Construction method for bathtub temperature control model
A construction method and bathtub technology, applied in instrumentation, design optimization/simulation, calculation, etc., can solve problems such as waste of water resources, troublesome addition of hot water, and reduction of people's bathing comfort
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[0122] In the process of building the temperature control model of this embodiment, it is first necessary to determine the model of the water temperature in the bathtub in terms of space and time. It is easy to think that this is a heat conduction problem in the mathematical physics equation, and the boundary conditions belong to the third type of boundary conditions . Since this is a three-dimensional problem, the amount of numerical calculation is large, which brings difficulties to the solution of the problem. The first problem we need to overcome is how to reduce the dimension. For a simple 3D partial differential equation:
[0123] u'=Δ 3 u+f (1)
[0124] where u is a three-dimensional space-time variable function u(x,y,z,t), Δ 3 is the three-dimensional Laplace operator f(x,y,z,t) is the source-sink term. According to Beer Lambert's law, it can be assumed that it has a solution of separating variables:
[0125] u=f(x,y,t)g(z,t) (2)
[0126] In this paper, g(z, t)...
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