You are a Design Engineer at the petrochemical manufacturing company. As part of your design duties, your Boss asked you to design a heat exchanger to heat a mixture of $50wt.\%$ Benzene $(C_6{H}_6)$ and $50$ wt$.\%$ Toluene $(C_7{H}_8)$ at a rate of $10,000k\frac{g}{h}$ from room temperature $(22C)$ to $70C$ before entering a reactor. To achieve this goal, you need to select an appropriate hot utility stream and an appropriate heat exchanger type. You have just been informed that space is also an issue in the plant, and you are asked to design this heat exchanger with the minimum possible area and the best possible material. Since you are new in your role, your Boss has given you the below guidelines and asked you to report the results by May $6$th before $9$:$30$ am through Canvas $().$

Task #$1)$ Consider using hot air as the hot utility to heat the benzene$-$toluene mixture by designing two different types of crossflow heat exchangers. The benzene$-$toluene mixture will flow through the tubes, and the hot air will flow outside and in a normal direction into the tubes. Design these crossflow heat exchangers as "both fluid unmixed" and "one fluid mixed and one fluid unmixed." How much hot air and what pressure$/$temperature will you use for this purpose? Calculate the area of each heat exchanger and comment on the design, cost, and type of their materials and suitability for this plant.

Task #$2)$ Consider condensing steam as the hot utility in a shell and tube heat exchanger. How much steam and what pressure$/$temperature will you use for this purpose? Consider designing three types of shell and tube heat exchangers of $1-1,1-2,$ and $2-4,$ through which benzene$-$toluene mixture is flowing in the tubes, and steam will condense on the shell side.