Flow through doubly connected ducts

Fluid flow in doubly connected ducts, bounded externally by a circle and internally by a regular polygon of various shapes, is analysed using the finite element method. Hydrodynamically developed, steady, laminar flow of a constant-property fluid is considered. Velocity profiles as well as friction factors (at the inner and outer walls, and average value) are presented. These compare well to previous results available in the literature. Salient characteristics of flow are identified. Correlations for the average friction factor with aspect ratio are suggested.     

An algorithm of finite element grid generation for three-dimensional complex connected domain

An automated quasi three-dimensional finite element grid generation method is presented for particular three-dimensional complex connected domain, across which some are simply connected two-dimensional.regions and some are multiply connected two-dimensional regions. A subdivision algorithm based on the variational principle has been developed to ascertain the smoothness and orthogonality of the generated grid in any cross sections. Smooth transition between the simply and multiply connected regions is maintained. For illustration, the method is applied to generate a finite element three-dimensional grid for human above knee stump.     

Forced convection heat transfer in doubly connected ducts

Forced convection heat transfer in doubly connected ducts bounded externaly by a circle and internally by a regular polygon of various shapes is analysed using a finite element method. Hydrodynamically and thermally developed, steady, laminar flow of a constant property fluid is investigated. An insulated outer tube and constant heat flux at the inner core are considered. Temperature profiles as well as Nusselt numbers are presented. Salient characteristics of the temperature field in such passages are identified. Correlations for the Nusself number with aspect ratio are suggested.     

A method for conformal mapping of a two-connected region onto an annulus

This paper presents a method for conformal of a two-connectedregion onto an annulus.The philosophy of the method is toconvert the problem into a Dirichlet problem and to prove thereal part of the analytic function transformation should be aharmonic function satisfying certain boundary conditions.Ac-cording to the theory of harmonic function we can determine theinner radius of the annulus from the condition that the harmonic function defined in two-connected region should be single-valued.It is then easy to see that the imaginary part can directly beobtained with the aid of Cauchy-Riemann conditions.The unknownconstants of integration only influence the argument of imagepoints and can easily be derived by using the one-to-one mappingof region onto an annulus.Without loss of generality,themethod can be used to conformally map other two-connected regionsonto an annulus if they can be subdivided into several rectang-ulars.The method has been programmed for a digital computer.It is demonstrated that the meth     

Viscous flow in pipes whose cross-sections are doubly connected regions

Slow and steady viscous fluid flow in a pipe whose cross-section is bounded by an ellipse and a circle is considered. The method used is in deriving general solutions independently on the two boundaries using one or two conformal mapping functions and an attempt is made to make the complex potentials continuous in the doubly connected region. Numerical results are found and compared with those for the case of concentric circles and the case of concentric ellipses.     

Dynamic plastic damage of simply and doubly connected elliptic plates

This paper studies the dynamic behavior of simply and doubly connected elliptic ideal rigidplastic plates with simply supported or clamped contours under shorttime intensive dynamic loads. It is shown that there are several mechanisms of dynamic deformation of plates. For each mechanism, equations of the dynamic behavior are obtained. Operating conditions of these mechanisms are analyzed. Analytical expressions for the ultimate, high and superhigh loads and the maximum final deflection are obtained. Numerical examples are given.     

Application of scattered-light photoelasticity to doubly connected tapered torsion bars

This paper reports the use of scattered-light photoelasticity to solve the doubly connected tapered-shaft problem. Some techniques are presented which help realize more fully the potential of scattered-light photoelasticity. These include the use of a continuousemission gas laser as a light source for the polariscope, the use of a photometer arrangement to read fringe spacings, and the use of curve-fitting techniques to analyze the data. Also, some design features for constructing a scattered-light polariscope are presented.