This paper deals with the modeling of flows of a Newtonian liquid dispersed with bubbles. We provide an averaging procedure that combines and gainfully exploits area, volume and ensemble averaging methods, and arrives at the governing equations for bubbly liquids. Expressions are suggested for the interaction mechanisms and other constitutive quantities that appear as a consequence of the averaging. Restrictions on the constitutive quantities due to the second law of thermodynamics are delineated and a specific boundary value problem solved within the context of the theory. It is found that the prediction of the theory compares favorably with experimental observations for the specific boundary value problem under consideration.

     We present a theoretical and experimental study of unloaded free surface mudflow in gradually varied conditions. First of all, a polymer gel following the same rheological law as the natural mud was identified, and its severe rheometric characterization was performed. Then the flow of this synthetic mud was generated in a 1-D open channel. The velocity and depth profiles were then systematically investigated. The theoretical study consisted in determining the velocity profiles in terms of the rheological parameters in uniform conditions as well as in determining the form parameter characterizing the gradually varied flow of yield stress fluids in open channels.

     A closed-form solution is obtained for the problem of dispersion of solute in a non-isothermal flow of a Newtonian fluid with temperature-dependent viscosity. The effect of wall-catalysed reaction on dispersion is investigated against the background of the no-reaction problem. The analytical result on dispersion of solute with wall catalysed reaction at long times is compared with the analytical solution when reaction is absent. The Taylor (1953) and Aris (1956) regimes of dispersion for the present problem are obtained as limiting cases from the study. The graphical results of the study serve as a jury on any numerical study that might be undertaken considering non-asymptotic all-time analysis. The results of the study indicate that heating from above is an effective means of controlling dispersion in variable-viscosity liquids.

     Theoretical considerations of the kinematic relationship between a rocking die and workpiece during rotary forging are described in here. According to friction conditions the skid or slip may cause the rising of circumferential forces at the die-workpiece interface. It was confirmed by the results of experimental invegations of the rotary forging process.

     A boundary layer analysis is presented to study the effects of a transverse magnetic field on natural boundary layer flow of a micropolar fluid in a porous medium. Four different vertical flows have been analyzed, those adjacent to an isothermal surface and uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source on a vertical adiabatic surface, or wall plume. The governing equations for momentum, angular momentum and energy have been solved numerically. Missing values of the velocity, angular velocity and thermal functions are tabulated for a wide range of the material parameters, Prandtl number and magnetic parameter of the fluid. A comparison has been made with the corresponding results for Newtonian fluids. Micropolar fluids display drag reduction and reduced surface heat transfer rate in a porous medium as compared with Newtonian fluids.

     This paper is concerned with the linear theory of heat propagation in a binary mixture of rigid heat conductors. First, the equilibrium theory is studied. A solution of Galerkin type is established and fundamental solutions are derived. The potentials of single-layer and double-layer are used to reduce the boundary value problems to singular integral equations. Existence and uniqueness results are established. The second part of the paper is concerned with the dynamical theory. A continuous dependence result and a spatial decay estimate are derived.

     Flow past a continuously moving semi-infinite vertical plate in the upward direction is studied here. With usual boundary layer transformations, the boundary layer equations are reduced to local non-similar ordinary differential equations which are solved numerically. Velocity and temperature profiles are shown on graphs and the numerical values of the skin-friction and the rate of heat transfer are listed in a Table. It is observed that there occurs separation of low Prandtl number fluids at large values of Gr/Re² where Gr is the Grashof number and Re is the Reynolds number. Greater viscous dissipative heat causes a fall in both the skin-friction and the rate of heat transfer.

     Propagation of acoustic waves in an elastic tube with compressible polymeric liquid is investigated. A dispersion equation is derived that accounts for viscoelastic effects in the fluid in coupling with inertia, radial and longitudinal deformations of the tube's wall. The equation is valid in the frequency range where sound wave length is greater from the tube radius and includes the Korteweg- Joukowski speed of water hammer as a limiting case. Analysis of the dispersion relation has shown a strong influence of the rheological properties of the liquid on dispersion and attenuation of pressure signals. The results indicate also that the model developed could give means to characterize the rheological parameters of a polymeric liquid with sufficiently simple acoustic technique.

     The present paper is concerned with the onset of Rayleigh-Bénard convection in an inclined porous layer with anisotropic permeability. Due to the temperature gradient and the inclination, a steady shear flow is set up. The critical Rayleigh number at marginal stability of this basic flow is calculated and the flow pattern occurring at convection onset is examined. It turns out that anisotropy in the permeability and the shear flow have an essential influence on the selected flow structure. Depending on the anisotropy ratio and the tilt angle, convection rolls are found either with axes parallel to the basic flow or with axes perpendicular to the flow.

     The spectrum of a two-dimensional flow, due to the presence of a circular liquid obstacle in a liquid layer, is investigated by using a boundary integral equation method.