I have a general question regarding MDMT in heat exchangers. Note that the scenario provided is theoretical, and is a situation that I would wish to avoid. However, I would like your input should I ever run across such a situation.

Consider a liquid-liquid heat exchanger. If the tube-side MDMT and shell-side MDMT of a heat exchanger MDMT are different, and one side contains a fluid that is above the MDMT of one side but below the MDMT of the other side, what would the tube temperature be? One side would have fluid that is below the MDMT whilst the other side would have fluid above the tube MDMT. The tube would have a temperature gradient, and the tube skin temps would be dependent on the film coefficients of each side.

If the cases exists where part of the tube is above the MDMT and part is below (looking at the cross-sectional area), what would one consider as the actual tube temp compared to the MDMT?

This is likely a very theoretical exercise, as I don't think the evaluation of tube temp has enough rigor to satisfactorily prove the tube temp is in the safe range. This also is quite literally walking the razor's edge of safety, which I would never do in practice.

This question likely has better applications for thick-walled vessels with high temperature differentials, looking at the maximum design temperature.