The energy aspect of the boundary layer flow due to Ohmic heating and frictional forces at a moving flat plate has been analyzed based on similarity transformations. The flow is assumed to take place in the presence of an externally applied transverse magnetic field. The velocity and temperature profiles in the boundary layer have been shown by numerically integrating the governing nonlinear ordinary differential equations. Furthermore, the variations of temperature, both close to and away from the boundary plate, have been illustrated graphically as a function of the Prandtl number. The effects of the dissipative processes on the skin friction and plate temperature have been discussed. The magnetic field increases both the skin friction and the wall temperature, whereas, for a fixed magnetic field, the effect of boundary motion is to decrease them.

     A mechanism of surface instability in non-Newtonian fluid is described using Rayleigh-Taylor instability as an example. The combined effects of non-Newtonian parameter n, normal stress 'delta', film thickness h, and surface tension 'gamma' on surface instability is studied using linear stability analysis. It is shown that stable, neutrally stable and unstable states are possible depending on the values of n, in contrast to the existence of only unstable state in Newtonian fluids. Further, the graph of dispersion curve reveals that both n and 'lambda'(='gamma'/'delta') control dispersion curve with the layer thickness just affecting the nature of growth rate of instability.

     Combined free and forced convection flow of water at 4^oC has been studied when the free-stream is of the form exp (mx/2) where m is a constant and x is the distance measured along the semi-infinite vertical plate from the leading edge. Similarity solutions are obtained and the velocity and temperature profiles are shown on graphs, whereas the numerical values of the skin-friction and the rate of heat transfer are listed in a table. The effects of the fall in the temperature of water from 20^oC to 4^oC are discussed. Also the effects of Gr/Re² (Gr - the Grashof number and Re - the Reynolds number) on the skin friction and the heat transfer are discussed.

     It is well known that the isoparametric element has certain drawbacks when applied to thin plates subjected to bending. The specific problem which creeps up for such cases is known as the shear locking phenomenon which becomes more and more pronounced as the thickness of the plate reduces. Though this can be taken care of by techniques such as the reduced integration, problems still linger for very thin plates which occur in many practical structures. The mapping concept used in the formulation of the isoparametric element has been utilised in developing a new four-noded plate bending element. The shear deformation which is not important for the analysis for thin plates has not been considered and thus the disturbing feature of shear locking does not creep into the analysis, yet like the isoparametric element the new element is able to analyse plates having arbitrary shapes.

     The thermal instability of electrically conducting Rivlin-Ericksen elastico-viscous fluid in porous medium is considered to include the Hall current in the presence of a vertical magnetic field. For the stationary convection, the Rivlin-Ericksen elastico-viscous fluid behaves like a viscous (Newtonian) fluid. The Hall current and medium permeability are found to have destabilizing effect, whereas the magnetic field has a stabilizing effect on the thermal instability problem for stationary convection. A sufficient condition for the non-existence of overstability is obtained.

     In this paper, a theory for nonlinear bending of shallow conical sandwich shells is established by means of the method of calculus of variations. Using the modified iteration method which was suggested by Yeh et al. (1965a, 1965b), analytic solutions of nonlinear stability for the shells with four types of boundary conditions under uniform pressure are obtained. The numerical discussions based on the analytic solutions have been given in detail, which indicate that our method is efficient for the analysis of shallow shells.

     Cylindrical vessels with ellipsoidal heads are widely used in engineering. They are subject mainly to internal pressure, however in some cases external pressure may also be present. The paper presents linear and non-linear analyses of stability of ellipsoidal heads subject to external or internal pressure. The calculations have been made by means of finite element methods, using the COSMOS/M system. The results have been compared with existing analytical solutions of ellipsoidal shells specified in literature.

     A simple methodology to trace journal orbit under dynamic load conditions is presented. The non-linear fluid film bearing forces are derived using a closed-form two-dimensional pressure solution obtained from Reynolds equation for dynamic case. An implicit two-dimensional Newton-Raphson method is employed to determine journal center velocity by solving the equations of motion incorporating journal inertia and unbalance forces. A global technique is used to ensure convergence towards the root in each iteration. Finally, two connecting rod big end bearings are studied to demonstrate the effect of inertia forces at high speed.

     An equation of Rabinowitsch-Mooney type together with the corresponding relations for consistency variables has been adopted for an approximate calculation of pressure drop in flow of viscoplastic fluids through straight ducts. The suitability of the suggested procedure of calculation of pressure drop is demonstrated by the comparison of calculation results with the published analytical solution of flow of Robertson-Stiff fluid through an annulus and with numerical solution of flow of Bingham fluid through ducts of rectangular cross section.

     Fluidyne is an easy-to-build and quiet heat engine using low-grade heat sources and not having any moving solid parts. Although Fluidyne’s efficiency is quite low compared with efficiencies of other heat engines, it has an important advantage of using recovered heat. In this study, a mathematical model that analyses Fluidyne is developed. The model utilizes the equations of conservation of mass written for liquid columns and working fluid. Sets of differential equations are solved using Runge-Kutta Method. In order to investigate the validation of the model, theoretical results are compared with experimental results and the results in literature.

     A theoretical study is conducted in this paper for the development of the steady three-dimensional boundary layer, which is induced by a horizontal forced convection flow past an infinitely long vertical cylinder. It is assumed that the cylinder is partially prescribed with a constant heat flux q_w, while the other part of the cylinder is held at the ambient temperature T_. It is also assumed that the secondary flow is induced in the boundary layer by the buoyancy forces. A series solution method is used to solve the governing non-linear set of partial differential equations near the thermal leading edge. It is shown that the effect of the horizontal free stream on the boundary layer gradually increases as one moves upward away from the thermal leading edge along the cylinder. The solution has been obtained for different values of the Prandtl number, Pr, and it is shown that for Pr = 0.733 and Pr = 6.7 the present results are in excellent agreement with those known from the literature.

     Even with the present day extensive use of Computational Fluid Dynamics (CFD), simplified analytical expressions for Fluid Dynamic phenomena have their applications in highlighting significant mechanisms and aiding initial engineering estimates. The present work shows that experimental data for the trajectory of the centre line of jets exposed to a cross-flow can be found from a single expression. The expression is derived from first principles and unlike most other power law formulas the exponents are not empirically determined from measurements. In comparison with other single expressions based on dimensional analysis, which results in differing expressions for differing parts of the flow field, the equation presented here combines the asymptotic assumptions into a single expression.

     The effect of polymer concentration on the bifurcation structure of a bubble oscillator is theoretically examined in terms of bifurcation diagrams and phase diagrams. The equation describing the driven spherical oscillations of a gas bubble in CMC aqueous solutions is obtained by using a Williamson model fluid. The numerical results reveal the suppression of chaotic oscillations of bubbles by polymer additives.