Given the surmounting disagreement amongst researchers in the area of liquid flow behavior at the microscale for the past thirty years, this work presents a fundamental approach to analyzing the pressure losses experienced by the laminar flow of water (Re = 7 to Re = 130) through both rectangular straight duct microchannels (of widths ranging from 50 to 130 micrometers), and microchannels with sudden expansions and contractions (with area ratios ranging from 0.4 to 1.0) all with a constant depth of 104 micrometers. The simplified Bernoulli equations for uniform, steady, incompressible, internal duct flow were used to compare flow through these microchannels to macroscale theory predictions for pressure drop. One major advantage of the channel design (and subsequent experimental set-up) was that pressure measurements could be taken locally, directly before and after the test section of interest, instead of globally which requires extensive corrections to the pressure measurements before an accurate result can be obtained. Bernoulli's equation adjusted for major head loses (using Darcy friction factors) and minor head losses (using appropriate K values) was found to predict the flow behavior within the calculated theoretical uncertainty (~12%) for all 150+ microchannels tested, except for sizes that pushed the aspect ratio limits of the manufacturing process capabilities (microchannels fabricated via soft lithography using PDMS). The analysis produced conclusive evidence that liquid flow through microchannels at these relative channel sizes and Reynolds numbers follow macroscale predictions without experiencing any of the reported anomalies expressed in other microfluidics research. This work also perfected the delicate technique required to pierce through the PDMS material and into the microchannel inlets, exit and pressure ports without damaging the microchannel. Finally, two verified explanations for why prior researchers have obtained poor agreement between macroscale theory predictions and tests at the microscale were due to the presence of bubbles in the microchannel test section (producing higher than expected pressure drops), and the occurrence of localized separation between the PDMS slabs and thus, the microchannel itself (producing lower than expected pressure drops).

This report deals with the mathematical model of the transient behaviour of an existing ethane dehydrogenation furnace which is composed of two main sections: a preheating convection section and a radiant-heated section. The correlation of pressure drop with time has been found from the available data. The fractional carbon deposition and the multiplier coefficient of a pressure drop equation have been determined by the direct search optimization technique of Hooke and Jeeves. An optimal policy for the cyclic operation of the furnace was determined by considering plant temperature profile and hydrocarbon/ steam ration as parameters for maximizing average ethylene produced per day. The effect of temperature profile on the distribution of carbon deposited along the reactor was also predicted and discussed. / Thesis / Master of Engineering (ME)

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