Thermal stresses in a finite solid cylinder due to an axisymmetric temperature field at the end surface.

A three-dimensional rigorous solution for determining thermal stresses in a finite solid cylinder due to a steady state axisymmetric temperature field over one of its end surfaces is given. Numerical results for a solid cylinder having a length to diameter ratio equal to one and subjected to a symmetric temperature variation over half the radius of the cylinder at the end surfaces are included. These results have been compared with the results of the approximate solution given by W. Nowacki.

The effect of viscosity and surface tension on the Taylor instability of the surface of a cavitation bubble*

This paper is devoted to a consideration of the following problem: A spherical mass of fluid of density varrho1, viscosity μ1 and external radius R is surrounded by a fluid of density varrho2 and viscosity μ2.The fluids are immiscible and incompressible. The interface is accelerated radially by g1: to study the effect of viscosity and surface tension on the stability of the interface. By analyzing the problem in spherical harmonics the mathematical problem is reduced to one of solution of the characteristic determinant equation. The particular case of a cavity bubble, where the viscosity μ1 of the fluid inside the bubble is negligible in comparison with the viscosity μ2 of the fluid outside the bubble, is considered in some detail. It is shown that viscosity has a stabilizing role on the interface; and when g1 > T(n − 1) (n + 2)/R2(varrho2 − varrho1) the stabilizing role of both viscosity and surface tension is more pronounced than would result when either of them is taken individually.

Use of Abel integral equations in water wave scattering by two surface-piercing barriers

In this paper the classical problem of water wave scattering by two partially immersed plane vertical barriers submerged in deep water up to the same depth is investigated. This problem has an exact but complicated solution and an approximate solution in the literature of linearised theory of water waves. Using the Havelock expansion for the water wave potential, the problem is reduced here to solving Abel integral equations having exact solutions. Utilising these solutions,two sets of expressions for the reflection and transmission coefficients are obtained in closed forms in terms of computable integrals in contrast to the results given in the literature which,involved six complicated integrals in terms of elliptic functions. The two different expressions for each coefficient produce almost the same numerical results although it has not been possible to prove their equivalence analytically. The reflection coefficient is depicted against the wave number in a number of figures which almost coincide with the figures available in the literature wherein the problem was solved approximately by employing complementary approximations. (C) 2009 Elsevier B.V. All rights reserved.

Strong shock with radiation near the surface of a star

The propagation of a shock wave, originating in a stellar interior, is considered when it approaches the surface of the star and assumes a self-similar character, "forgetting" its initial conditions. The flow behind the shock is assumed to be spatially isothermal rather than adiabatic to simulate the conditions of large radiative transfer near the stellar surface. The adiabatic and isothermal flows behind such a shock are compared. The exact shock-propagation laws, obtained by solving the equations in similarity variables, for different values of the parameter δ in the undisturbed density law, ρ0 ∝ xδ, and γ, the ratio of specific heats, are compared with the approximate values calculated by Whitham's characteristic rule and the two show a generally good agreement.

Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation TW - T∞ = Nxn. The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.

Free convection heat transfer from vertical cylinders part II: Exponential surface temperature variation

Investigation on laminar free convection heat transfer from vertical cylinders and wires having a surface temperature variation of the form TW - T∞ = M emx are presented. As in Part I for power law surface temperature variation, the axisymmetric boundary layer equations of mass, momentum and energy are transformed to more convenient forms and solved numerically. The second approximation refines the results of the first upto a maximum of only 2%. Analysis of the results indicates that cylinders can be classified into the same three categories as in Part I, namely, short cylinders, long cylinders, and wires, heat transfer and fluid flow correlations being developed for each case.

Solution-Combustion Synthesized Nanocrystalline Li4Ti5O12 As High-Rate Performance Li-Ion Battery Anode

Nanocrystalline Li4Ti5O12 (LTO) crystallizing in cubic spinel-phase has been synthesized by single-step-solution-combustion method in less than one minute. LTO particles thus synthesized are flaky and highly porous in nature with a surface area of 12 m(2)/g. Transmission electron micrographs indicate the primary particles to be agglomerated crystallites of varying size between 20 and 50 nm with a 3-dimensional interconnected porous network. During their galvanostatic charge-discharge at varying rates, LTO electrodes yield a capacity value close to the theoretical value of 175 mA h/g at C/2 rate. The electrodes also exhibit promising capacity retention with little capacity loss over 100 cycles at varying discharge rates together with attractive discharge-rate capabilities yielding capacity values of 140 mA h/g and 70 mA h/g at 10 and 100 C discharge rates, respectively. The ameliorated electrode-performance is ascribed to nano and highly porous morphology of the electrodes that provide short diffusion-paths for Li in conjunction with electrolyte percolation through the electrode pores ensuring a high flux of Li.

