2016级美国大学生数学建模A题一等奖.pdfVIP

For office use only Team Control Number For office use only T1 ________________ F1 ________________ T2 ________________ 48074 F2 ________________ T3 ________________ F3 ________________ T4 ________________ F4 ________________ Problem Chosen A Summary For most people, having a hot bath is a pleasant experience. In this paper, we analyze the heat distribution of the water in bathtub combing the best inlet of water derived from the optimal model. And influences of the different shapes/inclination/volume of the tub, the motions made by the person and the addition of bubble additive on the models are discussed. Model 1 focuses on the heat distribution of the bathtub under steady state without person in it and establish the optimization model to obtain the best water inflow strategy. Firstly, we use the partial differential equation to describe the heat distribution with the boundary conditions derived from Fourier formula. Then we calculate the heat transfer coefficient of water-air, water-tub wall and bottom convection. After that, we study the uniformity of heat distribution by the variance of temperature and obtain the required flow of water with the help of Saint Venant’s Principle as and the energy conservation law. We find that when the inlet closes to the middle, the heat distributes more uniformly while more water flow. So we establish multi objective optimization model to fit the data polynomials after normalization and obtain the best inlet l