Re: Birthday Wish

[Brian McInnes <bmcinnes@PNC.COM.AU>]

Brian,
You pose a question
> I want to bring up a tank of liquid from 125degF to 140degF using
> hot liquid at 190degF. I want to raise its temperature at 4 degrees
> a minute.   What flow rate should I use?
>
> (This question is ill-posed enough to be 'real-world', don't you
> think?
> Could it be a dairy-farmer has an application for this answer?
> Just for fun, try giving an exact formulation assuming no losses.

An attack on this "real-life" situation requires
understanding of a number of concepts that play a part in a
physicist's model of thermal physics: thermal energy,
thermal contact, thermal equilibrium, temperature, energy
transfer, rate of energy transfer.
A naive application of a derivative of the formulation you
called attention to in your previous posting
> mass1 x specific heat1 x rise in temperature =
> mass2 x specific heat2 x fall in temperature
does not take into account many of the consequences of these
concepts in the application of the model.
For example, the amount of thermal mixing, the mechanics of
the thermal contact between the hot liquid and the liquid in
the tank, could well be more important in the warming of the
tank liquid than the flow rate of the hot liquid.

Brian McInnes