Time required to raise Temperature knowing heat transfer rate

Tamarisk

Knowing the heat transfer rate q, how long does it take to lower a fluid from temperature T0 to Tf?

This is for convective heat transfer from a heated body submerged in a fluid.
I'm looking for an appropriate formula (google isn't helping)

Thanks!

gneill

It's unlikely that the heat transfer rate will remain constant as the temperature difference changes; Usually the rate is proportional to temperature difference. If for some reason the heat transfer rate is kept constant in some fashion, then you can use the specific heat of the body (a constant for a given substance) to work out the body's heat content at a given temperature, and thus how it changes as heat is removed. Look up "specific heat". Your heat transfer rate, q, will tell you the rate that the heat content is changing.

Other issues arise with the rate that heat can move from the insides of the body to the surface where it can depart to the surrounding medium. This is a much more complex problem. However, if the thermal conductivity of the submerged object is much greater than the conductivity between the body/fluid interface, then the effects may be negligible. Look up "heat conductivity" or "thermal conductivity".

Also look up "Newton's law of cooling".