Research on Bathtub Water Temperature Control Strategy and Model

For the problem of how to keep water temperature constant and minimize water usage, this passage mainly discuss four parts to research. Consider that there exists thermal dissipation, and four types of thermal dissipation are heat conduction, thermal radiation, evaporative cooling and heat convection. The first step: discuss about the problem on condition of natural environment. There are two types of thermal dissipation of water in bathtub, one is by water contacting with air while another one is heat conduction of bathtub. Accumulate four types of thermal dissipation and then we obtain the relation of thermal dissipation with contacting area, initial water temperature in bathtub with stability of water in bathtub. Based on thermodynamic principle, we build three-dimensional partial differential equation of heat conduction from bathtub's surface. Finally, we have the distribution graph of relation between temperature and time, space variation. The second type: Based on principle of Energy Conservation, we obtain the generalized partial differential equation of process of water dynamic variation with entering water's temperature and outside temperature, and solve for problem that considering factors such as temperature variation with disturbance and bubble. The third step: Obtain the best designed model based on constant temperature, consider the minimum water usage and design length, volume and shape of the best designed bathtub. The fourth step: Use fuzzy PID algorithm to test and then obtain the convergence result. Proving that the built model is easy to adjust temperature and doesn't possess big errors.