A water model study of the flow asymmetry inside a continuous slab casting mold

The work studies the extent of asymmetric flow in water models of continuous casting molds of two different configurations. In the molds where fluid is discharged through multiple holes at the bottom, the flow pattern in the lower portion depends on the size of the lower two recirculating domains. If they reach the mold bottom, the flow pattern in the lower portion is symmetrical about the central plane; otherwise, it is asymmetrical. On the other hand, in the molds where the fluid is discharged through the entire mold cross section, the flow pattern is always asymmetrical if the aspect ratio is 1:6.25 or more. The fluid jet swirls while emerging through the nozzle. The interaction of the swirling Jets with the wide sidewalls of the mold gives rise to asymmetrical flow inside the mold. In the molds with lower aspect ratios, where the jets do not touch the wide side walls, the flow pattern is symmetrical about the central plane.

Cooling of a composite slab

A mixed boundary value problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite parallel-sided composite slab, is solved completely by using the Wiener-Hopf technique. An analytical expression is derived for the sputtering temperature at the quench front being created by a cold fluid moving on the upper surface of the slab at a constant speed v. The dependence of the various configurational parameters of the problem under consideration, on the sputtering temperature, is rather complicated and representative tables of numerical values of this important physical quantity are prepared for certain typical values of these parameters. Asymptotic results in their most simplified forms are also obtained when (i) the ratio of the thicknesses of the two materials comprising the slab is very much smaller than unity, and (ii) the quench-front speed v is very large, keeping the other parameters fixed, in both the cases.

Cooling of a composite slab in a two-fluid medium

A mixed boundary value problem associated with the diffusion equation that involves the physical problem of cooling of an infinite parallel-sided composite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speedv. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming the front layer of the fluid to be of finite width and the back layer of infinite extent. The main problem is solved through a three-part Wiener-Hopf problem of a special type and the numerical results under certain special circumstances are obtained and presented in the form of a table.

Study Of Fluid-Flow And Residence-Time Distribution In A Continuous Slab Casting Mold

The fluid-flow pattern and residence-time distribution (r.t.d.) of the fluid in a continuous casting mould have been studied using a water model. The two recirculating zones below the discharge ports have been found to be asymmetric. The effect of casting speed, discharge port diameter, shroud well depth and the immersion depth on r.t.d. have been investigated. The r.t.d. curve has been well represented by a model of two backmix cells of equal volume in series. The exist of the fluid has been found to be non-uniform across the cross-section of the mould. The fluid-flow pattern has been observed to change with time in a random fashion. Dead volume of upto 31.8% has been found with smaller discharge ports.

Cooling of an infinite slab in a two-fluid medium

A mixed boundary-valued problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speed. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming one layer of the fluid to be of finite extent and the other of infinite extent. The main problem is solved through a three-part Wiener - Hopf problem of a special type, and the numerical results under certain special circumstances are obtained and presented in the form of a table.

Water-modeling study of the surface disturbances in continuous slab caster

The present work is based on four static molds using nozzles of different port diameter, port angle, and immersion depth. It has been observed that the meniscus is wavy. The wave amplitude shows a parabolic variation with the nozzle exit velocity. The dimensionless amplitude is found to vary linearly with the Froude number. Vortex formation and bubble entrainment by the wave occurs at the meniscus beyond a critical flow rate, depending upon the nozzle configuration, immersion depth, and the mold aspect ratio.

Moving boundaries due to distributed sources in a slab

Analytical and numerical solutions have been obtained for some moving boundary problems associated with Joule heating and distributed absorption of oxygen in tissues. Several questions have been examined which are concerned with the solutions of classical formulation of sharp melting front model and the classical enthalpy formulation in which solid, liquid and mushy regions are present. Thermal properties and heat sources in the solid and liquid regions have been taken as unequal. The short-time analytical solutions presented here provide useful information. An effective numerical scheme has been proposed which is accurate and simple.

Punching shear strength of flat slab corner column connections .1. Reinforced concrete connections

This paper presents the details of an experimental study on punching shear strength and behaviour of reinforced concrete corner column connections in flat slabs; a quasi-empirical method is proposed for computing the punching shear strength. The method has also been extended for punching shear strength prediction at interior and edge column connections. The test results compare better with the strengths predicted by the proposed method than those by Ingvarson, Zaglool and Pollet available in the literature. Further, the experimental strengths of interior, edge and corner column connections have been compared with the strengths predicted by the proposed method and the two codes of practice, viz. ACI and BS code, to demonstrate the usefulness of the method.

