Heat Exchanger (LMTD)

The driving temperature difference in an exchanger varies along its length, so you use the log mean: ΔT_lm = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂). Counterflow always beats parallel flow for the same duty.

A temperature cross (an end ΔT ≤ 0) is impossible in the chosen arrangement — switch to counterflow or revisit the outlet temperatures. Shell-and-tube needs an F correction factor.