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
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 =
KNOWN: Boundary layer temperature distribution.
FIND: Surface heat flux.
PROPERTIES: Table A-4, Air (Ts = 300K): k = 0.0263 W/mK.
ANALYSIS: Applying Fouriers law at y = 0, the heat flux is
= k ( T Ts ) Pr exp Pr
KNOWN: Radius of coal pellets burning in oxygen atmosphere of prescribed pressure and
FIND: Oxygen molar consumption rate.
ASSUMPTIONS: (1) One-dimensional diffusion in r, (2) Steady-state conditions, (3) Constant
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
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.
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
c p 1006 J kg K
a) Uniform heat flux q 1000W m2 :
q DLq 471W
Total heat flux:
c p Tm ,out Tm
Homework # 6
Due in class Thursday February 25, 2016
Part a only. Remember to evaluate properties at the film temperature
Parts a and b only
Part a only
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
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:
1 exp Pr
Also note that y is th
Homework # 8 Solution
Due in class Thursday March 10, 2016
Textbook problems Assume fully developed flow if needed
Lets estimate the Grashof number: GrL
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
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
L 10mm 0.01m
Homework # 1 Due in class on Thursday Jan 14, 2016
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
KNOWN: Thermal conductivity and thickness of a wall. Heat flux through wall. Steady-state
FIND: Value of temperature gradient in K/m and in C/m.
k = 2.3 W/mK
qx = 10 W/m2
L = 20 mm
ASSUMPTIONS: (1) One-dimensional cond
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
KNOWN: Temperature and pressure of helium stored in a spherical pyrex container of prescribed
diameter and wall thickness.
FIND: Mass rate of helium loss.
ASSUMPTIONS: (1) Steady-state conditions, (2) Helium loss by one-dimensiona
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.
ASSUMPTIONS: (1) One-dimensional, steady-state conditions, (2) Stationary med
KNOWN: Heat flux and surface temperatures associated with a wood slab of prescribed
FIND: Thermal conductivity, k, of the wood.
ASSUMPTIONS: (1) One-dimensional conduction in the x-direction, (2) Steady-state
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.
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
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
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
KNOWN: Counterflow concentric tube heat exchanger.
FIND: (a) Total heat transfer rate and outlet temperature of the water and (b) Required length.
ASSUMPTIONS: (1) Negligible heat loss to surroundings, (2) Negligible thermal resis
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.
A CO2 , M A = 44 kg / kmol
B N 2 , M B = 28 kg / kmol