I think, the temperature at the top of the vessel is lower with just a few degrees because the steam (he has taken an example of water) is not superheated by it stills humid and this humidity has an effect on the temperature comparing to temperature liquid which is more than that of the steam or...
Hi,
I don't know what kind of liquid you use, but a should a reaction takes place and thus a heat generation will be produced , you have also a heat coming with the hot temperature due to motor driving ( may be you use a compressor) and the two factors can effect on the bioreactor effeciency...
He has to know the composition of each streams to calculate the Cp ,then for duty, he can calculate it by using enthalpies( knowing the flow).
or you just do it with HYSYS.