyvinylidene fluoride/nickel (Ni) composites by varying the Ni concentration. It is observed that the thermal effect/time of heat treatment play a crucial role in changing the value of P_C in a simple random continuum percolative ICC. The effect is attributed to decrease in: (i) intercluster distance, (ii) viscosity of the polymer, and (iii) wetting of the polymer to metal. The heat energy helps the polymer matrix to be melted as a result the metal particles/clusters come closure, that causes an increase in the cluster size of the metal particles. The overall effect is lowering of P_C mainly due to decrease in intercluster distance. A drastic enhancement in the dielectric permittivity with increase of metal content is explained using boundary layer capacitive effect arising due to Maxwell–Wagner–Sillars interfacial polarization of accumulated charges at the metal–polymer interfaces and blocking of charge carriers at the insulating boundary. The substantial enhancement of ac conductivity at the P_C is attributed to leakage of charge carriers across the insulating barrier. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Thermal strengthening of low-expansion glasses and thin-walled glass products by ultra-fast heat extraction

Thermal strengthening remains the primary method for enhancing the practical strength of commodity glass products, however, the process is limited in terms of applicable glass thickness and coefficient of thermal expansion. The primary reasons for this limitation are the achievable heat transfer coefficient when using conventional gas cooling, and the occurrence of transient surface tension in the early stages of rapid quenching. We revisit this problem for the case of thin borosilicate glass sheet. Using liquid gallium as the cooling medium, ultra-fast heat extraction is achieved, with a heat transfer coefficient exceeding 5000 Wm⁻² K⁻¹. The low vapor pressure of gallium even at high temperatures enables preheating to a wide range of sheet entrant temperatures. We demonstrate thermal strengthening of low-expansion borosilicate glass with persistent surface compression of up to 85 MPa, and quenching to a fictive temperature of ~190 K above the glass transition temperature. Glass sheet obtained in this way exhibits notably enhanced surface defect resistance to sharp indentation. In addition to thermal strengthening, the extraordinarily high heat extraction rates achieved by liquid metal immersion enable exploitation of high-T_f glass properties beyond small and thin sample geometry.     

New deviate observer (JF‐DO) obtained from experimental color‐matching functions for small fields of real observers

The CIE established the Standard Deviate Observer (SDO) CIE 1989 for fields of 10°, enabling the evaluation of discrepancies caused by the variability among these observers. This observer could also be applied to smaller fields, depending on the physiological causes of this variability in color‐matching functions (cmf's) among observers. Here, we have obtained a new Deviate Observer (which we call JF‐DO) established from the cmf's for small fields (2°) corresponding to two groups of real observers: JAM, MM and CF; AY, JR, MR, JL, JA and FA. Both groups of cmf's were measured experimentally in our laboratories using one for each of the different experimental methods and devices. All the new cmf's of the 9 real observers were referred to a new, unique system of unreal primaries, which we call X′Y′Z′ (derived in a way similar to that of the CIE 1931 XYZ system of unreal primaries). To establish a new JF‐DO for small fields, we followed a procedure similar to the one used by the CIE to establish the CIE 1989 SDO. A comparative study was also made between the cmf's of the CIE 1989 SDO (established for fields of 10°), the SDO from Stiles‐Burch (which we call Poza‐SDO, developed for small fields), and our JF‐DO. For this comparison, the cmf's of all these deviate observers were referred to the new system of unreal primaries X′Y′Z′. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 209–215, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10146     

