Thermal stresses in a spherical shell with a conical nozzle

A thermal stress problem of a spherical shell with a conical nozzle is solved using a continuum approach. The thermal loading consists of a steady temperature which is uniform on the inner and outer surfaces of the shell and the conical nozzle but may vary linearly across the thickness. The thermal stress problem is converted to an equivalent boundary value problem and boundary conditions are specified at the junction of the spherical shell and conical nozzle. The stresses are obtained for a uniform increase in temperature and for a linear variation of temperature across the thickness of the shell, and are presented in graphical form for ready use.

On the uniformity of film thickness on rotating spherical substrates on a planar work holder

Curves for the uniformity in film thickness on spherical substrates are drawn for various geometries. The optimum source-to-substrate height for maximum uniformity of the film thickness is determined. These data are approximated to achieve uniform thickness on a large number of small planar substrates loaded on a large spherical substrate holder, the appropriate geometry being selected on the basis of the radius of curvature of the substrate holder.

Synthesis and characterization of spherical and rod like nanocrystalline Nd2O3 phosphors

Spherical and rod like nanocrystalline Nd2O3 phosphors have been prepared by solution combustion and hydrothermal methods respectively The Powder X-ray diffraction (PXRD) results confirm that hexagonal A-type Nd2O3 has been obtained with calcination at 900 C for 3 h and the lattice parameters have been evaluated by Rietveld refinement Surface morphology of Nd2O3 phosphors show the formation of nanorods in hydrothermal synthesis whereas spherical particles in combustion method TEM results also confirm the same Raman studies show major peaks which are assigned to F-g and combination of A(g) + E-g modes The PL spectrum shows a series of emission bands at similar to 326-373 nm (UV) 421-485 nm (blue) 529-542 nm (green) and 622 nm (red) The UV blue green and red emission in the PL spectrum indicates that Nd2O3 nanocrystals are promising for high performance materials and white light emitting diodes (LEDs) (C) 2010 Elsevier B V All rights reserved

Analytical and numerical solutions of inward spherical solidification of a superheated melt with radiative-convective heat transfer and density jump at freezing front

Analytical and numerical solutions of a general problem related to the radially symmetric inward spherical solidification of a superheated melt have been studied in this paper. In the radiation-convection type boundary conditions, the heat transfer coefficient has been taken as time dependent which could be infinite, at time,t=0. This is necessary, for the initiation of instantaneous solidification of superheated melt, over its surface. The analytical solution consists of employing suitable fictitious initial temperatures and fictitious extensions of the original region occupied by the melt. The numerical solution consists of finite difference scheme in which the grid points move with the freezing front. The numerical scheme can handle with ease the density changes in the solid and liquid states and the shrinkage or expansions of volumes due to density changes. In the numerical results, obtained for the moving boundary and temperatures, the effects of several parameters such as latent heat, Boltzmann constant, density ratios, heat transfer coefficients, etc. have been shown. The correctness of numerical results has also been checked by satisfying the integral heat balance at every timestep.

Analysis of heat and mass transfer during bulk hydraircooling of spherical food products

Hydraircooling is a technique used for precooling food products. In this technique chilled water is sprayed over the food products while cold unsaturated air is blown over them. Hydraircooling combines the advantages of both air- and hydrocooling. The present study is concerned with the analysis of bulk hydraircooling as it occurs in a package filled with several layers of spherical food products with chilled water sprayed from the top and cold unsaturated air blown from the bottom. A mathematical model is developed to describe the hydrodynamics and simultaneous heat and mass transfer occurring inside the package. The non-dimensional governing equations are solved using the finite difference numerical methods. The results are presented in the form of time-temperature charts. A correlation is obtained to calculate the process time in terms of the process parameters.

