Nonlinear static and dynamic analysis of circular plates and shallow spherical shells using the collocation method

The present work investigates the efficacy and applicability of interior global orthogonal point collocation method to the axisymmetric nonlinear analysis of elastic circular plates and shallow spherical shells subjected to uniformly distributed transverse load. Spacewise discretisation has been carried out using a polynomial expansion with the zeros of a Chebyshev polynomial as collocation points. Timewise integration has been carried out with Newmark k-β scheme corresponding to average acceleration method. The static response and snap-through buckling results, as well as, the dynamic response and dynamic buckling results under a uniformly distributed step load have been obtained and found to agree closely with the available results.     

A scale model for fitting object shapes from fixed location data

In this paper we present a scale model for fitting an ideal shape to an object. The measurements of the object are taken corresponding to a fixed coordinate system at a set of well-defined locations on the surface of the object. We propose an algorithm to estimate the model parameters and hypothesis tests to make statistical inferences about several possible special cases of the general model. The model is tested with an example that analyzes data on the feet of people in Hong Kong.     

An asymmetric line-axis compound parabolic concentrating single basin solar still

An asymmetric line-axis compound parabolic concentrating single basin solar still of concentration 1.15, exit aperture 0.24 metres and length 0.48 metres, 30° inclination and 60° half acceptance angle has been designed fabricated and tested.     

Non-darcy natural convection from a heated vertical plate in saturated porous media with mass transfer

The nonsimilar and self-similar flows for the steady natural convection over a vertical heated surface in a saturated porous medium with mass transfer using non-Darcy model have been studied under boundary layer approximations. The differential equations governing both the nonsimilar and self-similar flows have been solved numerically using an implicit finite-difference scheme developed by Keller. The results indicate that both heat transfer and velocity field are appreciably affected by the modified Grashof number and mass transfer except that the effect of the modified Grashof number on the heat transfer for large suction is very small. It is found that the maximum velocity occurs at the wall and it increases as the modified Grashof number or injection increases.     

A green route for the acylation of resorcinol with acetic acid

2',4'-Dihydroxyacetophenone, also known as resoacetophenone, is a commercially important intermediate which is generally prepared by the acylation of resorcinol with acetic acid in the presence of a molar excess of zinc chloride, which leads to waste disposal problems. The most frequently used acylating agents such as acetic anhydride and acetyl chloride have several disadvantages and need to be replaced by cheap and benign agents. In this connection, acetic acid is a better choice but with a non-polluting and reusable catalyst. The synthesis of 2',4'-dihydroxyacetophenone from resorcinol and acetic acid was carried out in the presence of a variety of solid acid catalysts such as montmorillonite clay (K-10), dodecatungstophosphoric acid (DTP) supported on K-10, sulfated zirconia and ion exchange resins. Amongst these catalysts, Amberlyst-36, an ion exchange resin, was found to be the most effective. The effects of various parameters on the rate of reaction and selectivity were investigated to establish the intrinsic kinetics of the reaction. It was possible to deduce the adsorption equilibrium constant and rate constant simultaneously for the reaction including the corresponding energies of activation. The catalyst is reusable. The process is in consonance with the principles of green chemistry. Electronic Publication     

A NEW APPROACH FOR THE CLASSIFICATION AND ENUMERATION OF UNIQUE REACTION ROUTES AND UNIQUE OVERALL REACTIONS IN MULTIPLE CHEMICAL REACTION SYSTEMS

The methodology of response reactions (RERs) introduced earlier from thermodynamic and kinetic considerations is used in this work to develop a new algorithm for the classification and enumeration of unique/direct reaction routes (RRs) and overall reactions (ORs). According to the RERs approach, a unique set of both RRs and ORs may be generated starting from any conceivable set of linearly independent RRs and ORs. In particular, the direct ORs may be most conveniently enumerated starting from the formula matrix of the terminal species (reactants and products), i.e., without any relation to the elementary reactions comprising the detailed mechanism. Depending on the type of ORs produced by the RRs one can distinguish between two distinct types of direct RRs. Namely, one option is to define a direct RR by specifying the intermediate species that need to be eliminated. This type of RR is referred to as Milner RRs. The other option is to require the direct RRs to produce RERs, thus resulting in RRs referred to as Happel-Sellers RRs.     

Effect of Calcium Lactate, 4-Hexyl Resorcinol and Vacuum Packing on Physico-chemical, Sensory and Microbiological Qualities of Minimally Processed Litchi (Litchi chinensis Sonn.)

Litchi (Litchi chinensis Sonn.) fruits are very susceptible to pericarp browning which adversely affects consumer acceptability even though the aril portion remains in excellent condition. Litchi arils (litchis) were treated with a solution containing 0–2% (w/v) calcium lactate (CL), 0–0.02% (w/v) 4‐hexyl resorcinol (4‐HR) and 1% potassium sorbate. The pH of solution was adjusted to 4.0 with citric acid. Treated litchis were packed in polystyrene trays, over‐wrapped with polypropylene film, vacuum‐packed (0, 47409.3, 94831.9 Pa) and stored at 4 ± 2 °C. Drip losses, pH, total soluble solids (TSS), sensory attributes and microbiological quality of stored samples were estimated. A four‐factor, three‐level experimental design (D₆ Hokes design) with 19 experiments was chosen. Mathematical models were developed to analyse and predict the effect of CL, 4‐HR, in‐package vacuum and storage time on the responses. TSS, pH and sensory scores decreased significantly (P 0.01), whereas drip losses and microbial count increased significantly (P 0.01) with time. Drip loss was significantly (P 0.1) reduced by addition of CL. 4‐HR prevented browning and changes in colour score during storage were significantly less. Vacuum in packages exerted significant (P 0.01) effect over pH, TSS, sensory and microbiological qualities of minimally processed litchis.     

Preparation,structural elucidation,molecular weight determination,and molecular recognition of first‐ and second‐tier dendrimer molecules

1,3,5‐Triglyceratetriazine [first tier (G₁)] and tri(1,3,5‐triglycerate) triazine [second tier (G₂)] dendrimers were prepared with 1,3,5‐trichlorotriazine and sodium glycerate in a 1 : 3 mass ratio in an ethanolic medium.G₁ and G₂ were amorphous, white, solid substances. Their structures were elucidated with IR, ¹H‐NMR, and ¹³C‐NMR, and their thermal stability was studied with thermogravimetric analysis. The activation energy was calculated with the Freeman–Carroll model. Densities, viscosities, and surface tensions for 0.01–0.08 mol/kg aqueous solutions increased at 0.01 mol/kg for sodium glycerate, 1,3,5‐trichlorotriazine, 1,3,5‐triazine triglycerate chloride, G₁, and G₂. These values were measured at 298.15 K. The apparent molal volume, reduced viscosity, and inherent viscosity were calculated from the densities and viscosities, respectively. The data were regressed for the limiting densities, limiting apparent molal volumes, intrinsic viscosities, limiting inherent viscosities, and limiting surface tensions for solute–solvent interactions. The positive limiting apparent molal volume values were noted in the order of G₂ > 1,3,5‐triazine triglycerate chloride > G₁ > 1,3,5‐trichlorotriazine > sodium glycerate, with weaker hydrophilic intermolecular interactions of G₂. The higher intrinsic viscosity and limiting inherent viscosity values for G₂ implied stronger G₂–H₂O hydrophilic interactions, and the higher limiting apparent molal volume of G₂ indicated slightly higher dynamic conformational changes in comparison with G₁, with stronger structural activities. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008