Consider a house lateral wall are realized with two layers of wood $($thickness of $0\mathrm{.}02$ m and thermal conductivity of $0\mathrm{.}2$W$/$mK$)$ and an inner layer of thermal insulation $($thermal conductivity of $0\mathrm{.}05$ W$/$mK$).$ The total surface of the lateral walls is $100$ m$\mathrm{²}.$ Assume that the temperature of the air inside the house is $293$K $(20$ ^oC$)$ and the convective heat transfer coefficient from the air inside to the wall is $10$ W$/$m$2$K$,$ whilst the temperature of the air outside the house is$263$K $(-10$ ^oC$)$ and the convective heat transfer coefficient from the wall to the air outside is $50$ W$/$m$\mathrm{²}$K$.$  

Calculate the thickness of the thermal insulation layer such that the heat transfer rate through the lateral walls of the house is below $2$ kW$.$