The thermal conductivity of a sheet of rigid, extruded insulation is reported to be \(k=0.029 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). The measured temperature difference across a 25 -mm-thick sheet of the material is \(T_{1}-T_{2}=12^{\circ} \mathrm{C}\).

(a) What is the heat flux through a \(3 \mathrm{~m} \times 3 \mathrm{~m}\) sheet of the insulation?

(b) What is the rate of heat transfer through the sheet of insulation?

(c) What is the thermal resistance of the sheet due to conduction?