Numerical Simulation of Heat Transfer in Bathtub

Abstract

Abstract. We analyze both the heat loss and heat absorption of water in the bathtub, establish the model of water temperature in time and space, by establishing a coordinate system in the shape of rectangular. We use the finite element method to solve the model and take interpolation method thinking about average temperature and water flow rate to find the best strategy to keep water temperature constant without wasting too much water. For example, a 1.7m tall man with normal weight has a bath in 40 degrees Celsius for ten minutes in the bathtub of which size is 1.6*0.8*0.7 . The best strategy to keep the temperature constant is to let the temperature of the hot water be 42.3 degrees Celsius and the flow rate of the faucet be 0.031 . Next, we change the shape and the volume of the bathtub, the shape, the volume, the temperature and the motions of the person respectively to simulate the different situation, with the introduction of the average temperature deviation degree, we analyze the change of the results of the model qualitatively. We find three primary elements, which are the volume of the bathtub, the volume of the person the motions of the person. The deviation of volume change of bathtub reaches 23% and the highest deviation of volume of the person reaches 25%, and the deviation of motions of the person reaches 17%. The deviation of the change of other elements reaches 5%. Therefore, this strategy is more related to the volume of the bathtub, the volume of the person and the motions of the person.