The Best Hot Water Strategy for Bathtub

Through the analysis of the heat distribution inside the bathtub affected by different tempe ratures. The paper finds that the best strategy the person in the bathtub can adopt to keep the temperature even throughout the bathtub and as close as possible to the initial temperature without wasting too much water. Furthermore, according to the requirements given by the problem, the authors propose a evaluation method to determine the extent to which the strategy depends upon given factors. The paper proposes one model and one algorithm. The model can be used to find the best strategy of bathtub problem. In the analysis of this model, according to the questions given by the problem, we proposed two main factors: quality of heating water and different ways of adding hot water. Then, the paper analyzes the changing speed of bathtub water as hot water added in two different ways, adding heat flux density Q and specific heat capacity of water C in order to construct energy conservation equation. Then, we proposed two ways of adding hot water as the best strategy in response to the condition given by the problem. For the first way of adding hot water continuously, PDE and CFD simulation are adopted to model the temperature of the bathtub water in space and time; for the other way of adding hot water at regular intervals, we use energy conservation equation and Recursive Computation of Space Multibody Dynamics, to develop a model in space and time. By comparing these two ways, we get the best strategy the person in the bathtub can adopt to keep the temperature even throughout the bathtub and as close as possible to the initial temperature without wasting too much water. Multiple linear regression equation is used to determine the extent to which our strategy depends up on given factors. These factors can also affect the heat conduction, heat convection and heat radiation which are taken into consideration in energy conservation equation.