The Model of Bathtub Water Temperature Control，

杨利霞

The Model of Bathtub Water Temperature Control

Abstract: In order to keep bath water closely to the start temperature, and the person could feel comfortable and
relaxed all the time with not wasting so much water, we establish the model to study change of water temperature
on adequate consideration of the shape/volume/ motion of the person in the bathtub.
First of all, without considering the factor of people and water, the convection and the thermal conductivity are
the main factors. We establish the model of the water temperature control. Secondly, two models are established on
the condition of water and people. In model one, people in the bathtub is stationary. The water is added to bathtub
when the temperature dropped to the lowest, while no water entering until the water temperature rises to a given
maximum temperature. Model two make the consideration of the movement of the people, other factors such as
bubble agent. Finally, we summary for the model established and provide suggestions.
Keywords water temperature control; mathematical model; heat convection; thermal conductivity