Asymptotic analysis of natural convection through horizontal porous layer

Two-dimensional cellular convection in a fluid saturated horizontal porous layer is studied using a simple asymptotic analysis. Based on the physical grounds, supported by experiments, the entire region of study is divided into no-slip regime governed by the Brinkinan equations and slip regime governed by the Darcy equations. Self-consistent solutions for velocity and temperature are obtained in a closed form using the technique of matched asymptotic expansion. The transition from the no-slip regime to the slip regime is followed exactly and the maximum value of velocity is obtained. It is shown that the point of maximum velocity gets close to the bounding walls as the permeability parameter decreases. This exhibits the boundary layer behaviour. It is: also shown that permeability has negligible effect on the temperature distribution. Close agreement between analytical and numerical results is observed.     

Comparison between solid and hollow reinforced concrete beams

Comparison between test results of seven hollow and seven solid reinforced concrete beams is presented. All of the fourteen beams were designed as hollow sections to resist combined load of bending, torsion and shear. Every pair (one hollow and one solid) was designed for the same load combinations and received similar reinforcement. The beams were 300 × 300 mm cross-section and 3,800 mm length. The internal hollow core for the hollow beams was 200 × 200 mm creating a peripheral wall thickness of 50 mm. The main variables studied were the ratio of bending to torsion which was varied between 0.19 and 2.62 and the ratio in the web of shear stress due to torsion to shear stress due to shear force which was varied between 0.59 and 6.84. It was found that the concrete core participates in the beams’ behaviour and strength and cannot be ignored when combined load of bending, shear and torsion are present. Its participation depends partly on the ratio of the torsion to bending moment and the ratio of shear stress due to torsion to the shear stress due to shear force. All solid beams cracked and failed at higher loads than their counterpart hollow beams. The smaller the ratio of torsion to bending the larger the differences in failure loads between the hollow and solid beams. The longitudinal steel yielded while the transverse steel experienced lower strain values.     

Heat and mass transfer in the binary laminary boundary layer with natural convection

We give approximate analytical solutions for the binary laminar boundary layer; these solutions are based on the Karman-Pohlhausen method and on the method of relative correspondence. The approximate solutions are compared with certain numerical solutions and with the experiment.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 6, pp. 961–971, June, 1969.     

Model and dimensional analysis of prestressed concrete hollow beam

The paper describes the model and dimensional analysis of a prestressed concrete beam. Non-dimensional quantities are formed as invariant of similarity to represent quantities having the same stresses and strains in the original and the model.

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Résumé La réponse d'une structure à une charge peut aussi être déterminée par les essais sur modèle. L'analyse dimensionnelle et les relations de similitude entre le modèle et le prototype déterminent la conception du modèle et les applications des résultats d'essai au prototype. L'analyse dimensionnelle donne les quantités non dimensionnelles entre les paramètres des variables. Les relations de similitude fournissent les facteurs d'échelle. Les quantités non dimensionnelles sont invariantes pour le modèle et pour le prototype. Afin de rendre effectifs les quantités non dimensionnelles et les facteurs d'échelle pour toutes les valeurs de chargement à la fois sur le modèle et sur le prototype, on doit satisfaire simultanément aux critères d'unité du facteur d'échelle de contrainte et du facteur d'échelle de déformation. Dans cet article on expose l'analyse dimensionnelle et l'étude sur modèle d'une poutre-caisson en béton précontraint, illustrées par un exemple. Si les quantités non dimensionnelles et les facteurs d'échelle sont déduits d'un cas particulier, la méthode peut être appliquée à d'autres cas. Comme la similitude de la contrainte de cisaillement ne pouvait pas être sauvegardée, l'effet d'échelle a été déterminé de sorte qu'on puisse introduire des corrections dans les calculs.

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Experimental study on cooling enhancement of crushed rock layer with perforated ventilation pipe under air-tight top surface

