Question

In a counter flow heat exchanger, cold fluid enters at ${30}^{o}C$ and leaves at ${50}^{o}C$, whereas hot fluid enters at ${150}^{o}C$ and leaves at ${130}^{o}C$. The mean temperature for this case is

• A. ${20}^{o}C$
• B. Indeterminate
• C. ${100}^{o}C$
• D. ${80}^{o}C$

Answer 1

The correct option is C ${100}^{o}C$

${\theta }_1=T_{h1}-T_{c2}={150}^{o}C-{50}^{o}C={100}^{o}C$

${\theta }_2=T_{h2}-T_{c1}={130}^o-{30}^o={100}^{o}C$



Now LMTD comes of the form 0/0. We have to apply L'Hospital's rule which uses derivatives to help evaluate limits involving indeterminates forms.
So, effective temperature difference is taken to be equal to ${\theta }_1$ and ${\theta }_2$ in this case i.e ${100}^{o}C$