Question

We have been asked to design a process to produce those individual Jell-O fruit cups that are sold in all grocery stores. To accomplish this, a gelatin solution must be prepared, heated to 100 oC, and then cooled and dispensed into the individual small polypropylene (PP) containers (melting temp. = 165oC ) where it is mixed with the fruit and allowed to gel. We have been asked to design the heat exchanger that will be used to heat the gelatin solution from 20oC to 100 oC. We have available to us a counter-current flow heat exchanger (often called a "steam chest") that was previously used for milk pasteurization, so it is approved for food grade processing. It is made of a stainless-steel shell with one 5 ft. long, 1" schedule 40 SS pipe running through it. It is heated on the shell-side with saturated steam at 2.0 bar (Ts = 120oC) that maintains the pipe wall at 120 oC at all times and exits as a saturated liquid. At this temperature and pressure, the density of steam is 1.13 kg/m3, and the enthalpy of vaporization of steam is 2201.6 kJ/kg. The gelatin solution to be processed enters from the mixing vessel at a flow rate of 20 L/min at 20oC. As a first approximation, since Jell-O is usually made at an approximately 1wt% concentration, all the thermophysical properties of the gelatin solution can be considered to be those of water at the appropriate temperature, except for viscosity which is 3 times the viscosity of water at any temperature. a) Sketch and label the heat exchanger (designate side #1 as the gelatin solution inlet).

Answer 1

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: