The local flow in a wedge between a rigid wall and a surface of constant shear stress

The viscous incompressible flow in a wedge between a rigid plane and a surface of constant shear stress is calculated by use of the Mellin transform. For wedge angles below a critical value the asymptotic solution near the vertex is given by a local similarity solution. The respective stream function grows quadratically with the distance from the origin. For supercritical wedge angles the similarity solution breaks down and the leading order solution for the stream function grows with a power law having an exponent less than two. At the critical angle logarithmic terms appear in the stream function. The asymptotic dependence of the stream function found here is the same as for the 'hinged plate' problem. It is shown that the validity of the Stokes flow assumption is restricted to a vanishingly small distance from the vertex when the wedge angle is above critical and when the region of nonzero constant shear stress is extended to infinity. The relevance of the present result for technical flow systems is pointed out by comparison with the numerically calculated flow in a thermocapillary liquid bridge.     

The Dynamics and Heat Transfer of a Droplet in a Dusty Gas in the Presence of Phase Transformations and Dust Catching

The dynamics and heat transfer of a droplet in a mixture of gas with fine particles (dusty gas) are investigated in the presence of deposition of fine particles on the droplet (dust catching) and of phase transformations (evaporation, condensation). Separately treated is a case in which only phase transformations occur. Analytical solutions of the problem are found in the limiting cases of Stokes and Newtonian flow past a droplet (corresponding to low and high values of the Reynolds number). The combined effect of dust catching and phase transformations on the droplet motion is investigated numerically.     

Singular Thermal Residual Stress Field near the Interface Corner of Bonded Dissimilar Materials

In this paper, a cooled composite interface corner consisting of two bonded dissimilar materials is considered as a plane problem. With the complex variable method, the thermal residual stress field is studied analytically. It is found that the regular stress term possesses the singularity either of lnr or ln²r. The exact expressions for the corresponding singular stress field are presented.     

Boundary element method based on a new second kind integral equation formulation

A boundary integral equation (BIE) formulation for elasticity problems with mixed boundary conditions, proposed by Parton and Perlin (Mathematical Methods of the Theory of Elasticity, Mir, Moscow, 1984), is implemented in this paper using quadratic boundary elements. The formulation is specialised to Stokes flow problems by setting the Poisson ratio to 0·5 in the relevant kernels. The implementation is used to analyse non-trivial three dimensional problems in elasticity and Stokes flows. The results compare well with those obtained by a direct boundary element method. An outline of the extension of the formulation to non-linear problems is also given.     

A modified least‐squares mixed finite element with improved momentum balance

The main goal of this contribution is to provide an improved mixed finite element for quasi‐incompressible linear elasticity. Based on a classical least‐squares formulation, a modified weak form with displacements and stresses as process variables is derived. This weak form is the basis for a finite element with an advanced fulfillment of the momentum balance and therefore with a better performance. For the continuous approximation of stresses and displacements on the triangular and tetrahedral elements, lowest‐order Raviart–Thomas and linear standard Lagrange interpolations can be used. It is shown that coercivity and continuity of the resulting asymmetric bilinear form could be established with respect to appropriate norms. Further on, details about the implementation of the least‐squares mixed finite elements are given and some numerical examples are presented in order to demonstrate the performance of the proposed formulation. Copyright © 2009 John Wiley & Sons, Ltd.     

Internal–external circumferential crack behaviour in the cement layer of total hip replacement

This study aimed to investigate crack behaviour at the internal and external surfaces of the cement layer in total hip replacement. A three‐dimensional model of the femur with the cemented prosthesis was developed and analysed. Cracks were placed on the internal, external and both internal and external surfaces of the cement layer. Stress intensity factors were measured during gait. Results revealed that the stress intensity factors modes I and III were the most dominant in the crack propagation in the cement layer. The domain of mode I was the medial and lateral sides of the cement layer. Meanwhile, the domain of mode III was the anterior and posterior sides of the cement layer. The stress intensity factor and distance from the distal end indicated an inverse relationship. The internal and external cracks had no significant interaction. Moreover, stress intensity factors at the external surface of the cement layer were higher than those on the internal surface.     

Unsteady flows of a binary mixture of incompressible Newtonian fluids in an annulus

This paper is concerned with applying the mixture theory of two chemically inert incompressible Newtonian fluids to some simple unsteady flows in the annular region between two infinitely long coaxial cylinders. The equations governing the motion of the binary mixture under discussion are reduced to a system of coupled partial differential equations. With the help of finite Hankel transforms, the exact solutions of these equations are obtained in series form for the following three problems: (i) unsteady axial Couette flow in an annulus, (ii) unsteady Poiseuille flow in an annulus, (iii) unsteady circular Couette flow in an annulus.