The continual advance in manufacturing processes has resulted in significantly more compact, high performance, devices. Consequently, heat extraction has become the limiting factor, and of primary concern. Therefore, a substantial amount of research has been done regarding high efficiency micro heat exchangers, employing novel working fluids. This dissertation numerically investigated the thermal behaviour of microchannel elements cooled by Newtonian and non-Newtonian fluids, with the objective of maximising thermal conductance subject to constraints. This was done, firstly, for a two-dimensional simple microchannel, and secondly, for a three-dimensional complex microchannel. A numerical model was used to solve the governing equations relating to the flow and temperature fields for both cases. The geometric configuration of each cooling channel was optimised for Newtonian and non-Newtonian fluids, at a fixed inlet velocity and heat transfer rate. In addition, the effect of porosity on thermal conductance was investigated. Geometric optimisation was employed to the simple and complex microchannels, whereby an optimal geometric ratio (height versus length) was found to maximise thermal conductance. Moreover, analysis indicated that the bifurcation point of the complex microchannel could be manipulated to achieve a higher thermal conductance. In both cases, it was found that the non-Newtonian fluid characteristics resulted in a significant variation in thermal conductance as inlet velocity was increased. The ii characteristics of a dilatant fluid greatly reduced thermal conductance on account of shear-thickening on the boundary surface. In contrast, a pseudoplastic fluid showed increased thermal conductance. A comparison of the simple and complex microchannel showed an improved thermal conductance resulting from greater flow access to the conductive area, achieved by the complex microchannel. Therefore, it could be concluded that a complex microchannel, in combination with a pseudoplastic working fluid, substantially increased the thermal conductance and efficiency, as opposed to a conventional methodology. / Dissertation (MEng)--University of Pretoria, 2012. / gm2014 / Mechanical and Aeronautical Engineering / unrestricted