There is a functional polymer that can dissolve itself according to human body temperature and release the drug it contains. For the experiment, the drug$-$loaded polymer was prepared

by applying a thin coating on a $1$ mm$\backslash$times $1$ mm electrothermal substrate. The sample was placed

in a $5$ cm diameter and $30$ cm long circular tube with water flowing in a laminar fashion with

a pressure difference of $0\mathrm{.}01$ N$/$m$^2,$ and a detector for drug detection was installed $10$ cm behind the film and in the center of the circular tube. The temperature of the heat sink was set to $50$ and the detector detected the drug signal after $1$ minute. Estimate the actual temperature at which the polymer under development was dissolved, taking into account the heat transfer by the heater and the drug's travel time. Assume that the electrothermal substrate is small enough that it has no effect on the behavior of the fluid in the tube, that the diffusion

of the drug in the fluid is negligible, and that the polymer film dissolves immediately when it reaches the dissolution temperature and that it is impossible to release the drug before it dissolves.