I am trying to find a solution for the thermal conduction equation:
d ( K[T(z)] * d T(z) ) = -H0* e (-z/d)
dz dz
Some publications have proposed methods based on stochastic models and nonlinear transformations. However, I would like to know if there is another way to estimate continental geotherms considering the temperature-dependent thermal conductivity. I am following the next relation for the thermal conductivity of the crust:
K [T(z)] = 2.26 - 618.241/ T(z) +K0 * (255.576/ T(z) - 0.030247)
I will appreciate any help.