Steady flow of a maxwell fluid in a porous cylindrical annulus with circular cross-section

When a fluid with memory is injected into any flow region some assumptions regarding the initial state of stress have to be made in order to determine the state of stress at any subsequent instant. For a Maxwell fluid, it is assumed that the fluid near the surface of injection is suddenly stressed and responds by starting flow in accordance with the mechanical model chosen. The flow of a Maxwell fluid with a single relaxation time has been determined under the above assumption in the following two cases: (i) annulus between two porous concentric circular cylinders, and (ii) space between two porous and infinitely extending parallel plates. The nature of flow in the present case is similar to that of the Reiner-Rivlin fluids obtained by Narasimhan2).

Slow rotation of a sphere in a non-Newtonian fluid with or without suction or injection

The flow generated by the rotation of a sphere in an infinitely extending fluid has recently been studied by Goldshtik. The corresponding problem for non-Newtonian Reiner-Rivlin fluids has been studied by Datta. Bhatnagar and Rajeswari have studied the secondary flow between two concentric spheres rotating about an axis in the non-Newtonian fluids. This last investigation was further generalised by Rajeswari to include the effects of small radial suction or injection. In Part A of the present investigation, we have studied the secondary flow generated by the slow rotation of a single sphere in non-Newtonian fluid obeying the Rivlin-Ericksen constitutive equation. In Part B, the effects of small suction or injection have been studied which is applied in an arbitrary direction at the surface of the sphere. In the absence of suction or injection, the secondary flow for small values of the visco-elastic parameter is similar to that of Newtonian fluids with inclusion of inertia terms in the Oseen approximation. If this parameter exceeds Kc = 18R/219, whereR is the Reynolds number, the breaking of the flow field takes place into two domains, in one of which the stream lines form closed loops. For still higher values of this parameter, the complete reversal of the sense of the flow takes place. When suction or injection is included, the breaking of the flow persists under certain condition investigated in this paper. When this condition is broken, the breaking of the flow is obliterated.

Flow of a power law fluid in an annulus with porous walls

The steady flow of a power law fluid in annuli with porous walls is investigated. The solution for the axial velocity component is obtained as a power series in terms of the cross flow Reynolds number, the first term of the series giving the solution for the case of the solid wall annulus. The cross flow is restricted to be such that the rate of injection of fluid at one wall of the annulus is equal to the rate of suction at the other wall and also we have considered only very small values of the cross flow velocity. The velocity profiles are drawn for different values of n and for different gaps and the results are discussed in detail. The behaviour of the average flux, in different eases is also discussed.

Generalised vortex motion of compressible fluid with and without magnetic field and suction

The laminar boundary layer over a stationary infinite disk induced by a rotating compressible fluid is considered. The free stream velocity has been taken as tangential and varies as a power of radius, i.e. v∞ ˜ r−n. The effect of the axial magnetic field and suction is also included in the analysis. An implicit finite difference scheme is employed to the governing similarity equations for numerical computations. Solutions are studied for various values of disk to fluid temperature ratio and for values of n between 1 and −1. In the absence of the magnetic field and suction, velocity profiles exhibit oscillations. It has been observed that for a hot disk in the presence of a magnetic field the boundary layer solutions decay algebraically instead of decaying exponentially. In the absence of the magnetic field and suction, the solution of the similarity equations exists only for a certain range of n.

Power extraction studies in a gasdynamic laser

A generalized two‐dimensional flow‐radiation coupled model to extract power from a gasdynamic laser is proposed. The model is used for the study of power extraction from a 9.4‐μm CO2 downstream‐mixing gasdynamic laser, where a cold CO2+H2 stream is mixed with a vibrationally excited N2 stream at the nozzle exits. This model is developed by coupling radiation with the two‐dimensional, unsteady, laminar and viscous flow modeling needed for such systems. The analysis showed that the steady‐state value of 9.4‐μm intensity as high as 5×107 W/m2 can be obtained from the system studied. The role of H2 relaxant in the power extraction process has also been investigated.

Structural Relationships in 2,3-Bis-n-decyloxyanthracene and 12-Hydroxystearic Acid Molecular Gels and Aerogels Processed in Supercritical CO2

Supercritical carbon dioxide is used to prepare aerogels of two reference molecular organogelators, 2,3-bis-n-decyloxyanthracene (DDOA) (luminescent molecule) and 12-hydroxystearic acid (HSA). Electron microscopy reveals the fibrillar morphology of the aggregates generated by the protocol. SAXS and SANS measurements show that DDOA aerogels are crystalline materials exhibiting three morphs: (1) arrangements of the crystalline solid (2D p6m), (2) a second hexagonal morph slightly more compact, and (3) a packing specific of the fibers in the gel. Aggregates specific of the aerogel (volume fraction being typically phi approximate to 0.60) are developed over larger distances (similar to 1000 angstrom) and bear fewer defaults and residual strains than aggregates in the crystalline and gel phases. Porod, Scherrer and Debye-Bueche analyses of the scattering data have been performed. The first five diffraction peaks show small variations in position and intensity assigned to the variation of the number of fibers and their degree of vicinity within hexagonal bundles of the related SAFIN according to the Oster model. Conclusions are supported by the guidelines offered by the analysis of the situation in HSA aerogels for which the diffraction pattern can be described by two coexisting lamellar-like arrangements. The porosity of the aerogel, as measured by its specific surface extracted from the scattering invariant analysis, is only 1.8 times less than that of the swollen gel and is characteristic of a very porous material.

