Exact Analytical Solutions of Static Electroelastic and Thermoelectroelastic Problems for a Transversely Isotropic Body in Curvilinear Coordinate Systems

An approach to the solution of three-dimensional static problems for a transversely isotropic (rectilinear anisotropy) body is expounded and the solutions for piezoceramic canonical bodies are systematized. The result of the study is explicit analytical solutions of three-dimensional problems. Bodies are examined whose boundary surface is the coordinate surfaces in coordinate systems that permit the separation of the variables in the three-dimensional Laplace equation. The stress concentration in bodies near necks, cavities, inclusions, and cracks is investigated. The stress intensity factors of the force field and electric induction near elliptic and parabolic cracks are determined. The contact interaction of a piezoceramic half-space with elliptic and parabolic dies is studied. The bodies are under various mechanical, thermal, and electric loads     

Stationary Transverse Diffusion in a Horizontal Porous Medium Boundary-Layer Flow with Concentration-Dependent Fluid Density and Viscosity

Stable transport of high-concentrated solute is considered in horizontal boundary-layer flows above a wall of constant concentration. Mixing is accomplished by advection and molecular diffusion only. The utilized boundary-layer approximation allows to investigate the exclusive influence of gravity on vertical diffusion. The hydrodynamic dispersion mechanism was disregarded in the present study which confines its applicabilty to flows with small molecular Péclet numbers. A linear variability of both the fluid's density and viscosity with changing concentration is taken into account as well as the complete set of mass-fraction based balance equations. Steady-state concentration and velocity distributions above the horizontal wall have been obtained using the series truncation method which recently had proven successful to solve the corresponding problem using the Boussinesq assumption. The impact of the latter on these distributions is discussed by what has been additionally-facilitated by the existence of an exact analytical solution for the simpler Boussinesq case. Whereas no density variability influence exists with use of the Boussinesq assumption the complete system of mass-fraction based equations predicts opposing effects of density and viscosity differences between oncoming and near-wall fluids on concentration distributions. Larger density differences narrow the transition zone between both fluids, larger viscosity differences widen it. Thus, a compensation of both effects can be observed for individual fluids and for certain regions of the flow field.