Time decay function model based on Newton's Law of cooling

Summary

Newton's cooling law mathematical models are generally used for time-related attenuation of the model, such as the change in time, the user to a certain category of product attenuation process changes, the user in the voting process of the number of votes attenuation process simulation and other basic principles are based on the Newton's cooling law, increase the corresponding boundary conditions, To get a model that suits your own application scenario.

Newton's model of cooling law

Newton's cooling law describes one thing is that a relatively hot object, in a temperature than this object under the environment, the temperature of the hotter object is to be reduced, the ambient temperature is to rise, the temperature of the object and the surrounding temperature to achieve a balance, in the process of temperature change is not a regular ah? Our great scientist, Newton, considered the problem, and found the law, which is the rate at which the temperature of the object is lowered and the object and

The difference between the current temperature and the surrounding is proportional, and the mathematical representation is:

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Where: T (t): The current temperature of the object

H: for the ambient temperature

K: for the scale factor

The above formula can be seen as a differential equation

The solution of Newton's cooling law model

It can be seen as a differential equation, and it is a simple differential equation that can be solved with a slight change:

To do a transformation of the above style is as follows:

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The alignment is changed again, and the equivalence is obtained on both sides of the equation:

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So the above is the two most basic two formula to calculate the integral:

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Therefore, the solution of Newton's cooling law can be obtained:

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B is the solving factor of differential equation, and the conversion can be obtained as follows:

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There is also a variable C in the final result, which we need to solve according to the initial conditions: T (0): The initial temperature of the object, H: The temperature of the ambient, t0 the initial moment, with the upper formula can be obtained:

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The expression of C is brought into the formula to be solved:

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When h equals 0, you can get the following formula:

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You can see the decay of the Newton cooling formula, K is our own set of attenuation coefficient, after t time, the object is the current problem is the initial temperature and decay rate product

Based on the Newton cooling formula combined with our own application scenario, we can give our own mathematical model of time decay, but these models are based on the Newton cooling formula.

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Time decay function model based on Newton's Law of cooling