The formula for the logarithmic mean temperature difference (LMTD) for a counter-flow heat exchanger is:
ΔTlm = &frac[(th1 - tc2) - (th2 - tc1)] {ln[(th1 - tc2) / (th2 - tc1)]}
Where:
th1 is the inlet temperature of the hot fluid.
th2 is the outlet temperature of the hot fluid.
tc1 is the inlet temperature of the cold fluid.
tc2 is the outlet temperature of the cold fluid.
Comparing this to the given options, the closest one is:
Δt = [(t/1 - t//2) - (t//1 - t/2)] / ln[(t/1 - t//2)/(t//1 - t/2)]
Assuming 't' represents hot fluid temperatures and 't//' represents cold fluid temperatures, and the order of subtraction is consistent with the LMTD formula.