Channel Volatiles Of South Indian Cordierites As Indicators Of Metamorphic Fluid Composition

The channel volatiles in cordierites of the Precambrian high-grade metapelites from southern and eastern Karnataka northern Tamil Nadu and southern Kerala were analyzed in an attempt to use them as metamorphic fluid fugacity indicators. Infrared powder absorption spectra, used to characterize the channel volatiles, showed that all the 21 analyzed cordierites have H2O and CO2 as the channel volatiles, indicating the predominantly H2O-CO2 composition of the metamorphic fluids. The H2O fraction in the metamorphic fluid was computed using a published thermodynamic method in conjunction with gravimetrically determined cordierite channel H2O content, available P - T estimates and an appropriate equation of state for the H2O - CO2 fluids. The IR data and these calculated X(H2O) values indicate an overall correlation between the variation in the relative proportion of H2O and CO2 in the fluids and the metamorphic grade. The average computed X(H2O) values are: 0.78 for the amphibolite facies eastern Karnataka pelites, 0.36 for the amphibolite facies southern Karnataka pelites, 0.19 for the southern Karnataka transitional zone rocks and 0.13 for the northern Tamil Nadu granulites. Consistently low X(H2O) values, at about 0.2, were obtained for the orthopyroxene-bearing assemblages.

A note on the slow rotation of a disc in a bounded fluid with a surfactant surface layer

A method involving eigenfunction expansion and collocation is employed to solve the axisymmetric problem of a slowly and steadily rotating circular disc in a fluid of finite extent whose surface is covered with a surfactant film. The present method (originally described by Wang (Acta Mech. 94, 97, 1992)) is observed to produce results of practical importance associated with the problem more quickly and more easily than the one used earlier by Shail and Gooden (Int. J. Multiphase Flow 7, 245, 1992). (C) 1994 Academic Press, Inc.

The sputtering temperature of a cooling cylindrical rod without and with an insulated core in a two-fluid medium

Utilising Jones' method associated with the Wiener-Hopf technique, explicit solutions are obtained for the temperature distributions on the surface of a cylindrical rod without an insulated core as well as that inside a cylindrical rod with an insulated inner core when the rod, in either of the two cases, is allowed to enter, with a uniform speed, into two different layers of fluid with different cooling abilities. Simple expressions are derived for the values of the sputtering temperatures of the rod at the points of entry into the respective layers, assuming the upper layer of the fluid to be of finite depth and the lower of infinite extent. Both the problems are solved through a three-part Wiener-Hopf problem of special type and the numerical results under certain special circumstances are obtained and presented in tabular forms.

Vibration and Stability of Fluid Conveying Pipes with Stochastic Parameters

Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is-first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity

The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free stream velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the velocity profile of the primary flow and the magnetic field reduces/removes the velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall velocity strongly affects the flow field. When the wall velocity is equal to the free stream velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation. (C) 2002 Published by Elsevier Science Ltd.

Modeling the solubilities of fatty acids in supercritical carbon dioxide

A thermodynamic model was developed for modeling the solubilities of fatty acids in supercritical carbon dioxide. The model combines the Peng-Robinson equation of state (EOS) with the two parameter van der Waal's mixing rules. The model is applied to predict the solubilities of various fatty acids. The two adjustable interaction parameters in the model are found to vary linearly with the chain length of the fatty acids. Thus this model can be used to predict the solubilities of various fatty acids in supercritical carbon dioxide. (C) 2003 Elsevier Science B.V. All rights reserved.

Kinetics of Sulphation of Nickel and Cobalt Ferrites with Na$O, Melt Containing F'e3+ Ions

It has been experimentally established that nickel and cobalt can be extracted from their ferrites with sodium sulphate melt containing femc ions. The kinetics of extraction from synthetic ferrites using a melt of sodium and ferric sulphates of eutectic composition has been studied as a function of the particle size of the ferrite and temperature in the range 900 to 1073 K. The divalent ions in the ferrite exchange with the ferric ion in the melt, leaving a residue of hematite.The rate of reaction conforms to the Crank-Ginstling-Brounshtein diffusion model. The reaction rate is governed by the counter-diffusion of ~ e an~d ~+i ' +(or co2+) ions in the hematite lattice. Analytical expressions for the rate constants have been derived from the experimental data as a function of particle size and temperature. The activation energy for the extraction of nickel from nickel ferrite is 154(+10) kJ mol-' and the corresponding value for cobalt is 142(+10)kJ mol;'. In sulphation roasting of minerals containing nickel, the yield of nickel is generally limited to 75% due to the formation of insoluble ferrites. The use of melts based on sodium sulphate provides a possible route for enhancing the recovery of nickel to approximately 98%.