Effects of non-uniform temperature gradient, vertical transport of momentum and vertical transport of perturbation temperature due to throughflow are investigated on the Rayleigh-Bénard convection for different hydrodynamic boundary conditions. The eigenvalue problem for the conducting boundaries is solved by the higher-order Galerkin method. It is shown that the throughflow in one particular direction destabilizes the system depending on the value of the Prandtl number. Also a comparison between the results of single-term and higher order Galerkin methods is made and limitations of the single-term Galerkin method are clearly brought out.

     Using appropriate transformations, the differential equations of free longitudinal vibration of bars with variably distributed mass and axial stiffness are reduced to Bessel’s equations or ordinary differential equations with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of mass and axial stiffness. Exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for a one step non-uniform bar are derived and used to obtain the general solution and the frequency equation of a multi-step non-uniform bar with various boundary conditions, including non-classical cases. This approach which combines the transfer matrix method and closed form solutions of one step bars leads to a single frequency equation for any number of steps.

     Residual stress analysis is carried out in a thermoplastic composite laminated plate for in-plane loading. Low density polyethylene thermoplastic matrix (LDPE) and steel fibers are used to produce the composite plates by using moulds. The first order shear deformation theory and nine node Lagrangian finite element are used. Mathematical formulation is given for the residual stress analysis of a laminated plate for small deformations. Yield points and stresses are obtained for symmetric and antisymmetric laminated plates without and with a circular hole. Elastic, elasto-plastic and residual stresses in plates are given in tables. The expansion of plastic zones is illustrated for 100, 200 and 300 load steps. Yield points and the expansion of plastic zones are compared for different plates without and with a circular hole.

     In this paper, we determine a boundary integral formulation for the motion and deformation of a compound drop due to its interaction with a solid particle. The problem is reduced to a system of Fredholm integral equations of the second kind. We prove that this system has a unique continous solution when the boundaries of the flow are Lyapunov surfaces and the boundary data are continous.

     An analysis is presented for the unsteady heat transfer characteristics of a laminar forced convective flow over a circular pin by the conjugate convection-conduction theory including radiative effects under the optically thick limit approximation. The dimensionless form of the governing equations is solved numerically and results are presented for the temperature distribution and local heat transfer rates. Both constant root temperature and constant root heat flux boundary conditions are considered. The radiative effect tends to increase the surface temperature.

     Two commonly used methods for predicting unsteady airloads are: 1) the panel method based on the surface distribution of singularity elements and 2) the indicial method for unsteady problems governed by the linearized partial differential equation and linearized boundary conditions. The panel method considered here involves a piecewise linear continuous distribution of singularities (sources and doublets) over the airfoil surface. Since the linearity assumptions of the indicial method do not allow for variations in the form of the chordwise pressure, this approach seems to be more economical from the computational point of view. The present study is aimed at the systematic assessment of the two approaches by considering a number of unsteady two-dimensional flows. Good agreement was found with measured airloads data for the two methods.

     Residual stress analysis is carried out in a thermoplastic composite laminated plate for in-plane loading. Low density polyethylene thermoplastic matrix (LDPE) and steel fibers are used to produce the composite plates by using moulds. The first order shear deformation theory and nine node Lagrangian finite element are used. Mathematical formulation is given for the residual stress analysis of a laminated plate for small deformations. Yield points and stresses are obtained for symmetric and antisymmetric laminated plates without and with a circular hole. Elastic, elasto-plastic and residual stresses in plates are given in tables. The expansion of plastic zones is illustrated for 100, 200 and 300 load steps. Yield points and the expansion of plastic zones are compared for different plates without and with a circular hole.

     In hybrid bearings, the carrying effect is produced by supplying under pressure and by the relative motion of the bearing surfaces. Because the pressure distribution in the bearing is the solution to a nonlinear partial differential equation of second order, the two causes cannot be studied separately and solving the problem is a difficult task. The mathematical model considered by us is the Reynolds equation for compressible fluids in a multiple connected domain. The boundary conditions on the inner boundaries are derived from the flow-rate continuity through the supplying orifices and are expressed as nonlinear integral-differential equations, which are solved numerically.

     The thermal instability of Walters' (model B') fluid in a porous medium is considered in the presence of a uniform vertical magnetic field to include the effect of Hall currents. For the case of stationary convection, the magnetic field has the stabilizing effect on the system, whereas the Hall currents have destabilizing effect on the system. The porous medium permeability has both stabilizing and destabilizing effects on the system depending on the Hall parameter M. The kinematic viscoelasticity has no effect on stationary convection. The kinematic viscoelasticity and magnetic field (and corresponding Hall currents) introduce oscillatory modes in the system, which were nonexistent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

     Mixed convection flow past a semi-infinite vertical porous plate is studied here when the plate temperature is oscillating about a non-zero mean. Mean velocity, mean temperature, in-phase and out of phase components of unsteady part of the temperature are shown graphically. It is observed that an increase in suction velocity leads to an increase and an increase in injection velocity leads to a decrease in the amplitude of the rate of heat transfer. Also at large values of frequency ?, the oscillating component of temperature is superimposed on the mean temperature and is found to be unaffected by ? and suction-injection velocity.

     Gas hold-up for self-aspirating disk impellers was determined experimentally. Process parameters such as rotations frequency, impeller size and height of liquid level over the impeller were found to have the greatest impact on its value. The effect of viscosity of the liquid being aerated is much weaker - the investigations were carried out with several liquids differing in viscosity. It was also found that the width of the outlet slots of the impeller had a slight influence on gas hold-up.

     Making use of the hypersurface theory, the ray theory and the method of asymptotic expansion of multiple scales, a study of weakly non-linear high frequency waves, through “homogeneous” media characterized by dissipative or dispersive hyperbolic systems of partial differential equations, is proposed in covariant formalism. Within the present theoretical framework, asymptotic waves in a heat-conducting relativistic fluid are considered.

     A numerical and analytical investigation of the compressible axisymmetric boundary-lager flow over a circular cylinder is presented for both adiabatic flow and the case of heated or cooled walk. First, a numerical solution to the governing equations is presented for a variety of wall conditions. The remainder and majority of the paper is then concerned with an analysis of the far-downstream flow where curvature becomes a dominant feature. Here the flow takes on a double structure, with an Oseen type of outer flow. The problem reduces to matching to an inner solution which, in contrast to the incompressible case, is found to be non-trivial. Three forms of the inner solution are constructed, firstly to justify obtaining a new result and secondly to rebut the assertion that matching is only possible for a single approach. Further the use of a general power law form for the viscosity law is considered. The resulting asymptotic forms are then compared with the numerical results of the far downstream flow.