Heat and Mass Transfer
A designer chooses the values of fluid flow rates and specific heats in such a manner that the heat capacities of the two fluids are equal. A hot fluid enters the counter flow heat exchanger at 100°C and leaves at 60°C. A cold fluid enters the heat exchanger at 40°C. The mean temperature difference between the two fluids is

20°C
60°C
40°C
66.7°C

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

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