# DBT JRF 2020 — Question 15

Exam: DBT JRF 2020 · Section: B · Topic: Bioprocess Engineering · Difficulty: Hard

## Question

A fermentation medium is being cooled from 70 °C to 32 °C in a double pipe heat exchanger. Fluid flowing counter currently with this stream is heated from 20 °C to 46 °C. The log mean temperature difference (in °C) for the two streams is

## Options

- **A.** 17.3
- **B.** 8.5
- **C.** 12.6
- **D.** 4.8

## Answer

Option A

## Explanation

Counter-current heat exchanger LMTD calculation: Hot fluid (fermentation medium): inlet $T_{h,in}=70°C$ , outlet $T_{h,out}=32°C$ . Cold fluid (counter-current): inlet $T_{c,in}=20°C$ (enters at the hot-fluid outlet end), outlet $T_{c,out}=46°C$ . Temperature differences at each end: $\Delta T_1 = T_{h,in} - T_{c,out} = 70 - 46 = 24°C$ ; $\Delta T_2 = T_{h,out} - T_{c,in} = 32 - 20 = 12°C$ . $\text{LMTD} = \dfrac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)} = \dfrac{24-12}{\ln(24/12)} = \dfrac{12}{\ln 2} = \dfrac{12}{0.6931} \approx 17.3°C$ .

Source: https://mypyqbuddy.com/questions/a-fermentation-medium-is-being-cooled-from-70-6a05a8a02adafec470293227