An analogy between vortical and thermal fields subject to the large pressure gradient

Local thermal disturbances generated by a small confined mechanical forcing on the curved surface are under consideration within the framework of the interacting boundary layer in the limit of large Reynolds number. The variations of the self-induced pressure and temperature are found to be explicitly related, and an analytic solution of a linear perturbation analysis is presented. The heat flux associated with the self-induced pressure may attain values comparable with the heat flux existing in the oncoming boundary layer. The analogy between the normal-to-wall vorticity and spanwise derivative of temperature is rigorously derived to supersede locally the well-known analogy by Reynolds. Heavily increased thermal loads can cause severe damage to the engine in operation.     

Helical flows of a heated generalized Oldroyd-B fluid subject to a time-dependent shear stress in porous medium

This paper presents an analysis for helical flows of a heated generalized Oldroyd-B fluid subject to a time-dependent shear stress in porous medium, where the motion is due to the longitudinal time-dependent shear stress and the oscillating velocity in boundary. The exact solutions are established by using the sequential fractional derivatives Laplace transform coupled with finite Hankel transforms in terms of generalized G function. Moreover, the effects of various parameters (relaxation time, fractional parameter, permeability and porosity) on the flow and heat transfer are analyzed in detail by graphical illustrations.     

The temperature field in a heat-sensitive space with a cubic cavity subject to heat flux

We obtain the solution of the stationary heat-conduction problem for a space with a cubic cavity under the assumption that the coefficient of thermal conductivity depends on the temperature. The surfaces of the cavity are subject to heat flux. By using the Kirchhoff variable and the method of continuation of functions we reduce the problem to a linear differential equation with singular coefficients on the right-hand side. We conduct a numerical study of the temperature distribution as a function of the spatial coordinate and the Kirpichev criterion that characterizes the thermal flux density. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 94–100.     

Temperature distribution in a laminar plane wall jet due to variably heated wall

The heat transfer in a laminar incompressible plane wall jet due to a variably heated wall has been studied. It is assumed that the difference of temperatures between the wall and the issuing jet is inversely proportional to an arbitrary exponent of the distance from the slit. A similar solution of the energy equation is possible. The solutions, for arbitrary values of the Prandtl number and of the exponent are obtained. It is found that in some cases the heat transfer at the wall may become zero or negative.     

The relationship between stress and deformation of polymers in the linear stress state

The relation between stress, strain and strain rate is proposed as a means of describing the deformation properties of polymers. The equation describes the stress-strain curve, aftereffect, and stress relaxation in polymers. The theoretical conclusions are in good agreement with the results of creep tests on kapron (nylon-6).Mekhanika Polimerov, Vol. 1, No. 5, pp. 25–29, 1965     

Exact solutions for the flow of a viscoelastic fluid induced by a circular cylinder subject to a time dependent shear stress

The velocity field and the adequate shear stress corresponding to the flow of a Maxwell fluid with fractional derivative model, between two infinite coaxial cylinders, are determined by means of the Laplace and finite Hankel transforms. The motion is due to the inner cylinder that applies a longitudinal time dependent shear to the fluid. The solutions that have been obtained, presented under integral and series form in terms of the generalized G and R functions, satisfy all imposed initial and boundary conditions. They can be easy particularizes to give the similar solutions for ordinary Maxwell and Newtonian fluids. Finally, the influence of the relaxation time and the fractional parameter, as well as a comparison between models, is shown by graphical illustrations.     

A note on the unsteady flow of a generalized second-grade fluid through a circular cylinder subject to a time dependent shear stress

The unsteady flow of a generalized second-grade fluid through an infinite straight circular cylinder is considered. The flow of the fluid is due to the longitudinal time dependent shear stress that is prescribed on the boundary of the cylinder. The fractional calculus approach in the governing equation corresponding to a second-grade fluid is introduced. The velocity field and the resulting shear stress are obtained by means of the finite Hankel and Laplace transforms. In order to avoid lengthy calculations of residues and contour integrals, the discrete inverse Laplace transform method is used. The corresponding solutions for ordinary second-grade and Newtonian fluids, performing the same motion, are obtained as limiting cases of our general solutions. Finally, the influence of the material constants and of the fractional parameter on the velocity and shear stress variations is underlined by graphical illustrations.     

