Thesis Ph.D. ((Applied Mathematics)) -- University of Limpopo, 2022 / The world is under threat from the devastating effects of the continued depletion of the Ozone layer. Increased global warming is causing catastrophic ecological damage and imbalance due to accelerated melting of glaciers, rampant runaway veld res, widespread floods and other extreme events. The delegates to the Cop26 Climate Change Summit were reminded that the continued burning of fossil fuels is releasing carbon into the atmosphere at an unprecedented pace and scale and that the world is already in trouble. Complete substitution of fossil fuels with clean energy sources is the only solution through which the world can be saved from the deleterious effects of global warming. However, total dependence on renewable energy sources can only be possible through novel technology that enables efficient energy utilization and conservation. For instance, the evolution of advanced techniques in manufacturing processes has led to the reduction in the size of various industrial and engineering designs that consume reduced amounts of energy. Efficient energy utilization in thermo-fluid flow systems can be achieved through entropy generation minimization. Entropy is a thermodynamic quantity that represents the unavailability of a system's thermal energy for conversion into mechanical work. In this study, thermodynamic analysis of reactive variable properties third-grade fluid flow in channels with varied geometries and subjected to different physical effects was investigated with the second law of thermodynamics as the area of focus. Entropy generation and inherent irreversibility analysis were the main focus of the study where the sensitivities of these quantities to the embedded parameters were numerically and graphically described and analysed. The semi-analytic Adomian decomposition method, the semi-implicit fi nite difference scheme and the spectral quasilinearisation method were employed to solve the nonlinear differential equations modelling the flow systems. The results reveal that the effects of the parameters on flow velocity, fluid temperature, entropy generation and inherent irreversibility cannot be neglected. In particular, conditions for entropy generation minimization were successfully established and documented. / University of Limpopo