Answer:
To design a heat exchanger for heating the gelatin solution from 20oC to 100oC, we can use a counter-current flow heat exchanger, also known as a "steam chest." This heat exchanger is made of a stainless-steel shell with a 5 ft. long, 1" schedule 40 SS pipe running through it.
The gelatin solution enters the heat exchanger at a flow rate of 20 L/min and a temperature of 20oC. The gelatin solution will be heated by the shell-side of the heat exchanger, which is in contact with saturated steam at 2.0 bar. The steam maintains the pipe wall at a constant temperature of 120oC and exits the heat exchanger as a saturated liquid.
To design the heat exchanger, we need to determine the heat transfer rate required to heat the gelatin solution from 20oC to 100oC. We can use the following equation:
Q = m * Cp * ΔT
where Q is the heat transfer rate, m is the mass flow rate of the gelatin solution, Cp is the specific heat capacity of water (considering the thermophysical properties of the gelatin solution are similar to water), and ΔT is the temperature difference.
First, let's calculate the mass flow rate of the gelatin solution:
m = volume flow rate * density
Given that the volume flow rate is 20 L/min and the density of water is approximately 1000 kg/m3, we can calculate:
m = (20 L/min) * (1000 kg/m3 / 1000 L) = 20 kg/min
Now, let's calculate the temperature difference:
ΔT = 100oC - 20oC = 80oC
The specific heat capacity of water (Cp) is approximately 4.18 kJ/kg·K.
Using the equation Q = m * Cp * ΔT, we can calculate the heat transfer rate:
Q = (20 kg/min) * (4.18 kJ/kg·K) * (80oC) = 67,120 kJ/min
This heat transfer rate is the amount of energy that needs to be transferred from the saturated steam to the gelatin solution to raise its temperature from 20oC to 100oC.
In summary, to design the heat exchanger, we need to ensure that it can transfer at least 67,120 kJ/min of heat from the steam to the gelatin solution. The specific design details, such as the surface area and flow arrangement, can be determined based on factors like pressure drop and available resources.
Step-by-step explanation: