A cold-storage company considers adding an insulating layer to the outer surface of an existing concrete wall. The wall has thickness Lc and thermal conductivity kc. The proposed insulating material has thermal conductivity ki and is to be applied with variable thickness Li. The inner surface of the concrete is maintained at a constant temperature Tin, while the outer surface of the insulation is exposed to outside air at temperature Tout. Edge effects can be neglected, and only one-dimensional conduction need be considered.
(a) Derive a general expression for the steady-state rate of energy transfer per unit area, RA, through the two-layer wall in terms of kc, ki, Lc, Li, and the temperature difference (Tin−Tout).
(b) The company wants to reduce RA by 40% relative to the uninsulated concrete wall. Determine the required ratio Li/Lc in terms of kc and ki that meets this target.
(c) Suppose kc=1.3W⋅m−1⋅∘C−1, ki=0.04W⋅m−1⋅∘C−1, and Lc=0.20m. Calculate the numerical insulation thickness needed to achieve the 40% reduction.
(d) Critically discuss one practical advantage and one potential drawback of adding such a thick insulation layer from a structural or economic standpoint.