Under the warm and ice-rich nature of permafrost and the scenarios of climate warming on the Qinghai-Tibet Plateau, it will be necessary to use combinatorial techniques of cooling the ground temperature in the proposed Qinghai-Tibet Express Highway of construction. For the crushed rock highway embankment embedded a perforated ventilation pipe in permafrost regions of the Qinghai-Tibet Plateau, the mechanism of impact on the cooling capability enhanced by a perforated ventilation pipe in the air-tight crushed rock layer was studied using laboratory experiment. All boundary conditions at each edge of the crushed rock sample with dimensions of 100 × 60 × 100 cm except the inlet and outlet of the perforated pipe are air-tight. A ventilation steel pipe with an inner diameter of 8 cm was drilled with many small holes with a diameter of 1 cm and horizontally embedded in the length direction of the crushed rock sample with a depth of 53 cm. The laboratory experiments with a periodically fluctuating air temperature in the inner test tank regulated by program control were performed. The perforated pipe is only ventilated during the negative temperature fluctuation period in the inner test tank. The results show that the heat transfer processes in the crushed rock layer embedded a perforated ventilation pipe with an air-tight surface include pure heat conduction, forced convection that occurs in the crushed rock layer forming directly a pore air circulation in conjunction with the in-duct air by the small holes of perforated pipe wall absorbed from the inner test tank, and convective heat transport between the in-duct air and the inner surface of ventilation pipe wall. When air temperatures in the inner test tank are colder than the pore air temperatures in the crushed rock region around the perforated ventilation pipe, the perforated ventilation pipe can produce a significantly enhanced cooling of the crushed rock layer base due to the direct formation of a complete pore air circulation in the crushed rock layer in conjunction with the in-duct air via the small holes of the perforated pipe wall. When the fluctuating air temperature in the inner test tank rises from a minimum value to a warmer one than the pore air temperature in the crushed rock region around the perforated pipe during the negative temperature ventilating period, a warming process begins to occur in the crushed rock layer due to a warmer in-duct air absorbed from the inner test tank. This stronger warming process in the crushed rock region around the perforated pipe may decrease the cooling capability of the air-tight crushed rock layer. Thus, in order to avoid this warming process at this stage before ventilating end, the ventilating end time of ventilation pipe ought to be brought forward.     

Numerical analysis of the stability and transient behavior of natural convection loops

A general numerical model is developed for analyzing the transient thermal-hydraulic behavior of a single-phase, toroidal, natural convection loop (thermosyphon) connected to a pressurizer. The thermosyphon torus is positioned vertically, with heat sources and sinks distributed over its lower and upper sections, respectively. A set of three basic simultaneous time-dependent conservation equations for 1-dimensional flow is solved, coupled with a lateral momentum equation in one of the volume cells interacting with an external pressurizer. The unknown dependent variables are the mass velocity, enthalpy, pressure and the lateral mass velocity into/from the pressurizer. Other fluid thermodynamic and transport properties are accurately determined using tabulated steam/water table module incorporated in the model. A parametric study is performed over a wide range of operational parameters and angular displacements of the heated and cooled sections, which was impracticable in previous studies. Steady-state, transient behavior, and instability characteristics are studied and discussed. The main conclusions obtained are; (i) The prediction of dynamic instability largely depends on the assumptions related to the heat transfer coefficient and friction factor and their transient dependence on local and instantaneous thermodynamic and transport properties, (ii) In the turbulent flow regime the instability threshold qas found to be sensitive to cooling section wall temperature, (iii) Rotation of the heated/cooled sections in the vertical plane by angles of $\text{θ}{}_0\text{>20°}$ about the horizontal axis $\text{θ}{}_0\text{= 0}$, stabilizes the system's operation for all heat fluxes and wall temperatures. Good agreement is obtained between the present predictions and experimental results available in the literature.     

Batch study of liquid-phase adsorption of methylene blue using cedar sawdust and crushed brick

This paper presents a study on the batch adsorption of basic dye, methylene blue, from aqueous solution (40 mg L(-1)) onto cedar sawdust and crushed brick in order to explore their potential use as low-cost adsorbents for wastewater dye removal. Adsorption isotherms were determined at 20 degrees C and the experimental data obtained were modelled with the Langmuir, Freundlich, Elovich and Temkin isotherm equations. Adsorption kinetic data determined at a temperature of 20 degrees C were modelled using the pseudo-first and pseudo-second-order kinetic equations, liquid-film mass transfer and intra-particle diffusion models. By considering the experimental results and adsorption models applied in this study, it can be concluded that equilibrium data were represented well by a Langmuir isotherm equation with maximum adsorption capacities of 142.36 and 96.61 mg g(-1) for cedar sawdust and crushed brick, respectively. The second-order model best describes adsorption kinetic data. Analysis of adsorption kinetic results indicated that both film- and particle-diffusion are effective adsorption mechanisms. The Influence of temperature and pH of the solution on adsorption process were also studied. The extent of the dye removal decreased with increasing the solution temperature and optimum pH value for dye adsorption was observed at pH 7 for both adsorbents. The results indicate that cedar sawdust and crushed brick can be attractive options for dye removal from dilute industrial effluents.     

