浴缸水温控制的最优注水方案研究

Optimal water injection scheme for water temperature control of bathtub

浴缸是人们日常生活中必不可少的一种生活用具。基于流体流动和热量传递的原理,本文研究了水经热水器加热后再输送至浴缸过程中水温的控制模型以及浴缸热水温度分布状态。理论推导得到了浴缸中水的传导传热和对流传热的传递方程,通过联系人体皮肤与外界环境的热量交换方程,获得单位时间内应注入浴缸的热水量体积为:Q_V=∫Ω(T)(t/T+U·▽t-λ/cp·▽~2t+ηA_f/cpV·(T_(water)-T_(outside)-XA_P/cpV·(T_(average)-T_(outside)))dV/T_(hotwater)-T_(water)。给定边界条件,以C语言程序得到近似数值解并利用Matlab绘制浴缸内水的温度场分布图,最后将三维温度场简化为一维温度场,求得热水流量数值8.227×10^(-3)m^3/s,符合实际情况。

Bathtub is an indispensable living tool in people’s daily life. Based on the principle of fluid flow and heat transfer, the control model of water temperature and the temperature distribution of hot water in bathtub are studied in this paper. The heat transfer equation of water conduction and convection in bathtub is deduced theoretically. By connecting the heat exchange equation between human skin and external environment, the volume of hot water to be injected into bathtub per unit time is obtained as follows： QV=∫Ω（τ）〔 t/ τ＋U· t -λ/cρ· 2t＋ηAf/cρV·（Twater-Toutside）-χAD/cρV·（Taverage-Toutside）〕dVgiven the boundaryconditions, the approximate numerical solution is obtained by C language program, and the temperature field distribution of the water in the bathtub is plotted by using MATLAB. Finally, the three-dimensional temperature field is simplified into one-dimensional temperature field, and the value of hot water flow is obtained by 338.227× 10-3m3/s, it is in line with the actual situation.