A reactor is thermally stratified as in the following table: Depth, m00.5 11.52 2.53Tempe...

A reactor is thermally stratified as in the following table:

Based on these temperatures, the tank can be idealized as two zones separated by a strong temperature gradient or thermocline. The depth of the thermocline can be defined as the inflection point of the temperature-depth curve—that is, the point at which d2 T/dz2 = 0. At this depth, the heat flux from the surface to the bottom layer can be computed with Fourier's law:

Use a clamped cubic spline fit with zero end derivatives to determine the thermocline depth. If k = 0.01 cal/ (s • cm • °C)  compute the flux across this interface.