This paper describes a 25‐year project in which we defined problem solving, identified effective methods for developing students' skill in problem solving, implemented a series of four required courses to develop the skill, and evaluated the effectiveness of the program. Four research projects are summarized in which we identified which teaching methods failed to develop problem solving skill and which methods were successful in developing the skills. We found that students need both comprehension of Chemical Engineering and what we call general problem solving skill to solve problems successfully. We identified 37 general problem solving skills. We use 120 hours of workshops spread over four required courses to develop the skills. Each skill is built (using content‐independent activities), bridged (to apply the skill in the content‐specific domain of Chemical Engineering) and extended (to use the skill in other contexts and contents and in everyday life). The tests and examinations of process skills, TEPS, that assess the degree to which the students can apply the skills are described. We illustrate how self‐assessment was used.

This study was undertaken to ascertain the accuracy of finite-difference solutions for flow around spherical particles in the intermediate Reynolds number range. Comparison of the results with experimental data on drag coefficients, frontal stagnation pressure, and wake geometry indicated good agreement. The approximate solutions, in which the Galerkin method and asymptotic analytical predictions were utilized, were evaluated by using the finite-difference solutions as a standard. These methods were used to calculate the effect of uniform and nonuniform mass efflux on the drag and flow characteristics around a sphere. Theoretical solutions indicated that nonuniform mass efflux can significantly reduce the drag on a submerged object. Ranges of applicability of the approximate methods were established.The laws of motion of a single spherical partical in an undisturbed fluid stream (that is, one in which there is no secondary motion) have been the sub'ect of many investigations (1, 2 ) . The macroscopic hy a! rodynnmical characteristics, exemplified by the drag coefficient, are wellestablished over a large Reynolds number range by numerous experimental studies ( 3 to 7). Obtained from these data are a number of quite accurate experimental correlations (8 to 10) over the range of interest in the present study (0 7 N R~ 7 500). More detailed investigations (11 to 14) reveal not only widely differing flow patterns in the various Reynolds number regimes, but also indicate that the region of present interest is very little understood. This lack of knowledge is best exemplified by conflicting evidence of the first appearance of a vortex ring (1 5 to 1 7 ) .We believe that the most reliable experimental investigation of the wake region is that of Taneda ( 1 7).An analytical solution of the complete Navier-Stokes equations is impossible at the present time owing to their nonlinearity. Although numerous approximate solutions have been obtained (18 to 21, 22 to 39), virtually the only exact solutions available are those of Stokes ( 4 0 ) (that is, N R e z I ) and the potential flow solution. The most successful approximate solutions have been obtained by use of the boundary-layer assumptions (22 to 3 2 ) . Although the literature contains an almost endless number of techniques for solving the boundary-layer equations, the most rigorous and accurate solution is that of Frossling (32). For the frontal stagnation point the theoretical treatment of Ilomann ( 4 2 ) probably yields the most accurate results.Although the lower Reynolds number limit of applicability of the boundary-layer solutions should be well above 200, they have been widely applied well below this value. Experimental justification of this extrapolation, for example, by the comparison of theoretical and experimental drag coefficients, has not been possible as the boundarylayer solutions are only applicable up to the flow separation point. At present there is no adequate mathematical description of the wake region. Thus, the boundary-layer solutions, although yield...

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The catalytic hydrogenolysis of n-butane was investigated in an integral packed bed reactor (0.70 mi. ID by 25 cni. long). The catalyst was 105; nickel on silica gel. A block factorial set of experiments was performed at hydrogen-to-butane feed ratios of 4. to 9., temperatures of 240% to 282OC and feed flowrates of 1.0 to 1.8 ml/sec. T h e predominant reaction appeared to be the r e m a d of terminal methyl groups.Kinetic rate expressions were developed to predict the product distribution, taking into account a five-fold change in catalytic activity. A parameter estimation strategy, applying non-linear regression theory, was used to obtain the ten kinetic parameters. Error analysis of the parameters was performed using likelihood ratios. Models were developed to describe the catalyst activity changes observed during experinrentation. The kinetic model predicts the experimental observations very accurately over all conversions and shows some deviation only a t the combination of high temperature and low feed ratio.nvestigations have been reported in the literature

An experimental study of the rate of evaporation of stationary droplets of water, methanol, cumene, pentane and benzene was carried out in an electrically‐heated 9‐inch stainless steel sphere. The gaseous environment consisted of the superheated vapor of the liquid under investigation and, in all cases, the wall and gas temperatures were the same. Drop diameters ranged from 0.4 to 1.4 mm., and temperatures from 100°C. to 550°C. The evaporation rate of stationary droplets in high temperature surroundings does not appear to be governed by the rate of heat transfer by natural convection, since no dependency of the Nusselt Number on the Grashof Number was found. Attempts to correlate the results on the basis of Godsave's model (conduction across the boundary layer controlling) or Spalding's modified approach to the latter were equally unsuccessful. The experimental evaporation rates could, however, be very satisfactorily correlated in terms of Spalding's Transfer Number B. The correlation obtained indicates that the mechanism of the evaporation process is governed by the effect of the evolved vapors on the boundary layer flow.