Punching shear strength of flat slab corner column connections .2. Fibre-reinforced concrete connections

This paper gives the details of the studies undertaken to examine the strength and behaviour of fibre-reinforced concrete corner column connections in flat slabs. Tests have been conducted on 16 specimens with varying reinforcement ratio, moment/shear ratio (load eccentricity) and volume fraction of fibres. A quasi-empirical method has been proposed for computing the punching shear strength. The method has also been extended to fibre-reinforced concrete interior column connections, tests on which are available in the literature. The test results have been compared with the strength predicted by the proposed method for corner column as well as interior column connections and a satisfactory agreement noticed.

Analytical approximation solutions for 3-D optical waveguides: Review

The rectangular dielectric waveguide is the most commonly used structure in integrated optics, especially in semi-conductor diode lasers. Demands for new applications such as high-speed data backplanes in integrated electronics, waveguide filters, optical multiplexers and optical switches are driving technology toward better materials and processing techniques for planar waveguide structures. The infinite slab and circular waveguides that we know are not practical for use on a substrate because the slab waveguide has no lateral confinement and the circular fiber is not compatible with the planar processing technology being used to make planar structures. The rectangular waveguide is the natural structure. In this review, we have discussed several analytical methods for analyzing the mode structure of rectangular structures, beginning with a wave analysis based on the pioneering work of Marcatili. We study three basic techniques with examples to compare their performance levels. These are the analytical approach developed by Marcatili, the perturbation techniques, which improve on the analytical solutions and the effective index method with examples.

Bismuth tungsten-oxide bronzes - a study of intergrowth phases and related aspects

Reaction of bismuth metal with WO$_3$ in the absence of oxygen yields interesting bronze-like phases. From analytical electron microscopy and X-ray photoelectron spectroscopy, the product phases are found to have the general composition Bi$_x$ WO$_3$ with bismuth in the 3+ state. Structural investigations made with high resolution electron micrscopy and cognate techniques reveal that when x < 0.02, a perovskite bronze is formed. When x $\geqslant$ 0.02, however, intergrowth tungsten bronzes (i.t.b.) containing varying widths of the WO$_3$ slab are formed, the lattice periodicity being in the range 2.3-5.1 nm in a direction perpendicular to the WO$_3$ slabs. Image-matching studies indicate that the bismuth atoms are in the tunnels of the hexagonal tungsten bronze (h.t.b.) strips and the h.t.b. strips always remain one-tunnel wide. Annealed samples show a satellite structure around the superlattice spots in the electron diffraction patterns, possibly owing to ordering of the bismuth atoms in the tunnels. The i.t.b. phases show recurrent intergrowths extending up to 100 nm in several crystals. The periodicity varies considerably within the same crystal wherever there is disordered intergrowth, but unit cell dimensions can be assigned from X-ray and electron diffraction patterns. The maximum value of x in the i.t.b. phases is ca. 0.07 and there is no evidence for the i.t.b. phase progressively giving way to the h.t.b. phase with increase in x. Hexagonal tungsten bronzes that contain bismuth with x up to 0.02 can be formed by starting from hexagonal WO$_3$, but the h.t.b. phase seems to be metastable. Optical, magnetic and electron transport properties of the i.t.b. phases have been measured and it appears that the electrons become itinerant when x > 0.05.

Effectiveness factor for zeroth-order catalytic reactions with volume change and nonuniform catalyst activity profiles

Analytical solutions are presented for the effectiveness factor of a zeroth-order reaction with volume change and nonuniform catalyst activity profile in slab, cylinder and spherical pellets. The possibility of shape normalization is considered for a variety of activity profiles and pellet shapes. When the catalyst activity at the external surface of the pellet is non-zero, shape normalization is obtained, which makes the asymptotic behavior of the effectiveness factor identical for small and large values of Thiele modulus, however, the normalization can lead to significant errors, particularly for the case of activity profiles decreasing towards the outer surface of the catalyst.