High Heat Flux Laser Testing of HfB2 Cylinders

Hafnium diboride (HfB₂) is one of a family of ultra‐high temperature ceramics (UHTCs) which are being considered for application in environments with a substantial heat flux such as hypersonic flight. In order to characterize transitions in the material response with heat flux and therefore predict the in‐service behavior of UHTCs, a range of tests were conducted in which small cylindrical bars of HfB₂ were laser heated using heat fluxes from 25 to 100 MW/m². After testing, the external damage as well as damage observable in cross sections through the cylinders was characterized using photography, optical, and scanning electron microscopy. Experimental results were compared with finite element modeling of the heat flow, temperature distribution, and phase transition. Heat flux rather than total deposited heat was found to be the strongest determinant of the way in which damage develops in samples; for lower heat fluxes, the main damage mechanism is oxidation, progressing to oxidation‐induced melting and finally, at the highest heat fluxes, substantial ablation by melting irrespective of oxidation. The agreement between calculations and experimental observations indicates that such calculations can be used with confidence to guide the design of components.     

Thermal and chemical analysis of flammability and combustibility of fir wood in cone calorimeter coupled to FTIR apparatus

This paper deals with the thermal degradation of fir wood in a cone calorimeter under well‐ventilated atmosphere used with a piloted ignition. The thermal and chemical sample decompositions were studied with heat fluxes varying from 15 to 60 kW m^?2. With the cone calorimeter results and equations found in literature, the significant parameters of fir wood sample flammability and combustibility were deduced from ignition time (t_ig), mass loss and gas analysis. These parameters are thermal response parameter, critical heat flux, ignition surface temperature, thermal thickness, mass loss rate, thermal inertia, effective heat of combustion, heat release rate, heat of gasification and others. Moreover, during each experiment, the main gaseous species emissions were continuously and simultaneously monitored. Furthermore, the solid degradation and combustion process for fir wood were described in details. Experimental results from cone calorimeter were compared with data found in literature, and generally, a quite good accordance was found between the both sets of results. Copyright © 2013 John Wiley & Sons, Ltd.     

Influence of the recycled glass fibers from nonmetals of waste printed circuit boards on properties and reinforcing mechanism of polypropylene composites

The feasibility of reusing the recycled glass fibers (RGF) from nonmetals of waste printed circuit boards in polypropylene (PP) composites is studied by mechanical properties, vicat softening temperature and heat distortion temperature. The influence of RGF on reinforcing mechanism of the composites is watched under scanning electron microscopy (SEM) in situ tensile test. The results show that the mechanical and thermal properties of the RGF/PP composites can be significantly improved by adding the RGF into PP. In situ SEM observation results show that the RGF are the excellent supporting bodies and can effectively lead to mass microcracks. Crack initiation, propagation, and fiber breakage dissipate tremendous energy. Therefore, the mechanical properties are reinforced. All the above results indicate that the reuse of RGF in the PP composites represents a promising way for closing the recycling loop and realizing the high added value utilization. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Exploration of alternative models for the aging of fouling deposits

The effect of fouling in heat‐transfer devices (HTDs) is complicated by aging of the fouling deposits. Aging is, like deposition, often sensitive to temperature, so that heat transfer, deposition, and aging are coupled phenomena. Ishiyama et al. (AIChE J. 2010;56:531–545) presented a distributed model of the aging of deposits formed by chemical reaction fouling and illustrated its effect on thermal and hydraulic performance of a HTD operating in the turbulent flow regime. Two‐layer models, simpler than the distributed model, are explored. The deposit is considered to consist of two layers, fresh and aged; this simple picture is shown to be sufficient to interpret thermal and hydraulic aspects of deposit aging when HTDs are operated at constant heat flux (as reflecting laboratory experiments) but not in cases where the constant wall temperature approximation is more realistic. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Development of soft‐sphere contact models for thermal heat conduction in granular flows

Conductive heat transfer to flowing particles occurs when two particles (or a particle and wall) come into contact. The direct conduction between the two bodies depends on the collision dynamics, namely the size of the contact area and the duration of contact. For soft‐sphere discrete‐particle simulations, it is computationally expensive to resolve the true collision time because doing so would require a restrictively small numerical time step. To improve the computational speed, it is common to increase the “softness” of the material to artificially increase the collision time, but doing so affects the heat transfer. In this work, two physically‐based correction terms are derived to compensate for the increased contact area and time stemming from artificial particle softening. By including both correction terms, the impact that artificial softening has on the conductive heat transfer is removed, thus enabling simulations at greatly reduced computational times without sacrificing physical accuracy. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4526–4535, 2016     

