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

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