I’m interested in solving the heat equation: d[K[z] d[T[z],z],z]=0, equipped with T(-h/2)=Tm and T(h/2)=Tc.

Is it possible to get a symbolic solution in Mathematica using the power series method?

The solution they provide in literature is attached in the picture.

Where: K(z)=Km+(Kc-Km)(1/2+z/h)^n