The Model of Water Temperature Change in the Bathtub

This paper describes model testing of bathtub with the purpose of remaining the water temperature in the bathtub constant and reducing water waste. I establish a model and draw a conclusion. The model describes changes in the temperature of the bathtub water. The model has two parts: the one is endothermic process that a constant trickle of hot water reheats the bathing water and the other one is exothermic process. The exothermic process is divided into three parts: on the water surface, on the bathtub wall and between bathtub bottom and ground. Finally, I get a formula about the temperature of the water according to the theory of thermology. I find that it is effective for bubble bath additive to help to keep the temperature constant in the extended model I carry out numerical calculation by using Runge-Kutta method and compare analytic and numerical results with reality, using default parameters; I validate that my method is correct and robust.