Consider a composite wall with an internal honeycomb structure of cells of square cross-sections, sandwiched between solid slabs. The cells contain stagnant air space. All dimensions are given, and the wall surface convective heat transfer coefficients are also given.

Develop a model to estimate the heat transfer rate per unit area of the wall if all thermal properties are assumed to be constant.
If the internal cross sections are made of smart materials whose thermal conductivity is a given function of temperature, develop a model to estimate the heat transfer rate per unit area of the wall if thermal properties of other parts remain constant.