you calculate the heat loss of your tank (kW)
you calculate the amount of heat to be retracted from the medium (kJ) (from t1 to t2)
you define the max time to cool from t1 to t2
you calculate the heat retraction required
delta t and kJ result in kW
I guess zz1402's question is: if you have an insulated tank (filled will hot liquid, gas, etc. with no internal heat source, I assume), how long will it take to cool down (naturally in ambient air, inside steadily flowing cooling gas, etc., I assume).
To me, it is similar to 'how long should I wait for a glass of hot water to cool down?'.
But, if do not define 'cool down' with an non-zero temperature differential value, then it is going to take forever.
Why does the temperature need to be specified? Isn't that what algebra is all about? Presumably, the OP is looking for an equation whose inputs include the temperature delta, and the result is cooldown time.
if the insulation is defined as perfect (no heat loss)
the specific heat (kj/kg/degC) multiplied with the temperature differential (degC) multiplied with content tank (kg) gives you required heat.
required cooling capacity (kW)=required heat multiplied with time (sec)
You are talking about "batch operations", right? It is not steady-state. The differential equations have been solved many years ago for several practical situations. Look in the heat transfer chapters in your Perry's under "Batch Operations".
Well, if it were perfect, cooling time would be infinite, wouldn't it? ;-)
The key assumption is that the insulation is high enough that the cooling process always looks like steady state, i.e., the "stuff" inside the tank is roughly in thermal equilibrium at all times, in which case, the cooling time is as you've indicated.
Otherwise, the OP needs to consider the convection and conduction of his "stuff" as part of a transient cooling problem
Perhaps we should ask the original poster to define his* process in more detail rather than trying to guess what he** is wanting. At the least, it should be obvious that the conditions need to be defined in more detail than already presented (presuming, of course, that this was not a homework assignment.)
*Although the original poster gave no clues as to gender, the male pronoun is used as engineering as a profession is weighted more heavily towards males than females.***
*or she, of course.
***which just goes to show that we shouldn't make assumptions when there isn't information available, such as in the original poster's thread.
Patricia Lougheed
******
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