Calculate the heat transfer area needed for this heat exchanger, based on an overall heat transfer coefficient of 500 W/m²K.

3:

2.3. Calculate the heat transfer area needed for this heat exchanger, based on an overall heat transfer coefficient of $500 \text{ W/m}^2\text{K}$.

Step 1: Calculate the Log Mean Temperature Difference ($\Delta T_{lm}$) for counter-current flow.
The temperatures are:

• Hot oil inlet ($T_{h,in}$): $200 \text{ °C}$
• Hot oil outlet ($T_{h,out}$): $40 \text{ °C}$
• Cooling water inlet ($T_{c,in}$): $30 \text{ °