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. $=165$oC $)$ 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 $20$oC to $100$ oC$.$

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 a single $1$ schedule $40$ SS pipe running through it$.$ It is heated on the shell$-$side with saturated steam that enters at $2\mathrm{.}0$ bar $($Ts $=120$ oC$)$ and exits as a saturated liquid at TL $=120$ oC$.$ The shell$-$side convective heat transfer coefficient $($hs$)$ has been measured to be hs $=2500$ W$/$m$2-$K$.$

The gelatin solution to be processed enters from the mixing vessel at a flow rate of $20$ L$/$min at $20$oC$.$ 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$)(10$pts$)$ Sketch and label the heat exchanger $($designate side #$1$ as the gelatin solution inlet$).$

b$)(5$pts$)$ 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$)(10$pts$)$ Calculate the heat load $($q$)$ on the heat exchanger to achieve the desired final Jell$-$O temperature?

d$)(20$pts$)$ Calculate the inside convective heat transfer coefficient. Clearly identify the temperature you use to evaluate the thermophysical properties.

e$)(20$pts$)$ 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$)(15$pts$)$ Calculate the required heat transfer area and tube length of the heat exchanger?in all grocery stores. To accomplish this, a gelatin solution must be prepared, heated to $100C,$ and

then cooled and dispensed into the individual small polypropylene $($PP$)$ containers $($melting temp.

$=165C)$ 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 $20C$ to $100C.$

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 a single

$1^{\text{s}\text{c}\text{h}\text{e}\text{d}\text{u}\text{l}\text{e}}40SS$ pipe running through it$.$ It is heated on the shell$-$side with saturated steam

that enters at $\frac{2\mathrm{.}0}{b}ar(T_5=120C)$ and exits as a saturated liquid at $T_L=120C.$ The shell$-$side

convective heat transfer coefficient $(h_5)$ has been measured to be $h_5=2500\frac{W}{m^2}-K$

The gelatin solution to be processed enters from the mixing vessel at a flow rate of $20\frac{L}{m}in$ at

$20C.$ 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$)(10$pts$)$ Sketch and label the heat exchanger $($designate side #$1$ as the gelatin solution inlet$).$

b$)(5$pts$)$ 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$)(10$pts$)$ Calculate the heat load $(q)$ on the heat exchanger to achieve the desired final Jell$-$O temperature?

d$)(20$pts$)$ Calculate the inside convective heat transfer coefficient. Clearly identify the temperature you

use to evaluate the thermophysical properties.

e$)(20$pts$)$ 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$)(15$pts$)$ Calculate the required heat transfer area and tube length of the heat exchanger?