Is Newton’s Law of Cooling as special case of the CSTR problem?

Mathematically, it clearly is, yet I would love to have the physical validation additionally, and also I' m stuck on one particular action.

The remedy to the CSTR trouble starts similar to this:

$$f’(t) = \frac{qw – qf(t)}{V}$$

where $f(t)$ is the focus sometimes $t$, $q$ is the circulation price, $w$ is the focus of the inlet circulation, and also $V$ is the quantity.

Using this to the scenario of an air conditioning body, it is very easy to recognize $qw$ as the quantity of "coolness" getting here, yet I am incapable to warrant the quantity of "hotness leaving" as $qf(t)$, due to the fact that the "mixing" existing in the CSTR trouble appears lacking when it comes to an air conditioning body. It feels like the air conditioning body is shedding warmth just like an onion could be peeled off. So, an image or example that would certainly warrant the $qf(t)$ term would certainly be valued.

History: CSTR represents "Continuous Stirred Tank Reactor", which is an acronym for "Continuous Flow Stirred Tank Reactor". Locating an expression for the focus in the container sometimes $t$ is a book instance in Differential Equations.


Mike Jones

22. May.2011 (Beijing time)

2022-06-07 14:34:15
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Answers: 1

Physically there is no such point as "coolness", yet there is warmth. Warmth leaves the air conditioning body at a price symmetrical to the temperature of the body (that represents the term $-q f(t)/V$) and also gets in the body at a price symmetrical to the temperature of the setting (that represents the term $qw/V$).

2022-06-07 15:06:51