Heat and Mass Transfer
A steam pipe is to be lined with two layers of insulating materials of different thermal conductivities. For the minimum heat transfer,

One should take into account the steam temperature before deciding as to which insulation is put where
The better insulation must be put outside
One could place either insulation on either side
The better insulation must be put inside

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Heat and Mass Transfer
The heat transfer by conduction through a thick cylinder (Q) is given by (where T₁ = Higher temperature, T₂ = Lower temperature, r₁ = Inside radius, r₂ = Outside radius, l = Length of cylinder, and k = Thermal conductivity)

Q = [2πlk (T₁ - T₂)]/2.3 log (r₂/r₁)
Q = [2π (T₁ - T₂)]/2.3 lk log (r₂/r₁)
Q = = 2πlk/2.3 (T₁ - T₂) log (r₂/r₁)
Q = 2.3 log (r₂/r₁)/[2πlk (T₁ - T₂)]

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