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Quite a general question...

I am referring to a scientific paper : http://www.springerlink.com/content/41p817v1584q1850/

I am trying to model water temperature over a year.

I have the initial value which is 30 for Tw (water temperature).

The author says that equation 1 should be easily integrated. Would I have to integrate all equations feeding into the equation?

Unfortunately the modeller for this paper has passed away and the remaining authors are unsure how he modelled for water temperature. Need a mathematician :)

For now I have made the input vatiables static assumptions over time.

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There are quite a number of quantities going into that equation; some of them seem to come from measurements; and a specific time-dependence is given for none of them. In that context, I can only understand the claim that "equation (1) can easily be integrated" as saying that it can be integrated numerically if you know all the inputs. If it's meant to claim more than that, that seems to be an unsubstantiated claim. –  joriki Oct 14 '12 at 15:25
    
I am also not sure if these inputs are for one second or a general input. May I ask how you would integrate equation 1 if you assumed all the input variables were static over time? Would you simply divide the left hand side by pw*cw*d? Many thanks –  katrinajames Oct 14 '12 at 16:14
    
Yes, that would give you the rate of change of the temperature of the temperature of the water pool. –  joriki Oct 14 '12 at 17:13
    
Brilliant thanks...I'd give you credit if I could for your help :) –  katrinajames Oct 14 '12 at 19:34
    
Thanks, but I intentionally only commented instead of giving an answer since there might be a lot more to say about this and someone else might be able to say it. –  joriki Oct 14 '12 at 19:35
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