Okay thank you! I will try that, since one interface requires a quite high underrelaxation, due to a big conductivity value.
To conclude the topic, the instability was indeed caused by the conductivity value of the solid. I have two solids, whereas one has a very high conductivity, therefore a low biot number and the other solid has a low conductivity and therefore a relatively high biot number. For the high conductivity I have coupled the heat flux on the solid boundary from the fluid and the temperature of the solid is given to the fluid. For the other case this is done in the normal way, where the fluid provides a temperature for the solid. An implicit scheme is also used to underrelax these values and get a stable simulation.
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