Final answer:
To determine the Log Mean Temperature Difference in a counter current heat exchanger, one must calculate the outlet temperature of the cold stream using the given flow rates and physical properties, then apply the LMTD formula with the temperature differences at both ends of the exchanger.
Step-by-step explanation:
The student is asking about the calculation of the Log Mean Temperature Difference (LMTD) in a counter current shell and tube heat exchanger where hot water enters at 80°C and exits at 50°C, while cold oil enters at 20°C. To find the LMTD, the outlet temperature of the oil must first be determined using the heat balance equation since the flow rates and physical properties of the oil are given First, calculate the heat capacity rates of both streams (hot water and cold oil), then use the heat balance to find the outlet temperature of the cold stream. Afterwards, apply the LMTD formula for a counter current heat exchanger: LMTD = ( ∆T1 - ∆T2 ) / ln ( ∆T1 / ∆T2) where ∆T1 and ∆T2 are the temperature differences between the hot and cold streams at each end of the exchanger. This calculation requires an understanding of heat transfer principles and formulas specific to shell and tube heat exchangers.