Table of contents

Static deformation of free surface is investigated for horizontal magnetic fluid layer in the presence of applied magnetic field induced by circular electric current situated horizontally below the layer. Shape of the deformed free surface is found by numerical calculation for various current intensity and size of circuit. The problems for a straight line current and a magnetic dipole are solved separately.

The complex function method is applied to screen printing flow with low Reynolds number assuming that the printing ink is Newtonian. The screen printing flow is expressed through a Taylor flow in the corner. The pressure distribution, vorticity distribution and stream lines of the Taylor flow can easily be obtained by using the complex function method. A new model of the flow which may better express the screen printing is obtained through this method by placing a sink at the origin of the Taylor flow. The appropriate corner angle for printing, theoretically derived from this method as 65.4°, corresponds to the empirical angle in industrial use. The pressure distribution of this model shows good agreement with the experimental results obtained in the present work.

The initial phase of transient natural convection around a suddenly heated circular cylinder is investigated. The Grashoff number is assumed to be large but finite. It is shown that, due the displacement effect, irrotational outer flow is caused in the outer region outside the boundary layer, which, together with the inner boundary-layer flow, forms vortices at both sides of the cylinder, and that the pressure drag D_p is equal to the skin-friction drag D_f up to the present order of approximation.

The steady, laminar, isothermal entrance region flow of the Hershel-Bulkley fluid in a tube has been investigated by using the momentum integral and the momentum energy integral techniques. The resulting nonlinear ordinary differential equations on the dimensionless boundary layer thickness have been solved numerically by using the Runge-Kutta method. The results for the plug core velocity, boundary layer thickness, pressure drop, entrance length and loss coefficient have been obtained for a wide range of yield numbers and the flow behaviour index. Significant effect of viscous dissipation has been observed on the velocity distribution and boundary layer growth, whereas the effect of viscous dissipation on pressure drop is negligible. In both the methods, the values of entrance length and loss coefficient have been found to be reduced with increasing values of Hershel-Bulkley number and flow behaviour index. However, in the case of the momentum energy method the values of entrance length and loss coefficient are appreciably higher than those obtained by using the momentum integral method.

Analytical and numerical solutions are presented for the steady flow of an inviscid fluid about symmetric lifting profiles at an angle of attack in a plane sheared onset flow for which conformal mapping plays a critical role. For uniform shear (i.e. the onset flow speed varies linearly with position) in two dimensions, the disturbance field is potential and hence a solution based on the conformal transformation technique may be constructed. The Moriya transformation, which employs a leading-term transformation coefficient that stretches and rotates the field at great distances from the foil (as distinct from other classical transformations which leave the far field unchanged) is used and, with a limited number of terms selected for the transformation, a simple elegant solution is obtained that may be easily evaluated at arbitrary points on the foil contour. An additional investigation is reported for the field solution — involving a locally similar but globally non-uniform sheared onset flow — about one of the foils for which a simple O-type grid is analytically generated from the mapping function. These data indicate that the uniform-shear solution overpredicts the lift and surface speed on the suction side of the foil relative to the more realistic onset flow: the numerical solution predicts surface speeds that generally lie between those for the uniform flow and the uniformly sheared flow solutions.