Global solutions describing the collapse of a spherical or cylindrical cavity

The collapse of a spherical (cylindrical) cavity in air is studied analytically. The global solution for the entire domain between the sound front, separating the undisturbed and the disturbed gas, and the vacuum front is constructed in the form of infinite series in time with coefficients depending on an ldquoappropriaterdquo similarity variable. At timet=0+, the exact planar solution for a uniformly moving cavity is assumed to hold. The global analytic solution of this initial boundary value problem is found until the collapse time (=(gamma–1)/2) for gamma le 1+(2/(1+v)), wherev=1 for cylindrical geometry, andv=2 for spherical geometry. For higher values of gamma, the solution series diverge at timet — 2(beta–1)/ (v(1+beta)+(1–beta)2) where beta=2/(gamma–1). A close agreement is found in the prediction of qualitative features of analytic solution and numerical results of Thomaset al. [1].

Stretch effects extracted from inwardly and outwardly propagating spherical premixed flames

Unsteady propagation of spherical flames, both inward and outward, are studied numerically extensively for single-step reaction and for different Lewis numbers of fuel/oxidizer. The dependence of flame speed ratio (s) and flame temperature ratio are obtained for a range of Lewis numbers and stretch (kappa) values. These results of s versus kappa show that the asymptotic theory by Frankel and Sivashinsky is reasonable for outward propagation. Other theories are unsatisfactory both quantitatively and qualitatively. The stretch effects are much higher for negative stretch than for positive stretch, as also seen in the theory of Frankel and Sivashinsky. The linearity of the flame speed ratio vs stretch relationship is restricted to nondimensional stretch of +/-0.1. It is shown further that the results from cylindrical flames are identical to the spherical flame on flame speed ratio versus nondimensional stretch plot thus confirming the generality of the concept of stretch. The comparison of the variation of (ds/dkappa)kappa=0 with beta(Lc - 1) show an offset between the computed and the asymptotic results of Matalon and Matkowsky. The departure of negative stretch results from this variation is significant. Several earlier experimental results are analysed and set out in the form of s versus kappa plot. Comparison of the results with experiments seem reasonable for negative stretch. The results for positive stretch are satisfactory qualitatively for a few cases. For rich propane-air, there are qualitative differences pointing to the need for full chemistry calculations in the extraction of stretch effects.

Stretch effects extracted from propagating spherical premixed flames with detailed chemistry

This paper is concerned with extracting stretch effects from outward propagating spherical flames with full chemistry. It is a continuation of a recently published study from this laboratory where it is shown that single-step chemistry is insufficient to explain the experimental results on methane, propane and hydrogen-air systems. Comparisons of the present full chemistry calculations with the experimental results for several fuel/air systems are good/excellent, with the exception of rich propane-air for which it is argued that soot chemistry with attendant radiation loss need to be invoked. The reversal in trends of stretch effects due to change in pressure, initial temperature and N-2 dilution (observed in experiments) can be predicted well by full chemistry but not with simple single-step chemistry. Analysis of the results shows the important role played by many intermediate species and explains why full chemistry is needed to predict stretch effects.

Thermal Stability of Spherical Nanoporous Aggregates and Formation of Hollow Structures by Sintering-A Phase-Field Study

Nanoporous structures are widely used for many applications and hence it Is important to investigate their thermal stability. We study the stability of spherical nanoporous aggregates using phase-field simulations that explore systematically the effect of grain boundary diffusion, surface diffusion, and grain boundary mobility on the pathways for microstructural evolution. Our simulations for different combinations of surface and GB diffusivity and GB mobility show four distinct microstructural pathways en route to 100% density: multiple dosed pores, hollow shells, hollow shells with a core, and multiple interconnected pores. The microstructures from our simulations are consistent with experimental observations in several different systems. Our results have important implications for rational synthesis of hollow nanostructures or aggregates with open pores, and for controlling the stability of nanoporous aggregates that are widely used for many applications.

Evaluation of relative growth limitation due to depletion of glucose and oxygen during fungal growth on a spherical solid particle

A mathematical model for glucose and oxygen consumption, and cell growth during fungal growth on a single solid particle is developed. A moving biofilm is assumed to be present on the surface of the solid particle. Initially only glucose is assumed to be growth limiting and later oxygen transferred from the gas phase on to the biofilm is also assumed to be growth limiting. Glucose is found to be severely growth limiting when assumed to be the only growth limiting factor and its limiting levels far less severe when oxygen limitation is also included. The objective of the model is to gain a better understanding of the mass transfer and relative growth limiting characteristics of glucose and oxygen in fungal growth systems. The results obtained from the model proposed here will be the subject of future work.

