By using the finite element method to solve the appropriate momentum and energy equations the friction factors and Nusselt numbers for fully developed laminar flow were determined for one- and two-dimensional flow systems. The Nusselt numbers were determined for domain boundaries subjected to a constant heat flux (H1) or a constant surface temperature (T) around the computational boundaries and in the axial directions. C++ programs, that were rewritten and extended from previous programs, were used to solve the laminar flow and to determine the values. The required wall shear stresses and heat fluxes were directly obtained for a duct as part of the primary finite-element solution; these values were then used to determine the Nusselt number and friction factor for the specific duct. The computations were performed for circular-, annular-, trapezoidal-, rectangular- and triangular ducts. Special emphasis was placed on trapezoidal ducts since only a limited number of studies have been performed on trapezoidal duct shapes and none of these studies employed the finite element method. Excellent agreement was found when the determined values were compared with the values reported in the literature. In general, the agreement of the values improved as the number of elements was increased. It was, therefore, concluded that the methods used in this study yielded friction factors and Nusselt numbers that are very accurate and usable. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2009.

By using the finite element method to solve the appropriate momentum and energy equations the friction factors and Nusselt numbers for fully developed laminar flow were determined for one- and two-dimensional flow systems. The Nusselt numbers were determined for domain boundaries subjected to a constant heat flux (H1) or a constant surface temperature (T) around the computational boundaries and in the axial directions. C++ programs, that were rewritten and extended from previous programs, were used to solve the laminar flow and to determine the values. The required wall shear stresses and heat fluxes were directly obtained for a duct as part of the primary finite-element solution; these values were then used to determine the Nusselt number and friction factor for the specific duct. The computations were performed for circular-, annular-, trapezoidal-, rectangular- and triangular ducts. Special emphasis was placed on trapezoidal ducts since only a limited number of studies have been performed on trapezoidal duct shapes and none of these studies employed the finite element method. Excellent agreement was found when the determined values were compared with the values reported in the literature. In general, the agreement of the values improved as the number of elements was increased. It was, therefore, concluded that the methods used in this study yielded friction factors and Nusselt numbers that are very accurate and usable. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2009.

The problem of laminar and turbulent conjugate mixed convection flow and heat transfer in shallow enclosures with a series of block-like heat generating components is studied numerically for a Reynolds number range of zero (pure natural convection) to typically 106, Grashof number range of zero (pure forced convection) to 1015 and various block-to-fluid thermal conductivity ratios, with air as the working medium. The shallow enclosure has modules consisting of heat generating elements, air admission and exhaust slots. Two problems are considered. In the first problem, the enclosure has free boundaries between the modules and in the second problem, there are partitioning walls between the different modules. The flow and temperature distributions are taken to be two-dimensional. Regions with the same velocity and temperature distributions can be identified assuming repeated placement of the blocks and fluid entry and exit openings at regular distances, neglecting end wall effects. One half of such rectangular region is chosen as the computational domain taking into account the symmetry about the vertical centreline. On the basis of the assumption that mixed convection flow is a superposition of forced convection flow with finite pressure drop and a natural convection flow with negligible pressure drop, the individual flow components are delineated. The Reynolds number is based on forced convection velocity, which can be determined in practice from the fan characteristics. This is believed to be more meaningful unlike the frequently used total velocity based Reynolds number, which does not vanish even in pure natural convection and which makes the fan selection difficult. Present analysis uses three models of turbulence, namely, standard k-ε (referred to as Model-1), low Reynolds number k-ε (referred to as Model-2) and an SGS kinetic energy based one equation model (referred to as Model-3). Results are obtained for aiding and opposing mixed convection, considering also the pure natural and pure forced convection limiting cases. The results show that higher Reynolds numbers tend to create a recirculation region of increasing strength at the core region and that the ranges of Reynolds number beyond which the effect of buoyancy becomes insignificant are identified. For instance, in laminar aiding mixed convection, the buoyancy effects become insignificant beyond a Reynolds number of 500. Results are presented for a number of quantities of interest such as the flow and temperature distributions, local and average Nusselt numbers and the maximum dimensionless temperature in the block. Correlations are constructed from the computed results for the maximum dimensionless temperature, pressure drop across the enclosure and the Nusselt numbers.