Real-World Applicationshard
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A counter-flow heat exchanger cools oil from T_{h,in} = 100^\\circC to T_{h,out} = 60^\\circC using cooling water that enters at T_{c,in} = 20^\\circC and leaves at T_{c,out} = 50^\\circC. The Log Mean Temperature Difference is defined as DeltaTlm=fracDeltaT1DeltaT2ln(DeltaT1/DeltaT2)\\Delta T_{lm} = \\frac{\\Delta T_1 - \\Delta T_2}{\\ln(\\Delta T_1 / \\Delta T_2)}, where DeltaT1=Th,inTc,out\\Delta T_1 = T_{h,in} - T_{c,out} and DeltaT2=Th,outTc,in\\Delta T_2 = T_{h,out} - T_{c,in}. What is the LMTD for this heat exchanger?