#Question id: 14232

Nutrient medium is to be heated from 10⁰C to 28⁰C is a single-pass countercurrent shell-and-tube heat exchanger before being pumped into a fed-batch fermenter. Medium passes through the tubes of the exchanger; the shell-side fluid is water which enters with flow rate 3 x 10^4 kg h^- 1 and temperature 60⁰C pre-heated medium is required at a rate of 50 m^3 h^-1. The density, viscosity and heat capacity of the medium are the same as water; the thermal conductivity of the medium is 0.54 Wm^- 1 ⁰C^ - 1. It is proposed to use 30 steel tubes with inner diameter 5 cm; the tubes will be arranged in line. The pipe wall is 5-mm thick; the thermal conductivity of the metal is 50 Wm^- 1 ⁰C^ - 1. The maximum linear shell-side fluid velocity is estimated as 0.15 m s^-1. What is the rate of heat transfer?