Advanced Modeling and Optimal Temperature Control Strategy for the Bathtub

Juan YANG, Linling DUAN

College of Civil Engineering, Chongqing Jiaotong University, Chongqing, CHINA

Abstract: The modeling goal is to instruct the person in bath to maintain a constant water temperature simultaneously minimizing the water consumption. Three sub-models: the heat-transfer model for determining the optimal shape of bathtub, the time-space-based temperature field model to seek the distribution of the temperature field, a minimum water flow optimization model are applied to output the best strategy. In model one, the innovative “line-plane-space” approach is invoked to describe the process of heat dissipation inside the bathtub system. For various shape corresponds with different dissipation rate, the optimal shape of bathtub determined is oval. In model two, we simplify the process of water flowing from the faucet heating the tub into the problem of point heat ｓｏｕｒｃｅ heating medium. Then the unsteady heat conduction differential equation is given via Fourier transform and finally apply the difference method and multigrid method to obtain the distribution of temperature field. Model three is the optimization model targeting the minimum water flow with the constraint condition guaranteeing the even water temperature. By involving the global search algorithm, the optimal water flow is output as 0.0028 2 m s .

Keywords: Heat-transfer; Time-space-based temperature field; Minimum water flow optimization