Lumped capacitance model if you insure the interior is well mixed?

[smithy360]

Hi everybody. I have been doing some experimental heat loss calculations on a sealed cube of fluid, filling the volume of the cube with hot water then sitting it in a larger tank of fluid at a fixed cooler temperature and monitoring the drop of temperature inside the box. I have also positioned a stirrer inside the cube to maintain a uniform temperature within.

I am struggling to verify if the lumped capacitance model is applicable in terms of Biot number, I don't know what would be best to take as the value for the heat transfer coefficient in this situation. Will Newton's law of cooling be okay to apply given I am insuring that the temperature within the cube stays uniform at all times? The values I get from the calculations certainly seem in line with what I would expect, I just want to be able to justify it. (I should also say I am adjusting for the slight heat flux put into the system from the stirrer).

Any tips would be helpful, or even some guidance on how to calculate the Biot number in this setup would be great.

Kind regards.

 

[smithy360]

Does anybody have any suggestions on how to calculate the Biot number in this setup as a starting point?

Many thanks again.