$($a$)$ A furnace is enclosed by walls made of $50mm$ kaolin fire bricks $)=(0\mathrm{.}0865(W)m^{-1}{C}^{-1}$ whieh are insulated by a layer of $70mm$ thick common bricks $)=(0\mathrm{.}259(W)m^{-l}{C}^{-l}.$ The brick layers are held together by $16$ stainless steel bolts $)=(45(W)m^{-1}{C}^l$ each having a length of $120mm.$ The bolts account for $2\mathrm{.}5\%$ of the total internal surface area $(2\mathrm{.}2m^2)$ of the furnace.

$($i$)$ If the inside face temperature of the furnace is $960C$ and the outside, which is in contact with the atmosphere, is $44C,$ determine separately, the heat loss from the furnace walls, the heat loss from the bolts and hence, total heat loss from the furnace.

$(7)$

$($ii$)$ The furnace is to be retrofitted to significantly reduce heat loss. The engineers plan to replace the common bricks with an equal thickness of heat resistant asbestos $)=(0\mathrm{.}00231(W)m^{-1}{C}^{-1}.$ Evaluate the proposed changes and highlight any strengths or weaknesses. Do you agree with the changes? Use calculations to support your analysis.

$(5)$