The nonsimilar laminar wall jet along a moving wall,in a free stream and in a free stream/moving wall

The flow of a laminar wall jet along either a moving plate, or in a free stream, or in combined moving plate and free stream is considered. The plate is isothermal and its temperature is different from that of the ambient fluid. The governing boundary-layer equations are converted into non-dimensional form and are solved numerically. Velocity and temperature profiles as well as the variation of wall shear stress and wall heat transfer are presented for all cases considered. For the case of a moving plate new results have been found although this problem has been investigated in the past. For the case of the free stream and the combined moving plate/free stream all the results are new and are presented for the first time in the literature. The three cases have been tackled with a unified way.     

On the separation of a slow linear shear flow from a cylindrical ridge or trough in a plane

A slow linear shear flow past a plane with a cylindrical ridge or trough is considered. It is shown that an infinite set of vortices exist in a finite region in the neighbourhood of the line of intersection between a cylindrical ridge and a plane if the angle of intersection is less than about 146.3°, the extent of the eddy region increasing as the angle of intersection decreases. For ridges with larger angles of intersection, separation of the flow from the boundary does not occur. However, with a depression or trough in the plane, separation of the flow from the wall of the trough occurs if the angle of intersection between the trough and the plane is more than about 65.15°. For angles greater than this value, there is a closed addy region consisting of one vortex. In the limit when the trough becomes a half-space, the flow is anti-symmetrical about the plane of the boundary.

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Zusammenfassung Es wird eine langsame Scherströmung über eine ebene Fläche mit einem zylindrischen Grat oder eine Vertiefung betrachtet. Es wird gezeigt, dass wenn der Schnittwinkel kleiner ist als etwa 146.3°, dann in einem begrenzten Gebiet nahe der Schnittlinie zwischen dem Zylinder und der Fläche eine unendliche Menge von Wirbeln existiert, wobei das Ausmass des Wirbelgebietes grösser wird, wenn sich der Schnittwinkel verkleinert. Für Gräte mit grösseren Schnittwinkeln entsteht keine Ablösung des Stroms von der Grenzlinie. Wenn jedoch die Fläche eine Senkung oder Vertiefung aufweist, dann ergibt sich eine Ablösung des Stroms von der Vertiefungswand, wenn der spitze Winkel der Schnittlinie zwischen Vertiefung und Fläche mehr als etwa 65.15° beträgt. Für Winkel die diesen Wert überschreiten, ergibt sich ein geschlossenes Wirbelgebiet, das nur aus einem Wirbel besteht. Im Grenzfall, wo die Vertiefung ein Halbraum wird, fliesst der Strom antisymmetrisch über die Grenzfläche.

     

Analysis of melting behavior of PCMs in a cavity subject to a non-uniform magnetic field using a moving grid technique

