Applying high-emissivity paints to radiating surfaces is a common technique used to enhance heat transfer by radiation.

(a) For large parallel plates, determine the radiation heat flux across the gap when the surfaces are at T₁ = 350 K, T₂ = 300 K, ε₁ = ε₂ = ε_s = 0.85.

(b) Determine the radiation heat flux when a very thin layer of high-emissivity paints ε_p = 0.98, is applied to both surfaces.

(c) Determine the radiation heat flux when the paint layers are each L = 2 mm thick and the thermal conductivity of the paint is k = 0.21 W/m · K.

(d) Plot the heat flux across the gap for the bare surface as a function of E.., with 0.05 < ε_s < 0.95. Show on the same plot the heat flux for the painted surface with very thin paint layers and the painted surface with L = 2-mm thick paint layers.