June 18, 2006
June 18, 2006
June 21, 2006
Energy Conversion and Conservation
11.389.1 - 11.389.14
Deductive Problem Solving Strategy Applied to the Optimization of Wall Insulation
The current approach to problem solving in undergraduate engineering education allows the students to use a combination of inductive and deductive methods. Problems are well defined with all the required input information provided in the problem statement. Students are able to hone their analytical skills well with these exercises. Unfortunately, this does not help them with problem formulation skills that they will need when they enter the work force. There when they are given a problem they will be fortunate if they have a well-defined objective.
This paper provides instructors and students with a method that will help them better formulate problems. Problems are presented without specifying the inputs needed for the solution. The student then applies the deductive approach to lead them to identify for themselves which inputs are required to solve the problem. Although the problems are open-ended the method provides the structure the student needs to break a large problem into manageable pieces.
The deductive approach begins by determining how the objective of the problem can be quantified. In design problems this is often an optimization. Most optimizations require a cost analysis to compare the competing forces on an equivalent basis. After that the laws of nature (e.g. conservation of energy, conservation of mass, Fourier’s Law of Conduction, etc.) are used to connect the desired result to variables that can be measured directly or specified.
The deductive approach was used extensively in a graduate level course on heat transfer in the summer of 2005 and is being used in the second semester of thermodynamics during the spring semester of 2006. The feedback from students has been positive. One graduate student stated in his course evaluation that the deductive approach is a wonderful tool for engineers. Out of a class of 27 thermodynamic students 21 thought it was beneficial to track the equations and unknowns, 19 found the systematic nature of the approach beneficial, 10 stated it was easier to follow the work and seven found it beneficial to solving open-ended problems when compared to standard textbook problems.
In this paper, an example is provided that shows how the method is applied to determining the optimal thickness of insulation in a building. For wall insulation the major competing forces in the optimization are initial costs of the insulation and energy costs. Since there is a high degree of uncertainty in many of the input variables a non-dimensional sensitivity analysis was useful to prioritize the data collection process. The example problem is relevant for undergraduate and graduate courses in heat transfer and optimization as well as air conditioning and refrigeration design courses. However, any textbook problem can be adapted to accommodate the deductive strategy by removing the specified inputs for the problem.
Zietlow, D. (2006, June), Deductive Problem Solving Strategy Applied To The Optimization Of Wall Insulation Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--13
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