Melting flow and heat transfer of electrically conductive phase change materials subjecting to a non-uniform magnetic field are addressed in a square enclosure. The top and bottom walls of the cavity are adiabatic, and the sidewalls are isothermal at different temperatures. The temperature of the hot wall is higher than the fusion temperature of PCM (T_f), and the cold wall is at the fusion temperature or lower. At the initial time, the cavity is filled with a solid saturated PCM. In the vicinity to the hot wall, there is an external line-source magnet, inducing a magnetic field. The location of the magnetic source (Y₀) can be changed along the hot wall. The cavity domain is divided into two parts of the liquid domain and the solid domain. The moving grid method is utilized to track the phase change interface at the exact fusion temperature of T_f. The governing equations for continuity, flow and heat transfer associated with the Arbitrary Lagrangian–Eulerian (ALE) moving mesh technique are solved using the finite element method. The results are investigated for the melting behavior of PCM by the study of Hartmann number (0 ≤ Ha ≤ 50) and the location of the magnetic source (0 ≤ Y₀ ≤ 1). Outcomes show that the effect of the magnetic field on the melting behavior of PCM is negligible at the initial stages of the melting (Fo < 1.15). However, after the initial stages of the melting, the effect of the presence of a magnetic field becomes significant. Moreover, the location of the magnetic source induces a feeble effect on the melting front at the initial melting stages, but its effect on the shape of the melting front increases by the increase of the non-dimensional time. The location of the magnetic source also significantly affects the streamlines patterns. Changing the position of the magnetic source from the bottom of the cavity (Y₀ = 0.2) to the almost middle of the cavity (Y₀ = 0.6) would decrease the required non-dimensional time of full melting from Fo = 10.4 to Fo = 9.0.     

An analysis of turbulent film condensation on a sphere with variable wall temperature under the effect of local shear stress

This paper presents an investigation into turbulent film condensation on a sphere with variable wall temperature. Under the wide range of vapor velocity, the wall temperature and the local film shear stress were considered. The result shows that under the high velocity vapor, the increase of the temperature amplitude will bring out a larger Nusselt number, and the increase is about 2.7–5.6%. Besides, under the effect of the local film shear stress, the mean Nusselt number will decrease about 0.65–0.8%. Furthermore, the paper then discusses the influence of shears and temperature amplitudes on the local dimensionless film thickness and heat transfer characteristics. Finally, the results developed in the current study are compared with those generated by previous theoretical results.     

The wall jet flow of a conducting gas over a permeable surface in the presence of a variable transverse magnetic field

The effects of the magnetic field, Mach number and the permeability parameter on the wall jet flow (radial or plane) of an electrically conducting gas spreading over a permeable surface have been investigated. Taking the Prandtl number of the fluid as unity and assuming a linear relationship between viscosity and temperature, it is found that similar solutions for the velocity distribution exist for a specified distribution of the normal velocity along the wall and the corresponding distribution of the transverse magnetic field. Previous non-magnetic flow results have been improved by adopting a new and simple transformation of variables.     

The diffusion of a discontinuity of the shear stress at the boundary of a viscoplastic half-plane

For the problem of the diffusion of a discontinuity of the shear stress at the boundary of a half-plane, which is a special case of the general problem of the diffusion of a vortex layer, the classes of media and types of assignment of boundary conditions for which self-similar solutions exist are discussed. For a viscoplastic medium in a half-plane the problem reduces to the problem in a layer of time-variable thickness, the solution of which does not possess the property of analyticity. The long-term asymptotic of this problem are investigated. In the case where, at an accessible boundary, it is possible simultaneously to measure both the shear stress and the horizontal velocity, an algorithm is proposed for finding a quantity that is difficult to measure, A namely, the thickness of the zone of viscoplastic flow.     

Numerical simulation and visualization of vortical structure transformation in the flow past a sphere at an increasing degree of stratification

Based on numerical simulation and visualization, the vortex structure of the flow past a sphere moving uniformly and horizontally in a linearly (density) stratified viscous fluid with an increasing degree of stratification (with the internal Froude number Fr decreasing from infinity to 0.005) at Re = 100 is analyzed in detail for the first time. The classification of the flow regimes is refined. The direct numerical simulation is based on the method of splitting with respect to physical factors (MERANZH) with an explicit hybrid finite-difference scheme, which is second-order accurate in space, monotone, and has a minimal numerical viscosity and dispersion.     

