Thesis submitted in fulfillment of the requirements for the degree Doctor of Technology: Mechanical Engineering Cape Peninsula University of Technology, 2013 / Fluid flow through a porous channel and cylindrical pipe walls are important area of research due to its wide applications in transpiration cooling, gaseous diffusion technology, cooling of rocket, mechanized irrigation and filtration processes. It is therefore necessary to examine the effect of Navier slip, combined effects of buoyancy forces and variable viscosity on the entire flow structure. Analyzing the magneto- hydrodynamics (MHD) of unsteady flow with buoyancy effect and also investigate numerically the entropy generation in an unsteady flow through porous pipe. We have also examined the thermal stability and entropy generation in the system. The problems were investigated theoretically using appropriate mathematical models for both transient and steady state scenario. Both analytical techniques and numerical methods are employed to tackle the model nonlinear equations derived from the law of conservation of mass, momentum and energy balance. Some definitions of terms to come across and introduction to fluid flow are given in chapter 1, together with literature reviews, statement of problem and objectives of the study. Chapter 2 lays the foundation for basic fundamental equations governing fluid flow. In chapter 3, the combined effect of suction/injection and asymmetric Navier slip on the entropy generation rate for steady flow of an incompressible viscous fluid through a porous channel subjected to different temperature at the walls are investigated. Chapter 4 analyze combined effects of buoyancy forces together with Navier slip on the entropy generation in a vertical porous channel wall with suction/injection wall. Analysis of MHD unsteady flow through a porous pipe with buoyancy effects are carried out in chapter 5, while chapter 6 investigates numerically entropy generation of unsteady flow through a porous pipe with suction and chapter 7 gives concluding remarks.

Title: Incompressible fluids with temperature dependent visco- sity, numerical analysis and computational simulations Author: RNDr. Oldřich Ulrych Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., DSc. Abstract: Flows of incompressible fluids connected with significant exchange of ther- mal and mechanical energy and with material moduli varying with the temperature and the shear rate, are described by the balance equations for linear momentum and energy, complemented by suitable constitution equations for the Cauchy stress and the heat flux. Assuming sufficient smoothness of quantities involved, the energy balance equation exhibits several equivalent formulations. However, within the context of weak solution, these formulations are, in general, not equivalent. This thesis is based on the existence theory for the generalized Navier-Stokes-Fourier system describing planar flow of fluids with a shear and temperature dependent vis- cosity. We specify parameters of a generalized power-law model under which weak formulations of balance equations are meaningful and both considered formulations of the energy balance equation are equivalent. Supported by the existence theory, we propose and numerically solve several problems pursuing the aim to systematically compare the...