tailieunhanh - Design and Optimization of Thermal Systems Episode 2 Part 10

Tham khảo tài liệu 'design and optimization of thermal systems episode 2 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Problem Formulation for Optimization 447 Similarly a third-order model for the response z is z 00 P1x 02 y 03 xy 04x 1 2 05 y2 06x 2 y 07 xy2 08x 3 4 5 09 y3 7-9 where the P s are coefficients to be determined from the data and x y are the two independent design variables. Once the response surface has been generated visual inspection can be used to locate the region where the optimum is located and a closer inspection can then be used to accurately determine the location of the optimum. Calculus can also be used to identify the minimum or maximum. Both local and global optimum locations can generally be identified. However since a limited number of data points are used in order to generate the response surface the surface approximates the actual behavior and the results are similarly approximate though for many practical problems this is quite adequate. OPTIMIZATION OF THERMAL SYSTEMS We have considered the basic formulation for optimization as well as different methods that are available for solving these problems. Several physical problems have been mentioned as examples to illustrate the general approach. Let us now briefly consider these aspects as related to the optimization of thermal systems. Important Considerations Thermal systems are mainly concerned with energy and fluid flow. Therefore the objective function is frequently based on energy consumption which involves considerations of energy transport and losses efficiency of the system and its components energy exchange with the environment fuel consumed etc. A useful objective function is the rate of energy consumption per unit output where the output may be power delivered heat removed products manufactured and so on. The design that requires the least amount of energy per unit output is then the optimum. Similarly the system that delivers the largest output per unit energy consumption is optimum. Since energy consumption can be expressed in terms of cost this objective function can also be .