Q$4(15$ pts$).$ A stream of bread dough is fed steadily through an oven in a large bread$-$baking

operation. The dough enters the oven at a rate of $110f\frac{t^3}{h}r$ and at a temperature of $70F.$ It

exits the oven at $400F.$ Other properties of the dough include density $=58\mathrm{.}7l\frac{b_m}{f}{t}^3,$ heat

capacity $=0\mathrm{.}9Bt\frac{u}{b_m}F.$ At what rate is heat being added to the dough by the heating coils of

the oven $($in Watts$)?$

Q$5(20$ pts$).$ We have solved the question below in the classroom $($Note: The question and

its solution is provided below$)$:

In patients with severe kidney disease, urea must be removed from the blood with a "hemodialyzer."

In that device, the blood passes by special membranes through which urea can pass. A salt solution

$("$dialysate$")$ flows on the other side of the membrane to collect the urea and to maintain the de$-$

sired concentrations of vital salts in the blood. One geometry for hemodialyzer design is with flat

membranes in a rectangular system. For such a geometry, consider the following typical values:

Blood side:

mass$-$transfer coefficient for the urea $,0\mathrm{.}0019c\frac{m}{s}$

average urea concentration within the dialyzer $,0\mathrm{.}020$gmo$\frac{l}{L}$

Dialysate side:

mass$-$transfer coefficient for the urea $,0\mathrm{.}0011c\frac{m}{s}$

average urea concentration within the dialyzer

$0\mathrm{.}003$gmo$\frac{l}{L}$

Membrane:

thickness

$0\mathrm{.}0016cm$

diffusivity of urea in the membrane

$1\mathrm{.}8{10}^{-5}c\frac{m^2}{s}$

total membrane area

$1\mathrm{.}2m^2$

porosity

$20\%$

Based on these values, what is the initial removal rate of urea?

Solution

$=\frac{0\mathrm{.}02-0\mathrm{.}003\text{g}\text{m}\text{o}\frac{l}{L}}{\frac{1}{(0\mathrm{.}0019\frac{cm}{s})(1\mathrm{.}2m^2)}+\frac{0\mathrm{.}0016(cm)}{(1\mathrm{.}8{10}^{-5}c\frac{m^2}{s})(1\mathrm{.}2m^2)(0\mathrm{.}2)}+\frac{1}{(0\mathrm{.}0011\frac{cm}{s})(1\mathrm{.}2m^2)}}\frac{1000(L)}{m^3}$

$\frac{1(m)}{100(cm)}\frac{60(s)}{\text{m}\text{i}\text{n}}=0\mathrm{.}0065\frac{\text{g}\text{m}\text{o}\text{l}}{\text{m}\text{i}\text{n}}$

Your company manufactures hemodialyzers that have the characteristics described in the

above example. A colleague in the company has proposed replacing the membranes with

better ones, which have the same thickness, area, and porosity but for which the urea diffusivity

in the membrane is $2\mathrm{.}7{10}^{-5}c\frac{m^2}{s}.$

Assuming that the average concentrations of urea in the blood and dialysate are the same as

with the old membranes, by what percentage would the new membranes increase the urea

removal rate? In terms of resistances, explain why this turns out to be such a small

improvement.

Q$6(25$ pts$).$ You are provided with data from a series of experimental runs in a chemical

reactor. The objective is to optimize the reaction rate by varying three factors: reaction

temperature, catalyst concentration, and stirring speed. Each factor is tested at two levels,

high and low.

Data Provided:

Use the data above to perform a two$-$level factorial ANOVA. Calculate the mean squares for

each factor and their interactions.

Determine the F$-$values to test the statistical significance of the model $($Note: Select the top

three factors or interactions based on the highest SS values$).$