Vapour phase synthesis of salol over solid acids via transesterification

The transesterification of methyl salicylate with phenol has been studied in vapour phase over solid acid catalysts such as ZrO2, MoO3 and SO42- or Mo(VI) ions modified zirconia. The catalytic materials were prepared and characterized for their total surface acidity, BET surface area and powder XRD patterns. The effect of mole-ratio of the reactants, catalyst bed temperature, catalyst weight, flow-rate of reactants, WHSV and time-on-stream on the conversion (%) of phenol and selectivity (%) of salol has been investigated. A good yield (up to 70%) of salol with 90% selectivity was observed when the reactions were carried out at a catalyst bed temperature of 200 degrees C and flow-rate of 10 mL/h in presence of Mo(VI)/ZrO2 as catalyst. The results have been interpreted based on the variation of acidic properties and powder XRD phases of zirconia on incorporation of SO42- or Mo(VI) ions. The effect of poisoning of acid sites of SO42- or Mo(VI) ions modified zirconia on total surface acidity, powder XRD phases and catalytic activity was also studied. Possible reaction mechanisms for the formation of salol and diphenyl ether over acid sites are proposed.

Plastic response of orthotropic spherical shells under blast loading

The plastic response of a segment of a simply supported orthotropic spherical shell under a uniform blast loading applied on the convex surface of the shell is presented. The blast is assumed to impart a uniform velocity to the shell surface initially. The material of the shell is orthotropic obeying a modified Tresca yield hypersurface conditions and the associated flow rules. The deformation of the shell is determined during all phases of its motion by considering the motion of plastic hinges in different regimes of flow. Numerical results presented include the permanent deformed configuration of the shell and the total time of shell response for different degrees of orthotropy. Conclusions regarding the plastic behaviour of spherical shells with circumferential and meridional stiffening under uniform blast load are presented.

Influence of propellant choice on MPD arcjet cathode surface current density distribution

The radial current density on an MPD arcjet cathode surface is theoretically investigated for five propellants. It is found that excessive current concentration at the upstream end of the cathode occurs in the case of hydrogen. This undesirable effect is traced to the higher electrical conductivity of hydrogen plasma.

Stress induced phase transition in monomolecular perfluroalkylsilane film self assembled on aluminium surface

We control the stiffnesses of two dual double cantelevers placed in series to control penetration into a perflurooctyltrichlorosilane monolayer self assembled on aluminium and silicon substrates. The top cantilever which carries the probe is displaced with respect to the bottom cantilever which carries the substrate, the difference in displacement recorded using capacitors gives penetration. We further modulate the input displacement sinusoidally to deconvolute the viscoelastic properties of the monolayer. When the intervention is limited to the terminal end of the molecule there is a strong viscous response in consonance with the ability of the molecule to dissipate energy by the generation of gauche defects freely. When the intervention reaches the backbone, at a contact mean pressure of 0.2GPa the damping disappears abruptly and the molecule registers a steep rise in elastic modulus and relaxation time constant, with increasing contact pressure. We offer a physical explanation of the process and describe this change as due to a phase transition from a liquid like to a solid like state.

Surface freshwater from Bay of Bengal runoff and Indonesian Throughflow in the Tropical Indian Ocean

According to recent estimates, the annual total continental runoff into the Bay of Bengal (BoB) is about 2950 km 3, which is more than half that into the entire tropical Indian Ocean (IO). Here we use climatological observations to trace the seasonal pathways of near surface freshwater from BoB runoff and Indonesian Throughflow (ITF) by removing the net contribution from precipitation minus evaporation. North of 20 degrees S, the amount of freshwater from BoB runoff and ITF changes with season in a manner consistent with surface currents from drifters. BoB runoff reaches remote regions of the Arabian Sea; it also crosses the equator in the east to join the ITF. This freshwater subsequently flows west across the southern tropical IO in the South Equatorial Current.