Partial eigenvalues problem in the analysis of hydrodynamic stability during natural convection

A numerical method is outlined by which the first few eigenvalues in the spectrum of finite-difference approximation equations can be determined for the case of small perturbations in problems concerning natural convection in a homogeneous incompressible fluid.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 4, pp. 675–682, April, 1972.     

Heat and mass transfer in a binary turbulent boundary layer with natural convection at vertical surface

An approximate solution is given for binary turbulent natural convection, with allowance for diffusive heat conduction. Analytic expressions are obtained for the boundary-layer outlet characteristics (coefficients of heat exchange and mass transfer). The solution is compared with experiments on heat and mass transfer during condensation of vapors from mixtures with various gases.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.17, No. 2, pp. 226–232, August, 1969.     

Combined heat and mass transfer in natural convection between vertical parallel plates

Abstract

This study is to examine the effects of latent heat transfer associated with liquid film vaporization on heat transfer in the natural convection flows driven by the simultaneous presence of combined buoyancy forces of thermal and mass diffusion. Results are especially presented for an air‐water system under various conditions. The influences of channel length and system temperatures on the momentum, heat and mass transfer in the flow are investigated in great detail. The important role of transport of latent heat of vaporization under the situations of buoyancy‐aiding and opposing flows is clearly demonstrated.     

Dynamic sorption of methylene blue by cedar sawdust and crushed brick in fixed bed columns

The dynamic removal of methylene blue by cedar sawdust and crushed brick was studied in packed bed columns. The values of column parameters were predicted as a function of flow rate and bed height. On evaluating the breakthrough curves, the sorption isotherms of methylene blue onto cedar sawdust and crushed brick in 20 degrees C aqueous solution were experimentally determined in batch conditions. Both the Freundlich and the Langmuir models were found to fit the sorption isotherm data well, but the Langmuir model was better. A series of column tests using cedar sawdust and crushed brick as low-cost sorbents were performed to determine the breakthrough curves with varying bed heights and flow rates. To predict the breakthrough curves and to determine the characteristic parameters of the column useful for process design, five kinetic models; Bohart and Adams, bed depth service time (BDST), Clark, Wolborska, and Yoon and Nelson models were applied to experimental data. All models were found suitable for describing the whole or a definite part of the dynamic behavior of the column with respect to flow rate and bed height, with the exception of Bohart and Adams model. The simulation of the whole breakthrough curve was effective with the Yoon and Nelson and the Clark models, but the breakthrough was best predicted by the Wolborska model.     

Finite-element analysis and optimization of the process of reconditioning hollow cylinders by thermoplastic deformation

Using the Bodner-Partom model of viscoplastic flow and the finite-element method, we develop an approach to studying the process of reconditioning hollow parts of machines by thermoplastic deformation. A part yields plastically under the action of localized mobile heat sources. The process variables are optimized considering the stress intensity and temperature restrictions. We discuss process-related recommendations to lower the time-dependent and residual stresses. Translated from Problemy Prochnosti, No. 3, pp. 73–82, May–June, 1999.     

Effect of a non-constant magnetic field on natural convection in a horizontal porous layer heated from the bottom

An analytical and numerical investigation is conducted to study the effect of an electromagnetic field on natural convection in a horizontal shallow porous cavity filled with an electrically conducting fluid. The magnetic field is assumed to be induced by two long wires, carrying current, parallel to the horizontal boundaries of the system. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. The governing parameters of the problem under study are the thermal Rayleigh number, Ra, Hartmann number, Ha, position of the electrical wires, d, current intensity ratio, r, and aspect ratio of cavity, A. An analytical solution, valid for a shallow layer (A ? 1), is derived on the basis of the parallel flow approximation. The critical Rayleigh number, Ra _c , for the onset of motion is derived in closed form in terms of the parameters of the problem. For finite-amplitude convection the heat and flow characteristics predicted by the analytical model are found to agree well with a numerical study of the full governing equations.     

Effect of the prandtl number on the convection field and the heat transfer during natural convection

The spectrum of heat convective structures is analyzed over a wide range of the Prandtl number. An empirical formula is derived for determining, at any value of the Prandtl number, the range of the Rayleigh number within which the heat transfer and the temperature field can be described by the Rayleigh number alone.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 24, No. 5, pp. 842–849, May, 1973.     

