3) (80 pts) The Production of Jell-O Fruit Cups using a Double- Pipe Heat Exchanger 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 °C, and then cooled and dispensed into the individual small polypropylene (PP) containers (melting temp. = 165°C) 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 20°C to 100 °C. We have available to us counter-current shell-and-tube heat exchanger (basically a steam chest) that is approved for food grade processing. It is made of a stainless-steel (SS) shell with one 5 ft. long, 1" schedule 40 SS pipe running through it. It is heated on the shell-side with saturated steam that enters at 2.0 bar (T=120 °C) and exits as a saturated liquid at T₁ = 120°C. The shell-side convective heat transfer coefficient (h) has been measured to be h, = 2500 W/m²-K. The gelatin solution to be processed enters from the mixing vessel at a flow rate of 20 L/min at 20°C. As a first approximation, since Jell-O is usually made at an approximately 1wt% gelatin concentration, all the thermophysical properties of the gelatin solution can be considered to be those of water at the appropriate temperature. a) (10pts) Sketch and label the heat exchanger (designate side #1 as the gelatin solution inlet)/nThe gelatin solution to be processed enters from the mixing vessel at a flow rate of 20 L/min at 20°C. As a first approximation, since Jell-O is usually made at an approximately 1 wt% gelatin concentration, all the thermophysical properties of the gelatin solution can be considered to be those of water at the appropriate temperature. a) (10pts) Sketch and label the heat exchanger (designate side #1 as the gelatin solution inlet). b) (5pts) With reference to a), sketch the expected temperature profile in the heat exchanger for both the steam/saturated liquid stream and the Jell-O stream (on the same figure). c) (10pts) Calculate the heat load (q) on the heat exchanger to achieve the desired final Jell-O temperature? d) (20pts) Calculate the inside convective heat transfer coefficient. Clearly identify the temperature you use to evaluate the thermophysical properties. e) (20pts) Calculate the overall heat transfer coefficient for this heat exchanger. Identify the resistances to heat transfer (convective and conductive). Where is the most significant resistance to heat transfer in this system? Explain. f) (15pts) Calculate the required heat transfer area and tube length of the heat exchanger?