A reactor is thermally stratified as in the following table: Depth, m Temperature, °C 0 0.5 1 1.5 2 2.5 3 70 70 55 22 13 10 10 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: J = -k- dT dz 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.