Heat and Mass Transfer
Upto the critical radius of insulation,

Added insulation will increase heat loss
Heat flux will decrease
Added insulation will decrease heat loss
Convective heat loss will be less than conductive heat loss

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

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