Regression models with correlated errors lead to nonadditivity of the information matrix. This makes the usual approach of design optimization (approximation with a continuous design, application of an equivalence theorem, numerical calculations by a gradient algorithm) impossible. A method is presented that allows the construction of a gradient algorithm by altering the information matrices through adding of supplementary noise. A heuristic is formulated to circumvent the nonconvexity problem and the method is applied to typical examples from the literature. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Numerical study of laminar convective cooling of ribs in a parallel plate channel is investigated. Single rib mounted on one channel wall in forced, mixed and free convection is analyzed. Furthermore, the series ribs array with in-line and staggered mounted on channel walls are considered. Through the use of a stream function vorticity transformation, solution of the transformed governing equations for the system is obtained using the control volume method with non-uniform grid. The effects of the Reynolds number, thermal conductivity ratio of rib to fluid and rib¡¦s profile area on heat transfer rate of single rib and rib array are presented. In addition, the effects of the length from inlet to the first rib and the space between ribs for rib array are carried out. A correlation for single and rib array in forced convection is presented to estimate the optimum aspect ratio of rib with various Reynolds number, thermal conductivity ratio of rib to fluid, rib¡¦s profile area. Furthermore, the results of different Gr/Re2 and various channel inclination angle in mixed convection are also examined numerically. The results indicate that both in forced and mixed convection, the optimum aspect ratio of a rib corresponding to the rib with maximum heat transfer rate increases with increasing Re but decreases with K for a fixed rib profile area. In forced convection the optimum aspect ratio of rib array increases with rib¡¦s space but decreases with the length from inlet to the first rib of channel. Then, numerical correlations to predict the optimum aspect ratio of single rib and rib array are developed for fixed rib¡¦s area with various Re, K and rib number. In mixed convection, the optimum aspect ratios of single rib and staggered rib array increase with not only the inclination angle but also Gr/Re2.

Waste oil emulsions are generated in several manufacturing processes. Such emulsions not only affect the efficacy of wastewater treatment but also influence the water quality of the effluent. Therefore, these waste oil emulsions that have to be treated before being released into the environment. Many processes have been developed for demulsifying such materials and microwave irradiation has been shown to be most effective in this respect. It does not require the addition of chemicals and the oil recovered from the emulsion can be reused. With microwave irradiation, there are two main mechanisms occurring simultaneously. One is the rapid increase of temperature which reduces the viscosity of the emulsion. The other is molecular rotation, which neutralizes the Zeta potential because of the rearrangement of electrical charges surrounding the water droplets. Hence, water droplets coalesce and result in the separation of the emulsion. Addition of inorganic salts has also been shown to improve the efficiency of microwave irradiation in demulsification owing to an increase in solvent conductivity, which accelerates the heating rate. This process is termed salt-assisted microwave irradiation. In the present study, we propose that NaCl and artificial seawater can be an economical source of cations required in salt-assisted microwave demulsification. Our experiments included batch tests of emulsion characteristics and the effects of microwave operating conditions on demulsification rate and separation efficiency of three oil-in-water (O/W) emulsions (mineral oil, vegetable oil, and mineral-oil/vegetable-oil mix). First study was aimed to examine the demulsification of an O/W cutting oil emulsion with the addition of NaCl under microwave irradiation. This work investigates the effect of a set of operating variables, including irradiation time, irradiation power, dosage of NaCl, settling time, pH and the initial oil concentration, on the separation efficiency in the treatment of an oil in water (O/W) type cutting oil emulsion by microwave assisted demulsification. As a result of a series of batch demulsification tests a set of optimum operating conditions was found, consisting of 2 min of microwave irradiation at 280 W, the addition of 14 g/L of NaCl, 60 min settling time, and at a pH of 9.5. A separation efficiency of 93.8% was obtained with these conditions for 50 mL of cutting oil emulsion with an initial oil content of 10 g/L. The objective of the second study was to examine the demulsification of an O/W cutting oil emulsion, an olive oil emulsion, and a 1:1 cutting-oil/olive-oil emulsion mix, using a proposed process termed as seawater-assisted microwave irradiation demulsification. We conducted batch demulsification tests on 50-mL aliquots with an initial oil content of 10 g/L, and found that the separation efficiencies of a cutting oil emulsion, an olive oil emulsion, and a cutting-oil/olive-oil mix reached 93.1%, 92.6%, and 93.2%, respectively, using our optimum operating conditions, which were 40 sec of microwave irradiation at 700 W, a 60 min settling time, and addition of 12%, 32%, and 20% (all v/v) of artificial seawater, respectively. Using this set of operating conditions, a decrease in solution pH was found to significantly increase the demulsification efficiency after addition of inorganic acid, whereas an increase in the concentration of surfactant, sodium dodecyl sulfate (SDS), resulted in a decrease in efficiency. In addition, our test data were explored using a stepwise regression method, yielding a multi-variable equation. This empirical equation was able to describe separation efficiency rather well, after exclusion of tests showing separation efficiency below 40% and temperature higher than the boiling point. This study could provide essential information related to O/W emulsions using salt-assisted microwave demulsification.

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