Math Modeling Research of Constant Temperature Bath

This paper studies how the temperature in the bathroom keeps changing when people bathe in the bathtub. Firstly, the shape, capacity, behavior and body posture of people in the bathroom are considered. In fluid mechanics point of view, we consider the impact of the flow of heat transfer, by the energy differential equations and boundary layer momentum to establish a set of partial differential equations, and use Laplace operator rewrite it .Then, using finite difference method (FDM), with Taylor series expansion. We use the function value of grid nodes of difference quotient instead of control equation of derivative, and discretize it, solve the heat conduction equation.