Problem solving examples

This problem-solving example addresses a complicated base-catalyzed reaction, using the system for proposing mechanisms summarized in Appendix 3A. The problem is to propose a mechanism for the base-catalyzed reaction of ethyl acetoacetate with methyl vinyl ketone. 

Twenty-nine of 31 successful problem-solving examples were described as open and free from outside influences that might have created road blocks . They involved very open brainstorming , open and honest communication , and open-mindedness to new ideas of stakeholders. Product engineers had authority to ask for help and direct control over design or process changes if needed . 

Characterization of fiber microstructure normally requires several microscopy techniques, as was shown in the simple example in the last section. An optical cross section of a fiber may have a dogbone shape (Fig. 5.2D), and yet this image does not reveal much about the internal fiber structure. On the other hand, a fracture surface of a fiber may reveal the presence of internal detail when viewed in the SEM (Fig. 5.11), and yet still not provide a complete picture of the structure. Clearly, complementary microscopy techniques and nonmicroscopy techniques must be applied to solving structural problems. Specific problem solving examples are described here which are representative of the wide range of studies conducted and documented in the many journals that publish polymer research. 

Isoparametric mapping removes tlie geometrical inflexibility of rectangular elements and therefore they can be used to solve many types of practical problems. For example, the isoparametric C continuous rectangular Hermite element provides useful discretizations in the solution of viscoelastic flow problems. 

Isoparametric mapping described in Section 1.7 for generating curved and distorted elements is not, in general, relevant to one-dimensional problems. However, the problem solved in this section provides a simple example for the illustration of important aspects of this procedure. Consider a master element as is shown in Figure 2.23. The shape functions associated with this element are... 

Over 50 solved example problems are sprinkled throughout the book. 

Seven of the tools of quahty have been summarized (43). The first tool is a flow chart, used to help understand the organizational flow of a procedure or process. A flow chart should be constmcted with the fiiU participation of the people who do the work. Its principal benefit is to enable teams, such as problem-solving or productivity improvement teams, to reach a common vision of the work flow. Its use enables the improvement effort to begin with this common understanding. Figure 3 contains an example for manufacture of a polymeric material. 

Application. In addition to providing a relatively simple means for estimating the production of separation cascades, the separative capacity is useful for solving some basic cascade design problems for example, the problem of determining the optimum size of the stripping section. 

Neural networks have the following advantages (/) once trained, their response to input data is extremely fast (2) they are tolerant of noisy and incomplete input data (J) they do not require knowledge engineering and can be built direcdy from example data (4) they do not require either domain models or models of problem solving and (5) they can store large amounts of information implicitly. 

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. 

Example 3 Shortcut Calculation Case A Let us solve the problem in Example 2 by using the shortcut calculation method assuming immiscible solvents, case A. 

Example 4 Shortcut Calculation Case B Let iis solve the problem in Example 2 hy assuming case B. The solute (acetic acid) concentration is low enough in the extract so that we may assume that the mutual solubilities of the solvents remain nearly constant. The material balance can be calculated by an iterative method. 

In problem solving and process studies, the front-end work is important. Proper definition and direction developed at the beginning will assure meeting corporate goals in a timely fashion. This section establishes the type of study example to be used for illustrating principles and philosophy, and presents the basic items necessary to begin such a study. 

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