Variational formulation of a modified couple stress theory and its application to a simple shear problem

A variational formulation is provided for the modified couple stress theory of Yang et al. by using the principle of minimum total potential energy. This leads to the simultaneous determination of the equilibrium equations and the boundary conditions, thereby complementing the original work of Yang et al. where the boundary conditions were not derived. Also, the displacement form of the modified couple stress theory, which is desired for solving many problems, is obtained to supplement the existing stress-based formulation. All equations/expressions are presented in tensorial forms that are coordinate-invariant. As a direct application of the newly obtained displacement form of the theory, a simple shear problem is analytically solved. The solution contains a material length scale parameter and can capture the boundary layer effect, which differs from that based on classical elasticity. The numerical results reveal that the length scale parameter (related to material microstructures) can have a significant effect on material responses.      

Variational formulation of a modified couple stress theory and its application to a simple shear problem

A variational formulation is provided for the modified couple stress theory of Yang et al. by using the principle of minimum total potential energy. This leads to the simultaneous determination of the equilibrium equations and the boundary conditions, thereby complementing the original work of Yang et al. where the boundary conditions were not derived. Also, the displacement form of the modified couple stress theory, which is desired for solving many problems, is obtained to supplement the existing stress-based formulation. All equations/expressions are presented in tensorial forms that are coordinate-invariant. As a direct application of the newly obtained displacement form of the theory, a simple shear problem is analytically solved. The solution contains a material length scale parameter and can capture the boundary layer effect, which differs from that based on classical elasticity. The numerical results reveal that the length scale parameter (related to material microstructures) can have a significant effect on material responses.     

The drag force on the grains in a permeable medium subjected to a water jet

Summary A theory for destruction of rock with a high speed water jet is derived on the basis of viscous flow through porous media. The theory yields that a grain in the rock exposed to a water jet is subjected to a hydraulic force proportional to the water pressure gradient in the rock and to the volume of the grain. If a semi-space of a presaturated rock is hit by a water jet of sufficient pressure the theory predicts the initial stage of the crater to be an annular crater the radius of which is twice the radius of the jet. In the case of a dry rock the theory predicts that the typical ring structure of the initial stage of the crater should not occur. The conclusion is that in destruction of rock with a high-pressure water jet the permeability is a very important parameter in contrast to the case of mechanical destruction.

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Zusammenfassung Eine Theorie über Gesteinsdestruktion mit Hochdruckwasserstrahl gründet sich auf die Theorie viskoser Strömung durch poröse Medien. Die Theorie besagt dass eine Partikel im Gestein durch einwirken eines Wasserstrahls einer hydraulischen Kraft ausgesetzt wird die proportional zum Gradienten des Wasserdruckes im eigentlichen Gestein und proportional zum Volumen der Partikel ist. Wenn ein Halbraum eines wassergesättigten Gesteins von einem Wasserstrahl mit ausreichend hohen Druck getroffen wird, sagt die Theorie, so soll das Anfangsstadium des sich bildenden Kraters ringförmig sein mit einem Radius doppelt so gross als der Radius des Wasserstrahls. Im Falle trockenen Gesteins, erklärt die Theorie, soll die typische Ringstruktur im Anfangsstadium des Kraters nich auftreten. Zusammenfassend kann man sagen die Permeabilität ist ein bedeutend wichtiges Parameter bei Gesteinsdestruktion mit Hochdruck wasserstrahl im Gegensatz zum Fall mechanischer Destruktion.

     

The relationship between the diagonal and the bar constructions on a bisimplicial set

The aim of this paper is to prove that the homotopy type of any bisimplicial set X is modelled by the simplicial set , the bar construction on X. We stress the interest of this result by showing two relevant theorems which now become simple instances of it; namely, the Homotopy colimit theorem of Thomason, for diagrams of small categories, and the generalized Eilenberg-Zilber theorem of Dold-Puppe for bisimplicial Abelian groups. Among other applications, we give an algebraic model for the homotopy theory of (not necessarily path-connected) spaces whose homotopy groups vanish in degree 4 and higher.