The logic is naive; capillary action act against gravity, thermal gravity is anti gravity. So, we set off to investigate temperature and capillary action. The metal should be of high heat capacity such that the portion surrounding the insulating fluid does not cool to the temperature of the insulating fluid.
An insulating fluid is used to maintain the the temperature gradient between the metal and the fluid as the measurement progresses.
Increase \(T_m\) and plot Temperature of Metal vs Height of Fluid; \(T_m\) (K) vs \(h\) (m) with \(d\), diameter of metal tube bore and \(T_f\) temperature of fluid as parameters. Viscosity plays a part as fluid in thermal contact with the metal wall experiences a net upward force due to thermal gravity and drags the fluid in the center of the bore upwards.
Maybe you can make a droplet of fluid flow upwards with a temperature gradient decreasing upwards on a hot surface with low drag.
Have a nice day.