MATHEMATICAL MODELLING OF INDIRECT CONTACT ROTARY DRTHRS

ABSTRACT

Two different approaches were used to predict the solid moisture content and solid temperature profiles along a continuous indirect contact rotary dryer heated with steam tubes. One of these uses heat and mass balances applied to the solid phase in a differential element of dryer length. Here the heat flux is computed through an overall heat transfer coefficient assumed constant. The other model is based on a previous work that calculates the heat transfer coefficient as a function of the time the solid particles are in contact with the heating surface. The advantage in using this second model lies in the fact that the calculated heat transfer coefficient can take into account the effects of the operational conditions. If this coefficient has a strong dependence on these conditions, then it would be inappropriate to use a fixed value. Although both approaches can predict the solid moisture content and temperature profiles along the dryer differences were detected.     

Crystallization behavior,heat resistance,and mechanical performances of PLLA/myo‐inositol blends

In this work, use of myo‐inositol as a biobased nucleating agent (NA) for PLLA was researched. Effects of myo‐inositol on non‐isothermal and isothermal crystallization behaviors of PLLA at temperatures ranged from 85 °C to 130 °C were studied by using DSC, POM and WAXD. Isothermal crystallization kinetics results showed that the incorporation of myo‐inositol enhanced significantly the crystallization rate of the PLLA samples. It was confirmed that the optimum isothermal crystallization temperature range was 100 to 110 °C. The above results were instructive to confirm proper heat treatment time and temperature for compression or injection molding to fabricate highly crystallized PLLA articles. The relations among heat treatment time, crystallinity, heat resistance, and mechanical performances of the neat PLLA and PLLA/1% myo‐inositol specimens prepared by compression molding were investigated. Compared with the PLLA specimens, the PLLA/1% myo‐inositol specimens showed a shorter heat treatment time to reach the maximum crystallinity. Vicat softening temperature, as well as tensile strength, modulus, and toughness of the PLLA/1% myo‐inositol specimens was improved when crystallinity increased from 5.4% to 38.1%. Considering the nontoxicity and biocompatibility of myo‐inositol, PLLA/myo‐inositol blends would be potential to prepare some products, which are required higher health standard and can be used in elevated temperature environments. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44732.     

Asymptotic solution of the problem of unsteady heat transfer into a stratified medium

An asymptotic expression is derived for the heat flux at the boundary of a semi-infinite region at long times under the assumption that the temperature at this boundary is a function of time. The solution is represented as a series expansion in positive powers of a fractional-order differentiation operator of this function. Thermal diffusivitya is assumed to be dependent on a single coordinatex. Two practically important cases were scrutinized, namely, when (1) the functiona(x) approaches a constant value asx is raised and (2)a(x) =a(x +l) (the function is periodic). In the latter case, the principal term of the asymptotic expansion att → ∞ has the same form as that for a medium with a constant effective thermal diffusivitya _*, which is the harmonic mean of the functiona(x) integrated over its periodl. The principal terms of the asymptotic expansions are also obtained for the case in which thermal conductivity λ, and specific heat at a constant volume,C, depend on the coordinatex.     

Comportement thermique et chimique de particules solides subissant une réaction de décomposition endothermique sous ľaction ďun flux de chaleur externe

The purpose of the present paper is an experimental and theoretical study of the behaviour of solid particles undergoing an endothermic reaction under the effect of an external heat flux. It is shown that after a pure heating period, the reaction occurs under quasi isothermal conditions as soon as the particles have reached a certain temperature T_R. T_R is normally much lower than the external heat source temperature. The variations of T_R and the effect of temperature stabilization are studied as a function of solid properties, chemical reaction (kinetic and thermodynamic), and heat transfer conditions. Data obtained from measurements of the decarbonation reaction of NaHCO₃ agree well with predictions of the theoretical study.     

