Temperature development based on technological analysis: Fast rolling as an example

Summary The mean rise in temperature with plastic strain due to the work of plastic deformation, taking account of the temperature-dependence of yield stress, is investigated when conduction effects are neglected and results for one particular example are presented. An adaptation of the well-known Siebel-Karman analysis for sheet rolling is examined, and results for the particular case of rolling a medium carbon steel are given in detail. The temperature-dependent property of the yield stress in cold-rolling at moderate reductions is shown not to have a large effect on factors such as roll-torque, though the actual temperature increase generated is a significant one. Examples are given of how the temperature of the material increases in its passage through the roll gap.     

Subcritical Motions of a Fluid with Temperature-Dependent Viscosity

Convective motions of a fluid with temperature-dependent viscosity are studied using numerical experiments. The results obtained provide data for laboratory experiments aimed at determining the hardness of the instability.     

Oscillations of the plastic wave front under high‐rate loading

Two models of elastoplastic wave propagation in metals under uniaxial deformation are considered. The first model treats plastic deformation as being due to dislocation motion during heterogeneous formation of dislocations. The second model assumes that plastic deformation occurs by motion of dipoles of partial disclinations. It is shown that in both cases, certain conditions can give rise to damped oscillations of the plastic wave front, which were detected in shock loading experiments with flat specimens made of 28Kh3SNMFA steel.     

The measurement of ?U?, ?V? and ?uv? inside the turbulent spot using conditionally sampled hot-wire anemometer signals

By means of a tripping wire turbulent spots are generated in a conditionally stable laminar boundary layer along a flat plate in a low-turbulence windtunnel. At several vertical and lateral positions the streamwise (U) and vertical (V) velocity components of the spot are measured using anX-shaped hot wire anemometer. The spot's leading edge (LE) and trailing edge (TE) are determined by a high frequency detection criterion.The derived ensemble averaged shear stress uv shows a remarkable plateau over the last 3/4 of the spot length and over about 1/2 of the spot width, approximately independent of the height above the plate. The measurements suggest that the velocities of the LE and the TE can be explained by simple advection of the active turbulent region. Other mechanisms seem to be responsible for the lateral spread of the spot, as is suggested by the measurements outside the plane of symmetry.     

Thermal free convection from a solid sphere

Summary Thermal free convection from a sphere has been studied by melting solid benzene spheres in excess liquid benzene (Pr=8,3; 10⁸<Gr<10⁹). Overall heat transfer as well as local heat transfer were investigated. For the effect of cold liquid produced by the melting a correction has been applied. Results are compared with those obtained by other workers who used alternative experimental methods.Nomenclature coefficient of heat transfer - d characteristic length, here diameter of sphere - thermal conductivity - g acceleration of free fall - cubic expansion coefficient - T temperature difference between wall and fluid at infinity - kinematic viscosity - density - c specific heat capacity - a thermal diffusivity (=/c) - D diffusion coefficient - Nu dimensionless Nusselt number (=d/) - Nu* the analogous number for mass transfer (=kd/D) - mean value of Nusselt number - Gr dimensionless Grashof number (=gd ³T/ ²) - Gr* the analogous number for mass transfer (=gd ³x/ ²) - Pr dimensionless Prandtl number (=/a) - Sc dimensionless Schmidt number (=/D)     

Cloud dispersion models

A new technique has been developed to compute mean and fluctuating concentrations in complex turbulent flows. An initial distribution of material is discretised into any small clouds which are advected by a combination of the mean flow and large scale turbulence. The turbulence can be simulated either by Kinematic Simulation or by a stochastic model for the motion of each cloud centroid. The clouds also diffuse relative to their centroids; the statistics for this are obtained from a separate calculation of the growth of individual clouds in small scale turbulence, generated by Kinematic Simulation. The ensemble of discrete clouds is periodically rediscretised, to limit the size of the small clouds and prevent overlapping. The model is illustrated with simulations of dispersion in uniform flow and in a coastal flow, and the results are compared with analytic, steady state solutions where available.     

Cavitated bifurcation for composed compressible hyper-elastic materials

The cavitated bifurcation problem in a solid sphere composed of two compressible hyper-elastic materials is examined. The bifurcation solution for the composed sphere under a uniform radial tensile boundary dead-load is obtained. The bifurcation curves and the stress contributions subsequent to the cavitation are given. The right and left bifurcation as well as the catastrophe and concentration of stresses are analyzed. The stability of solutions is discussed through an energy comparison. Project supported by the National Natural Science Foundation of China (No. 19802012).     

Mixed convection of an incompressible viscous fluid in a porous medium past a hot vertical plate

This paper analyses steady two-dimensional mixed convection of an imcompressible viscous fluid in a porous medium past a hot vertical plate. Assuming Darcy-Brinkman model for the flow in a porous medium, the boundary layer equations are integrated numerically to obtain the non-similar solution for the velocity and temperature distribution for several values of the permeability and viscous dissipation parameters. It is shown that for a fixed value of Prandtl number Pr and dissipation parameter E, the skin-friction at the plate decreases with increase in the permeability parameter K₁. However for the same value or Pr and E, the heat transfer rate at the plate increases with increasing K₁. The dimensionlcss velocity and temperature functions in the flow are plotted for several values of E and K₁ with Pr = 0.73. It is also shown that for fixed values of K₁, and KPr, the skin-friction increases with increase in the dissipation parameter E.     

Entrance flow of a yield-power law fluid

In the present work we have obtained the numerical solution of the momentum equation for a Yield-Pseudoplastic power-law fluid flowing in the entrance region of a tube. The accuracy of the numerical results is checked by comparing the asymptotic values of friction coefficients and velocity profiles with the corresponding results from the analytical solutions for the fully-developed region. The results of the entrance flow solution for the power-law exponent equal to unity (Bingham fluid) are also in agreement with the numerical solution for a Bingham fluid. Detailed results are presented for wide ranges of yield numbers and power law exponents.

Nomenclature

Nomenclature a constant - D diameter - F dimensionless pressure gradient in (4.3) - f _x friction factor in (5.1) - f _app total friction factor in (5.2) - K entrance pressure drop coefficient - n power law exponent - p pressure - r radial co-ordinate - R radius of a tube - Re Reynolds number (5.3) - s rate of shear, u/r - u axial velocity - average velocity - v velocity in radius direction - x axial co-ordinate - y normal co-ordinate - Y yield number in (4.4) - z dimensionless axial distance =(x/D)/Re - z ₁ 1/z Greek Symbols plug flow radius in (4.6) - _eff effective viscosity - density - shear stress - _y yield stress - dimensionless stream function     

Bending of a uniformly loaded clamped sector plate

The paper involves the expansion of the biharmonic deflection function in a series of non-orthogonal functions satisfying the condition of clamped edges. Each of these non-orthogonal functions is expanded in a series of orthogonal functions which satisfy a certain fourth order differential equation and the boundary conditions implied by the fact that the edges are clamped. This reduces the bending of a uniformly loaded clamped sector plate to the solution of a linear algebraic system of equations. Numerical results for the deflection of the central line are obtained when the semi-sector angle is 15 degrees.