Heat and Mass Transfer
The logarithmic mean temperature difference (tm) is given by (where Δt1 and Δt2 are temperature differences between the hot and cold fluids at entrance and exit)

tm = loge (Δt1/Δt2)/ (Δt1 - Δt2)
tm = loge (Δt1 - Δt2)/ Δt1/Δt2
tm = tm = (Δt1 - Δt2) loge (Δt1/Δt2)
tm = (Δt1 - Δt2)/ loge (Δt1/Δt2)

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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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