Explanation:
This is an interesting calculation. We know the inlet temperatures of both fluids (Tcoldi = 20 C, and Thoti = 90 C); we know their flow rates and heat capacities (66 kg/s, 1 kJ/kg K) and (5 kg/s, 2.2 kJ/kg K); we know the area for heat exchange (10 m2); and we know the overall heat transfer coefficient (2418 W/m2 K). We wish to determine the outlet temperatures of each fluid. We have three unknowns: the two outlet temperatures and the heat transferred. We can write three expressions: (1) Q = (66 kg/s)(1 kJ/kg K) (Tcoldo - 20) (2) Q = (5 kg/s) (2.2 kJ/kg K) (90-Thoto) (3) Q = (2418 W/m2 K) (10 m2) ΔTlm The first two of these can be rearranged to give Tcoldo = 35 - 0.166Thoto We can then expand 3 to read Q = 24.18ΔT1 - ΔT2 / ln (ΔT1/ΔT2) where Δ T1= 90 - Tcoldo and ΔT2=Thoto-20. We may then solve the system iteratively by guessing a value of Thoto, calculating Tcoldo from equation 4, and then computing Q from equations 2 and equations 5. We continue to guess Thoto until we find one for which the two values of Q (from equations 2 and 5) agree. A spreadsheet is an easy way to implement such a calculation. Note that the outlet temperature of the hot fluid does not change by much for this situation.