Spherical aberration and its correction using Lie algebraic methods

We discuss three methods to correct spherical aberration for a point to point imaging system. First, results obtained using Fermat's principle and the ray tracing method are described briefly. Next, we obtain solutions using Lie algebraic techniques. Even though one cannot always obtain analytical results using this method, it is often more powerful than the first method. The result obtained with this approach is compared and found to agree with the exact result of the first method.

Sub-micrometre spherical particles of TiO2, ZrO2, and PZT by nebulized spray pyrolysis of metal-organic precursors

Nebulized spray pyrolysis of metal-organic precursors in methanol solution has been employed to prepare powders of TiO2, ZrO2 and PbZr0.5Ti0.5O3 (PZT). This process ensures complete decomposition of the precursors at relatively low temperatures. The particles have been examined by scanning and transmission electron microscopy as well as X-ray diffraction. As prepared, the particles are hollow agglomerates of diameter 0.1-1.6 mu m, but after heating to higher temperatures the ultimate size of the particles comprising the agglomerates are considerably smaller (0.1 mu m or less in diameter) and crystalline.

Spherical piston problem in water

In this paper, we study the propagation of a shock wave in water, produced by the expansion of a spherical piston with a finite initial radius. The piston path in the x, t plane is a hyperbola. We have considered the following two cases: (i) the piston accelerates from a zero initial velocity and attains a finite velocity asymptotically as t tends to infinity, and (ii) the piston decelerates, starting from a finite initial velocity. Since an analytic approach to this problem is extremely difficult, we have employed the artificial viscosity method of von Neumann & Richtmyer after examining its applicability in water. For the accelerating piston case, we have studied the effect of different initial radii of the piston, different initial curvatures of the piston path in the x, t plane and the different asymptotic speeds of the piston. The decelerating case exhibits the interesting phenomenon of the formation of a cavity in water when the deceleration of the piston is sufficiently high. We have also studied the motion of the cavity boundary up to 550 cycles.

Size-dependent cohesive energy and melting of non-spherical nanoparticles

All most all theoretical models assume spherical nanoparticles. However, thermodynamic properties of non-spherical nanoparticles are the subject of recent interests. In this article, we have discussed the size-dependent cohesive energy and melting of non-spherical nanoparticles based on liquid-drop model. The surface to volume ratio is different for different shapes of nanoparticles and as a consequence, the variation of cohesive energy and melting of non-spherical nanoparticles is different from that of spherical case. By analyzing the reported experimental results, it has been observed that liquid-drop model can be used to understand the size-dependent cohesive energy and melting of non-spherical nanoparticles.

On a Novel Geometric Representation of Rotation

This paper presents a novel method of representing rotation and its application to representing the ranges of motion of coupled joints in the human body, using planar maps. The present work focuses on the viability of this representation for situations that relied on maps on a unit sphere. Maps on a unit sphere have been used in diverse applications such as Gauss map, visibility maps, axis-angle and Euler-angle representations of rotation etc. Computations on a spherical surface are difficult and computationally expensive; all the above applications suffer from problems associated with singularities at the poles. There are methods to represent the ranges of motion of such joints using two-dimensional spherical polygons. The present work proposes to use multiple planar domain “cube” instead of a single spherical domain, to achieve the above objective. The parameterization on the planar domains is easy to obtain and convert to spherical coordinates. Further, there is no localized and extreme distortion of the parameter space and it gives robustness to the computations. The representation has been compared with the spherical representation in terms of computational ease and issues related to singularities. Methods have been proposed to represent joint range of motion and coupled degrees of freedom for various joints in digital human models (such as shoulder, wrist and fingers). A novel method has been proposed to represent twist in addition to the existing swing-swivel representation.