Mechanical properties of cement-treated mixtures of milled bituminous concrete and crushed aggregates

Milled bituminous concrete and crushed limestone aggregates were combined in the laboratory in various proportions to simulate some of the combinations of materials that can be obtained when the method of mix-in-place recycling with cement is used. The influence of the milled bituminous concrete content of the various mixes is examined in terms of compressive strength (equivalent cubes, uniaxial prism strength), tensile strength (flexural and cylinder splitting strength) and modulus of elasticity (quasi-static, electrodynamic resonance). The effect of these mechanical properties on the traffic and temperature induced stresses as well as on the crack susceptibility of these materials is discussed. It is concluded that the incorporation of milled bituminous concrete in cement-stabilised granular materials imparts interesting properties in these materials, yet further research is needed, including fatigue tests as well as tensile strength and modulus of elasticity determinations at early ages (1–2 days).

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Résumé On a mélangé en laboratoire du béton bitumineux et des granulats calcaires concassés, dans des proportions variées, afin de simuler quelques unes des combinaisons de matériaux qu'on peut obeenir en utilisant la méthode de recyclage sur place par malaxage avec du ciment. On a examiné l'influence de la teneur en béton bitumineux broyé des différents mélanges vis-à-vis de la résistance à la compression (cubes équivalents, résistance uniaxiale du prisme), la résistance à la traction (résistance en flexion et résistance au fendage du cyclindre) et le module élasticité (quasi statique, résonance électro-dynamique). On discute l'effet de ces propriétés mécaniques sur les contraintes génŕées par le trafic et la température, et sur la fissurabilité de ces matériaux. On conclut que l'addition de béton bitumineux broyé à des matériaux granulaires stabilisés par le ciment communique des propriétés intéressantes à ces matériaux mais que, toutefois, une recherche ultérieure doit être conduite, comprenant des essais de fatigue et la détermination de la résistance à la traction et du module d'élasticité aux jeunes ages (1–2 jours).

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Editorial note Dr. Stelios Kolias is a RILEM Senior Member. He is the RILEM Delegate in Greece.     

Numerical simulations of the void distribution characteristics of crushed rock masses in mine gobs

The internal stress levels of the crushed rock masses will change the movement states of the rock masses in the gob, and then affect the void distributions of crushed rock mass, and finally change the flow of gas in the gob. In this study, under the Lagrange framework, based on a discrete element method and a Hertz-Mindlin contact model, self-programming was used to simulate the compaction processes of a rock mass in mining gobs. The compression amounts were set as 0%, 5%, 10%, 15%, 20%, and 25%, respectively. The effects on the void distributions of the crushed rock masses of the internal stress levels of the crushed rock masses under the external load conditions were examined by changing the motion state of the rock blocks within in the gobs. The results showed that during the compression processes, the external loads could not be uniformly transmitted from the top of the crushed rock masses to the lower sections. Therefore the stress levels in the upper sections of the crashed rock masses were significantly higher than those of the lower sections. In addition, due to the rock blocks in the upper section of the crushed rock masses experiencing higher degrees of interference from the external forces, the sliding speeds of the upper rock blocks were also larger. At the same time, the rock blocks in the upper sections of the crushed rock masses tended to slide downward down longer. The migration of the rock blocks caused the upper rock blocks to become densely packed, and the coordination numbers of the rock blocks were large. However, the lower rock blocks were loosely distributed, and the coordination numbers of the rock blocks were small. This resulted in the void ratios in the lower sections of the crushed rock masses being higher than the void ratios in other layers of the crushed rock masses, with the void ratios of the lower sections of the rock masses determined to be 1.1–1.4 times that of the upper sections.     

On the influence of natural convection on mass transfer process in gallium phosphide crystal growth from solution

Mass transfer process at various (space and terrestrial) conditions of crystal growing from solution have been considered. Dimensionless criteria from the reduced mass transport equation for the boundary layer approximation have been used to estimate the conditions at which natural convection occurs and how large it effect is. The data of the on-ground and Salyut-6 orbital station experiments have helped to determine the phosphorus diffusion coefficients in the liquid gallium in the temperature range 1000–1100°C and to give possible reasons for deviation of some parameters from experimental data given by other authors. Comparison of crystal growth results on Earth and in Space was used to reveal a quantitative relationship between the growth rate and convection intensity.     

Thermal convection in a fluid layer sandwiched between two porous layers of different permeabilities

Summary A linear stability analysis is carried out for the convective instability problem in a horizontal fluid layer sandwiched between two porous layers of different permeabilities. The velocity boundary condition is a general one and is via-media between the free and rigid boundary conditions. The thermal condition at the porous-fluid interface is assumed to be neither constant heat flux nor constant temperature, but a condition leading to a third-type of boundary condition. The principle of exchange of stability is valid for the problem and the critical eigenvalue is obtained for the general boundary condition using the single-term Rayleigh-Ritz technique. The results of several works are recovered as limiting cases of the present study.