Chapter 11 I Heat Exchangers
Like many real-world situations. the customer hasn't
revealed, or doesn’t know. additional requirements that
would allow you to proceed directly to a ﬁnal conﬁgu—
ration. At the outset, it is helpful to make a ﬁrst~cut
design

Problems
I Problems
to
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(itmtluvlion
1.1
1.2
The thermal conductivity of a sheet of rigid, extruded
insulation is reported to be it: 0029 me-K. The
measured temperature difference across a 20-mm-thick
sheet of the material is '1} — T2 =

PROBLEM 6.3
KNOWN: Boundary layer temperature distribution.
FIND: Surface heat flux.
SCHEMATIC:
PROPERTIES: Table A-4, Air (Ts = 300K): k = 0.0263 W/mK.
ANALYSIS: Applying Fouriers law at y = 0, the heat flux is
T
y
u y
u
= k ( T Ts ) Pr exp Pr
y=0

PROBLEM 14.30
KNOWN: Radius of coal pellets burning in oxygen atmosphere of prescribed pressure and
temperature.
FIND: Oxygen molar consumption rate.
SCHEMATIC:
ASSUMPTIONS: (1) One-dimensional diffusion in r, (2) Steady-state conditions, (3) Constant
pro

PROBLEM 14.32
KNOWN: Pressure, temperature and mole fraction of CO in auto exhaust. Diffusion coefficient for
CO in gas mixture. Film thickness and reaction rate coefficient for catalytic surface.
FIND: (a) Mole fraction of CO at catalytic surface and CO

PROBLEM 14.34
KNOWN: Radius of a spherical organism and molar concentration of oxygen at surface. Diffusion
and reaction rate coefficients.
FIND: (a) Radial distribution of O2 concentration, (b) Rate of O2 consumption, (c) Molar
concentration at r = 0.
SC

PROBLEM 14.44
KNOWN: Thick plate of pure iron at 1000C subjected to a carburizing process with sudden
exposure to a carbon concentration CC,s at the surface.
FIND: (a) Consider the heat transfer analog to the carburization process; sketch the mass and hea

Homework # 7 Solution
Due in class Thursday March 3, 2016
air 0.005 kg s , Tm ,in 20o C , h 25W m2 K
Circular pipe with D 50 mm, L 3m, m
8.18
c p 1006 J kg K
a) Uniform heat flux q 1000W m2 :
q DLq 471W
Total heat flux:
Exit temperature:
c p Tm ,out Tm

Homework # 6
Due in class Thursday February 25, 2016
Textbook problems:
7.9
Part a only. Remember to evaluate properties at the film temperature
1
2
Ts T
7.17
7.39
Parts a and b only
7.49
Part a only
7.54
7.67
Hint: This is a fin problem so you need to f

Homework # 4
This is a review before the midterm, so it will involve everything we had learned up to this week.
Since the midterm is coming up next week, I will not ask you to turn in this set of homework.
Instead, I ask you, for your own good, to give th

Homework # 5 Solution
Problem 6.3
Air flow over a heated surface. Normally one would have to solve the convection equation for
the temperature profile, but in this case its already done and given to us as:
T Ts
u y
1 exp Pr
T Ts
Also note that y is th

Homework # 8 Solution
Due in class Thursday March 10, 2016
Textbook problems Assume fully developed flow if needed
9.6
Lets estimate the Grashof number: GrL
15.9 106
k 0.0263
gL3T
2
Pr 0.707
For 1m high, 0.6m wide vertical plate, L=1 and:
Using (9.26) y

Homework # 6 Solution
Due in class Thursday February 25, 2016
7.9
2 m/s
0.2m
10 mm
There are 25 strips, each is 10 mm long. The x positions at the beginning and the end of each
strip can be obtained for the nth strip:
xb n 1L
xe nL
L 10mm 0.01m
where
We n

Homework # 1 Due in class on Thursday Jan 14, 2016
Given:
1. A sphere of area A, mass m0, specific heat C0, which is initially at a temperature T0.
2. A finite pool of liquid of mass m1, specific heat C1, which is initially at a temperature T1.
3. At time

PROBLEM 1.5
KNOWN: Thermal conductivity and thickness of a wall. Heat flux through wall. Steady-state
conditions.
FIND: Value of temperature gradient in K/m and in C/m.
SCHEMATIC:
k = 2.3 W/mK
qx = 10 W/m2
x
L = 20 mm
ASSUMPTIONS: (1) One-dimensional cond

PROBLEM 3.10
KNOWN: A layer of fatty tissue with fixed inside temperature can experience different
outside convection conditions.
FIND: (a) Ratio of heat loss for different convection conditions, (b) Outer surface
temperature for different convection cond

PROBLEM 14.25
KNOWN: Temperature and pressure of helium stored in a spherical pyrex container of prescribed
diameter and wall thickness.
FIND: Mass rate of helium loss.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Helium loss by one-dimensiona

PROBLEM 14.22
KNOWN: Oxygen pressures on opposite sides of a rubber membrane.
FIND: (a) Molar diffusion flux of O2, (b) Molar concentrations of O2 outside the rubber.
SCHEMATIC:
ASSUMPTIONS: (1) One-dimensional, steady-state conditions, (2) Stationary med

PROBLEM 1.6
KNOWN: Heat flux and surface temperatures associated with a wood slab of prescribed
thickness.
FIND: Thermal conductivity, k, of the wood.
SCHEMATIC:
ASSUMPTIONS: (1) One-dimensional conduction in the x-direction, (2) Steady-state
conditions,

PROBLEM 4.13
KNOWN: Electrical heater of cylindrical shape inserted into a hole drilled normal to the
surface of a large block of material with prescribed thermal conductivity.
FIND: Temperature reached when heater dissipates 50 W with the block at 25C.
S

PROBLEM 2.58
KNOWN: Qualitative temperature distributions in two cases.
FIND: For each of two cases, determine which material (A or B) has the higher thermal conductivity,
how the thermal conductivity varies with temperature, description of the heat flux

PROBLEM 8.34
KNOWN: Initial food temperature and mass flow rate. Length of heating and cooling sections in a
food sterilizer. Diameter of sterilizer tube. Time-at-temperature constraint, and constraint on local
maximum food temperature.
FIND: (a) Heat flu

PROBLEM 12.3
KNOWN: Thickness and temperature of aluminum plate. Irradiation. Convection conditions.
Absorptivity and emissivity.
FIND: Radiosity and net radiation heat flux at top plate surface, rate of change of plate temperature.
T = 30C
h = 40 W/m2K
S

PROBLEM 11.23
KNOWN: Counterflow concentric tube heat exchanger.
FIND: (a) Total heat transfer rate and outlet temperature of the water and (b) Required length.
SCHEMATIC:
ASSUMPTIONS: (1) Negligible heat loss to surroundings, (2) Negligible thermal resis

PROBLEM 14.3
KNOWN: Partial pressures and temperature for a mixture of CO2 and N2.
FIND: Molar concentration, mass density, mole fraction and mass fraction of each species.
SCHEMATIC:
A CO2 , M A = 44 kg / kmol
B N 2 , M B = 28 kg / kmol
ASSUMPTIONS: (1)