The flow field around a straight chain of multiple slip spherical particles rotating steadily in an incompressible Newtonian fluid about their line of centers is analyzed at low Reynolds numbers. The particles may vary in radius, slip coefficient, and angular velocity, and they are permitted to be unevenly spaced. Through the use of a boundary collocation method, the Stokes equation governing the fluid flow is solved semi-analytically. The interaction effects among the particles are found to be noteworthy under appropriate conditions. For the rotation of two spheres, our collocation results for their hydrodynamic torques are in good agreement with the analytical asymptotic solution in the literature obtained by using a method of twin multipole expansions. For the rotation of three spheres, the particle interaction effect indicates that the existence of the third particle can influence the torques exerted on the other two particles noticeably. The interaction effect is stronger on the smaller or less slippery particles than on the larger or more slippery ones. Torque results for the rotation of chains of many particles visibly show the shielding effect among the particles.

We investigate entropy generation in unsteady three-dimensional axisymmetric MHD nanofluid flow over a non-linearly stretching sheet. The flow is subject to thermal radiation and a chemical reaction. The conservation equations were solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasilinearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account when the nanofluid particle volume fraction on the boundary in passively controlled. The results show that as the Hartman number increases, both the Nusselt number and the Sherwood number decrease whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with the physical parameters.

Dynamic behavior of coaxial axisymmetric planar cracks in the transversely isotropic magneto-electro-elastic (MEE) material in transient in-plane magneto-electro-mechanical loading is studied. Magneto-electrically impermeable as well as permeable cracks are assumed for crack surface. In the first step, considering prismatic and radial dynamic dislocations, electric and magnetic jumps are obtained through Laplace and Hankel transforms. These solutions are utilized to derive singular integral equations in the Laplace domain for the axisymmetric penny-shaped and annular cracks. Derived Cauchy singular type integral equations are solved to obtain the density of dislocation on the crack surfaces. Dislocation densities are utilized in computation of the dynamic stress intensity factors, electric displacement and magnetic induction in the vicinity tips of crack tips. Finally, some numerical case studies of a single and multiple cracks are presented. The effect of system parameters on the results is then discussed.

Based on a very fast numerical procedure for the determination of the subsurface stress field beneath frictional contacts of axisymmetric elastic bodies under arbitrary 2D oblique loading, the contact mechanical influences of loading parameters and contact profile geometry on the Smith-Watson-Topper (SWT) fatigue crack initiation parameter in elastic fretting contacts with superimposed normal and tangential oscillations are studied in detail. The efficiency of the stress calculation allows for a comprehensive physical analysis of the multi-dimensional parameter space of influencing variables. It is found that a superimposed normal oscillation of the contact can significantly increase or decrease the SWT parameter, depending on the initial phase difference and frequency ratio between the normal and tangential oscillation. Written in proper non-dimensional variables, the rounded flat punch always exhibits smaller values of the SWT parameter, compared to a full paraboloid with the same curvature, while the truncated paraboloid exhibits larger values. A small superimposed profile waviness also significantly increased or decreased the SWT parameter, depending on the amplitude and wave length of the waviness. While both the load protocol and the profile geometry can significantly alter the SWT parameter, the coupling between both influencing factors is weak.

Clifford algebra is unified language and efficient tool for geometry and physics. In this paper, we introduce this algebra to derive the integrable conditions for Dirac and Pauli equations. This algebra shows the standard operation procedure and deep insights into the structure of the equations. Usually, the integrable condition is related to the special symmetry of transformation group, which involves some advanced mathematical tools and its availability is limited. In this paper, the integrable conditions are only regarded as algebraic conditions. The commutators expressed by Clifford algebra have a neat and covariant form, which are naturally valid in curvilinear coordinate system and curved space-time. For Pauli and Schr\"odinger equation, many solutions in axisymmetric potential and magnetic field are also integrable. We get the scalar eigen equation in dipole magnetic field. By the virtue of Clifford algebra, the physical researches may be greatly promoted.

The present work deals with the development of finite element methodology for obtaining the stress distributions in thick cylindrical HK40 stainless steel pipe that carry high temperature fluids. The material properties and loading are assumed to be random variables. Thermal stresses that are generated along radial, axial and tangential directions are computed generally using analytical expressions which are very complex. To circumvent such an issue, the probability theory and mathematical statistics have been applied to many engineering problems which allows to determine the safety both quantitatively and objectively based on the concepts of reliability. Monte Carlo simulation methodology is used to study the probabilistic characteristics of thermal stresses which is used for estimating the probabilistic distributions of stresses against the variations arising due to material properties and load. A 2-D Probabilistic finite element code is developed in MATLAB and the deterministic solution is compared with ABAQUS solutions. The values of stresses that are obtained from the variation of elastic modulus are found to be low as compared to the case where the load alone is varying. The probability of failure of the pipe structure is predicted against the variations in internal pressure and thermal gradient. These finite element framework developments are useful for the life estimation of piping structures in high temperature applications and subsequently quantifying the uncertainties in loading and material properties.

An overview is presented of several diverse branches of work in the area of effectively 2D fluid equilibria which have in common that they are constrained by an infinite number of conservation laws. Broad concepts, and the enormous variety of physical phenomena that can be explored, are highlighted. These span, roughly in order of increasing complexity, Euler flow, nonlinear Rossby waves, 3D axisymmetric flow, shallow water dynamics, and 2D magnetohydrodynamics. The classical field theories describing these systems bear some resemblance to perhaps more familiar fluctuating membrane and continuous spin models, but the fluid physics drives these models into unconventional regimes exhibiting large scale jet and eddy structures. From a dynamical point of view these structures are the end result of various conserved variable forward and inverse cascades. The resulting balance between large scale structure and small scale fluctuations is controlled by the competition between energy and entropy in the system free energy, in turn highly tunable through setting the values of the conserved integrals. Although the statistical mechanical description of such systems is fully self-consistent, with remarkable mathematical structure and diversity of solutions, great care must be taken because the underlying assumptions, especially ergodicity, can be violated or at minimum lead to exceedingly long equilibration times. Generalization of the theory to include weak driving and dissipation (e.g., non-equilibrium statistical mechanics and associated linear response formalism) could provide additional insights, but has yet to be properly explored.

This paper presents a new method to model the nonlinear behaviour of masonry double curvature structures, possibly reinforced by composite materials, by means of conventional elasto-plastic analyses. It is meant to be used in professional design, especially for assessment and retrofitting purposes, therefore based on the exploitation of the simplest nonlinear Finite Elements available in a commercial software, namely trusses with elasto-fragile and elasto-ductile behaviour (Cutoff Bars). The numerical static nonlinear analyses are carried out by considering elastic hexahedral elements for bricks and lumping nonlinearities on joints. These have been assumed in turn elastic-brittle and elastic-plastic by using 1D elements, respectively Point Contacts, under No-Tension Material hypothesis, and Cutoff Bars, assigning small tensile resistance to the material. The reinforcement, realised with FRP hooping strips, has been successfully modelled in a similar fashion, i.e. by applying perfectly bonded elastic-plastic Cutoff Bars at the extrados of the dome, where the debonding is accounted for in a conventional way limiting the tensile strength according to Italian Standards indications. The procedure is validated against benchmark models with the same geometry, using experimental data and more refined structural model results for comparison.