1) You recently started your new job at Big Pharma Inc. For your first assignment, you will test
catheters using a novel microfluidic device. This device can be modeled as an annulus with
cylindrical coordinates, with the catheter as the inner cylinder an
Homework 2; Due on Nov. 29th
(Problem 1) Tumor morphology and malignancy is highly dependent on the structure of nearby
tissue. For your summer research project, you are looking at characterizing hydraulic
conductivity for different cancer cell lines embe
FALL 2013: Tentative Syllabus for CHBE 472/594
Overview: The broad objective of this course is to introduce students to fundamental biophysical and engineering
concepts in biomolecular engineering.
The course covers fundamental biophysical properties of
b
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supplied at an inlet temperature Tm,i and a total mass
flow rate m (for the entire heat sink).
Water
Coolant passages
D = 10 mm, N = 10
Tm,i = 7C
m1 = 0.2 kg/s
W = 350 mm
Chip
L
L
Cold plate
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Internal Flow
of w ! 25 mm and is fabricated from a stainless steel
with a thermal conductivity of 15 W/m ! K.
y
T, h
T (x, w)
Platen
w
2Di
x
Solder
Insulation
Air
Tube
Di
T, h
S/2
Platen
Insulation
8.78
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583
Problems
8.82 A cold plate is an active cooling device that is attached
to a heat-generating system in order to dissipate the
heat while maintaining the system at an acceptable temperature. It is typically fabricat
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587
Problems
length of the coiled tube, Lcl (i.e., the product of
the tube pitch and the number of coils), necessary
to increase the mean temperature of the pharmaceutical to the desired value.
With coil insert
Pharmac
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!
Internal Flow
pipe, while the cooler combustion air flows through an
annular passage around the pipe.
Air
Ta,2
Ts,i,2
2
Di
Do
Inner pipe wall
L
qi
Annular passage
(a) Determine the inlet temperature of th
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!
Problems
.
8.48 Consider pressurized liquid water flowing at m ! 0.1 kg/s
in a circular tube of diameter D ! 0.1 m and length
L ! 6 m.
(a) If the water enters at Tm,i ! 500 K and the surface
temperature of the tube is
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Pro ! 104; the oil flow rate is m! o ! 500 kg/s; and the
pipe diameter is 1.2 m.
(a) Expressing your results in terms of D, L, z, t, m! ,
o
Tm,i, and Ts, as well as the appropriate oil (o),
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adjoining tubes at m! h ! m! c ! 0.2 kg/s, what is the
rate of heat transfer per unit length of tube? The wall
contact resistance is 10"5 m2 ! K/W. Approximate the
properties of both the hot
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575
Problems
an intermediate insulated sterilizing section, and a
downstream cooling section of length Lc ! 10 m. The
cooling section is composed of an uninsulated tube
exposed to a quiescent environment at T! ! 20"C.
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585
Problems
8.91 To slow down large prime movers like locomotives, a
process termed dynamic electric braking is used to
switch the traction motor to a generator mode in
which mechanical power from the drive wheels is
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581
Problems
(a) Estimate the average heat transfer coefficient for
the exhaust gas flowing inside the tube.
which is transferred to the water? What is the outer surface temperature of the Teflon tube?
(b) Estimate the
ChBE 523
1
Problem Set #1
From thermodynamics, the first law gives d U
C V , show that this gives
dU
CV d T
Fall 2012
T dS p dV . Combined with the definition of
p
T
p
TV
dV
Hint: you may require a Maxwell relationship for the deriavtive of S.
We start wi
ChBE 523
1
Problem Set #2
Fall 2012
A sphere of radius a is filled with a chemical species with a spherically symmetric initial concentration
u0(r). The sphere is immersed in a solvent which which keeps its surface at concentration u=0.
Solve the time dep
ChBE 523
1
Problem Set #2
Fall 2012
A sphere of radius a is filled with a chemical species with a spherically symmetric initial concentration
u0(r). The sphere is immersed in a solvent which which keeps its surface at concentration u=0.
Solve the time dep
ChBE 523
1
Problem Set #3
Fall 2012
Consider the diffusion problem for the steady state concentration c(x, y) in a perturbed two
dimensional domain. The governing equation and boundary conditions are
2
2
c
x2
where -
<x<
,
BC: c
c
0
y2
g<y<
cw
on
as
c
y
y
ChBE 523
1
Problem Set #3
Fall 2012
Consider the diffusion problem for the steady state concentration c(x, y) in a perturbed two
dimensional domain. The governing equation and boundary conditions are
2
c
x2
where -
<x<
,
2
BC: c
c
y2
g<y<
0
cw
on
as
c
y
y
2
Consider the following examples for heat transfer from a flat plate:
(i) a quiescent fluid (ii) oil flowing at high Pe (iii) molten metal flowing at high Pe
Which of these would yield the greatest increase in heat transfer rate if the thermal conductivi
ChBE 523
Problem Set #4
Fall 2012
PS#3, Problem 5 for reference
A cylindrical fiber is growing in a supercooled liquid. Far from the surface of the cylinder the
temperature gradient is T/ r = /r. Find the radius of the fiber as a function of time.
You may
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what pipe length L is needed to provide a discharge temperature of Tm,o ! 21"C? What is the fan power required
to move the air through this length of pipe if its inner surface is smooth?
8.3
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8.41 Water flows through a thick-walled tube with an inner
diameter of 12 mm and a length of 8 m. The tube is
immersed in a well-stirred, hot reaction tank maintained
at 85!C, and the conduc