The Models of Heat Transfer on Choosing Optimal Pans

Abstract:

Considering the influence of different-shaped pans on space utilization and heat distribution, two models are established to investigate a balanced solution. In order to handle the problem of heat distribution on the outer edge, the first model establishes differential equations of heat convection in unstable state and gets definite conditions. Then we discretize the area of pans and get numerical solution by finite difference method. Having analyzed the numerical solution, our model finally concludes that the temperature field of a regular polygon can be regarded as a series of circles centering at its circumcenter and the temperature increases with the increment of the radius. As for the second model, we first calculate the maximum value of pans N in the oven by the arrangements of aligned and staggered modes. Then we normalize N by min-max method. Next, based on the rule of temperature field in the first model, the uniformity of heat distribution can be measured by the area ratio of a regular polygon to its circumcircle. After that, we use the linear weighted method to transfer the problem of multi-objective optimization into a single-objective one and draw the conclusions below: In aligned arrangement, we select round pans when p<0.3, rectangular pans when and pans in regular octagons when . In staggered arrangement, we select round pans when the value of p is small and pans in regular hexagons when the value of p is large. Eventually, through sensitivity analysis , our model proves to be stable and applicable.

• Periodical: Advanced Materials Research (Volumes 805-806)
• Pages: 504-514
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.805-806.504
• Online since: September 2013
• Authors: Kang Zhang
• Keywords: Differential Equations, Finite Difference Method (FDM), Multi-Objective Optimization (MOP), Normalization

References

[1] Yang shiming and Tao wenquan. Heat Transfer. Beijing: Higher Education Press, 2006: 163-210.

[2] M. Zerroukat, H. Power, and C.S. Chen. A numerical method for heat transfer problems using collocation and radial basis functions. International Journal for Numerical Methods in Engineering. Volume 42, Issue 7, pages 1263–1278, 15 August (1998).

DOI: 10.1002/(sici)1097-0207(19980815)42:7<1263::aid-nme431>3.0.co;2-i

[3] Xu Zibin and Min Jianqing. The Numerical Simulation of Heat Conduction Based on pdetool. Journal of Jiamusi University, 2006, 24(2): 270-273.

[4] Li Nannan, Wu Qing and Cao huilin. Sample Couse of Matlab 7. BeiJing: Tsinghua University Press, (2006).

[5] Li Hao, Yang Tianchun and Wang qiren. Solution Of Mathematical Physical Equations based on Matlab7. 0 PDE Tool BOX. Computer Development & Applications, 2009, 22(1): 26-27.

[6] Liu Yi, Cao Ju and Ling Shaodong. Cricles'stock layout problem. Forging & Stamping Technology, 2005(5): 33-35.

[7] http: /baike. baidu. com/view/1333537. htm.

[8] Liang Miaomiao, Lin Qiang and Wang Yang. Appraisal of domestic nursing journals by using normalized weighting method. Journal of Nursing Science, 2011(11): 88-90.

[9] Xu An. Multi-objective Programming Problems and Solutions. Journal of JiNan Communications College, 1995, 3(4): 11-17.