Numerical studies of some problems in mixed convection boundary layer flows

Abstract

This thesis embodies the results of our investigations on some problems in mixed convection boundary-layer flows. It is divided into four chapters, the first being a general introduction to boundary-layer theory, mixed convection flows, flows with mass transfer and the various methods available for solving the equations of boundary-layer theory. The remaining three chapters are constituted of the problems investigated by us. Each chapter commences with an introduction briefly summarizing earlier work relevant to the problem, followed by the author’s contributions. The governing equations, initial and boundary conditions are then delineated after which the details of the method of solution are presented. The results are then discussed with the aid of graphs and tables collectively placed at the end of each chapter. The chapter is wound up by giving the conclusions in brief. References cited in the chapter are listed at the end of each chapter. The various symbols used are defined as and when they arise but the most commonly occurring among them are listed at the end of the thesis, for convenience. The second chapter deals with the problem of unsteady incompressible mixed convection heat and mass transfer at a three-dimensional stagnation point. Coefficients of skin-friction and heat-transfer have been discussed in detail. Both aiding and opposing flow are considered. The final chapter deals with steady incompressible mixed convection flow about a rotating sphere. Two cases have been considered. In the first, the surface of the sphere is maintained at a constant temperature while in the second there is uniform heat flux from the surface of the sphere. The transformed non-similar equations have been solved using the implicit finite-difference method known as Keller’s Box method. The effects of rotation, buoyancy, viscous dissipation and mass transfer on the components of velocity in the longitudinal and transverse directions, the corresponding coefficients of skin friction, temperature and coefficient of heat-transfer have been delineated in detail. Both aiding and opposing flows have been considered. Papers based on the work presented in this thesis will be communicated for publication shortly.