Graft polymerization of acrylonitrile onto paper and characterization of the grafted product

The chemical graft copolymerization reaction of acrylonitrile (AN) onto paper sheet was performed. The effect of initiator concentration, monomer concentration, and temperature on the reaction rate was studied. The reaction rate equation of the graft copolymerization reaction is found to be R_P = K₂ [initiator]^0.54[monomer]^1.13. The apparent activation energy (E_a) of the copolymerization reaction is found to be 35.99 KJ/mol. The infrared characteristic absorption bands for cellulosic paper structure and the paper gr‐AN are studied. Tensile break load, porosity, and burst strength were measured for the grafted and pure paper sheet. It was found that the mechanical properties are improved by grafting. The chemical resistance of the graft product against strong acid (HCl), strong alkali (NaOH), polar and nonpolar solvents was investigated. It was found that the resistance to these chemicals is enhanced by grafting. From the TGA and DTA data, it is clear that the grafted paper sheet is more thermally stable than pure paper sheet. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Experimental study on ignition and combustion characteristics of typical oils

The impact of radiant heat flux on ignition and combustion behavior of typical oils (diesel, lubricating oil, and aviation kerosene) was conducted in a cone calorimeter. A circular steel pan with a diameter of 10 cm was used to contain diesel, lubricating oil, and aviation kerosene without water sublayer. Using the standard oxygen consumption method, we obtained ignition time, heat release rate, mass loss rate, extinction coefficient, CO, and CO₂ yield, and average specific extinction area was calculated from the extinction coefficient. Janssens' method was adopted in this study to deal with ignition time and radiant heat flux under a 0.55 power rule. Results show that the fitting through Janssens' method is good for ignition time of diesel, lubricating oil, and aviation kerosene and radiant heat flux. Moreover, heat release rate, mass loss rate, and CO/CO₂ ratio appear to positively correlate with radiant heat flux, whereas average specific extinction area varies in a certain range. Copyright © 2013 John Wiley & Sons, Ltd.     

Heat-release measurement in “gasless” combustion of a titanium-carbon mixture in a nonhermetic shell

A calorimetric device and a technique for heat-effect measurement using aBKS-1 high-speed combustion calorimeter have been developed to study the heat release of fuel mixtures confined in the shell of a heat-releasing element. An equiatomic mixture of titanium and carbon powders was taken as a model. The mean value of heat release has been obtained for this system(3.0±0.1 MJ/kg).Translated from Fizika Goreniya i Vzryva, Vol. 32, No. 1, pp. 48–52, January–February, 1996.     

A numerical approach to the heat transfer in monolithic and SiC reinforced HfB2, ZrB2 and TiB2 ceramic cutting tools

Cutting tools are widely used in industry and must be hard enough for machining processes, which should work appropriately at low temperatures to improve cutting speed and productivity. In this research, a numerical method was employed to calculate the temperature distribution in the cutting tools made of different diborides. Monolithic and SiC reinforced HfB₂, ZrB₂ and TiB₂ ceramics were selected for investigation and comparison studies. In this regard, 3-dimensional heat conduction equation was solved in a cutting tool with radiative, convective and heat flux boundary conditions by finite element method using COMSOL Multiphysics. This study clarifies that the maximum temperature in the tools made of ZrB₂ and TiB₂ among the monolithic ceramics is lower than that of HfB₂. Moreover, the temperature variation slope versus time is the highest in HfB₂. All composite materials reinforced with SiC showed lower maximum temperature than the monolithic ones. The thermal performance of TiB₂–SiC and ZrB₂–SiC composites was acquired to be better than that of the other investigated materials. The dominant heat transfer mechanism in the cutting tools was conduction.