Research on the temperature of the bathtub water

When a person fills a bathtub with hot water and settles into the bathtub,the bath gets noticeably cooler.In order to study the temperature even throughout the bathtub and as close as possible to the initial temperature, we need develop a model of the temperature of the bathtub water in space and time.First,we figure out the heat loss,then replace three-dimensional partial differential equations with two two-dimensional equations.Based on the finite difference method,we make time domain and space domain discrete, list discrete node equations by using heat balance mothod and solve discrete node equations.