A composite wall occupies 0≤ x≤0.30 m and has unit area normal to heat flow

A composite wall occupies \(0\le x\le0.30\,\mathrm{m}\) and has unit area normal to heat flow. The conductivity is \(k=2\,\mathrm{W/(m\,K)}\) on \(0\le x\le0.10\,\mathrm{m}\) and \(k=8\,\mathrm{W/(m\,K)}\) on \(0.10<x\le0.30\,\mathrm{m}\). The first layer generates \(6000\,\mathrm{W/m^3}\), while the second has no internal generation. The boundary at \(x=0\) is insulated, and the boundary at \(x=0.30\,\mathrm{m}\) is held at \(40^\circ\mathrm{C}\). Use two-node linear elements on \([0,0.10]\), \([0.10,0.20]\), and \([0.20,0.30]\,\mathrm{m}\). Assemble and solve the finite-element model for all nodal temperatures. Then calculate the heat flux on each side of the material interface from the corresponding element temperature gradient and report whether the discrete solution satisfies interface flux continuity.

Use stiffness factors \(20\), \(80\), and \(80\) for the three elements.