**Unformatted text preview: **EGEE 304 Spring 2018
Heat and Mass Transfer Quiz 1: Introduction to Heat Transfer
Name: __________________________ PSUID: ____________________ 1. You have a plane wall that contains a heat source, as shown in the figure. Using
your knowledge of heat transfer, and the information in this figure:
a) What is an energy balance on a “thin” volume element in words. Hint:
there are four terms as suggested in the equation – write the energy
balance with one term in each ( ) set – 1 point each term (4 points total): A
·
Qx 0 ( )–( )+( ·
Egen Volume
element ·
Qx + ∆ x x )=( x + ∆x L Ax = Ax + ∆ x = A 2. What is the driving force for heat transfer (1 point)? 3. Draw a thermal circuit for the situation below labeling all resistances; note T1 > T2 (2 points). T!1 Wall
T1 T2
T!2 ·
Q R T R T R ) FIGURE 2–13
One-dimensional heat conduction
through a volume element
in a large plane wall. b) Write the heat equation that is represented by your energy balance in simplified form. State any
assumptions you made to write this equation (3 points). 135
CHAPTER 3 x (%/%t " 0 and e·gen " 0) dr !r dr " " 0 (2–29) EGEE 304 Spring 2018· Egen
Note that we again replaced the partial derivatives by ordinary derivatives inHeat and Mass Transfer
the one-dimensional steady heat conduction case since the partial and ordinary
Quizare
1: Introduction
to Heat
Transferdepends
(Make up)
derivatives of a function
identical when
the function
on a single
variable only [T " T(r) in this case]. –31) PSUID: ____________________
0
–20. Name: __________________________
n be
Heat Conduction Equation in a Sphere
Now
consider
a sphere
with wall
density
#,below.
specific
heat
c, the
andtemperatures
outer radius
R.are
The
1. Draw
a thermal
circuit
for the plane
shown
Please
note
that
given in this picture,
area
of
the
sphere
normal
to
the
direction
of
heat
transfer
at
any
location
is
and be sure to draw and label all resistances (3 points).
A " 4Insulation
pr 2, where r is the value of the radius at that location. Note that the heat
–32)
transfer area A depends on r in this case also, and thus it varies with location.
One-dimension
By considering a thin spherical shell element of thickness $r and repeating
A1
2
through
a volume e
the approach
described above for the cylinder by using A " 4 pr instead of
1
k1
A3 transient heat conduction equation for a
T1 A " 2prL, the one-dimensional
3
–33)
2 isk2determined to be (Fig. 2–17)
sphere
k3 A2 h, T$ ! " %T
1 % 2 %T
r k
! e·gen " rc
2 %r
%r
%t
r Variable conductivity: (2–30) which, inL1the
thermal conductivity, reduces to
= L 2case of constant
L3 –34) .
egen
1 % 2 %T
1 %T
r
conductivity:
!
"
(2–31)
2 %r
%r
a
and 2. QIs· it possible to over-insulate a· pipe? Why or
r why not? Explain based
k
on %t
your knowledge of heat transfer (2 points).
Q ons hird
lay- onal
the ! ·
Q1
Constant " R T1 1
where
· again the property a " k/rc is the thermal diffusivity of the material. It
Q2
$
R3
Rconv Tunder
reduces to the following
forms
specified conditions: .
R2
egen
(1) Steady-state:
1 d 2 dT
r
!
"0
FIGUREr 23–20
(%/%t " 0)
dr
dr
k
Thermal resistance network for
(2) Transient,
combined series-parallel arrangement.
1 % 2 %T
1 %T
r
"
no heat generation:
2 %r
%r
a %t
r
(e· " 0)
gen ! " (2–32) ! " (2–33) (3) Steady-state,
dT
d
dT
d 2T
" by
0 the form:
or
r 2 !2
"0
no heat
generation:
3. For a given
medium,
the heat equation ris2satisfied
dr
dr
dr
dr
·
(%/%t " 0 and egen " 0) ! " (2–34) where
again
we replaced
the partial
derivatives by ordinary
derivatives in the
a) Is heat
transfer
steady or transient
(1 point)?
________________________
one-dimensional steady heat conduction case.
b) Is there generation in the medium (1 point)? ________________________ c) Which coordinate system are we using (1 point)? ________________________ 4. How are flux and rate of heat transfer related (2 points)? ...

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