This preview shows page 1. Sign up to view the full content.
Chapter 2
Heat Conduction Equation
230
Consider a thin disk element of thickness
Δ
z
and diameter
D
in a long cylinder (Fig. P230). The
density of the cylinder is
ρ
, the specific heat is
C,
and the area of the cylinder normal to the direction of
heat transfer is
, which is constant. An
energy balance
on this thin element of thickness
Δ
z
during a small time interval
Δ
t
can be expressed as
AD
=
π
2
4
/
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
=
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
+
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
Δ
−
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
element
the
of
content
energy
the
of
change
of
Rate
element
the
inside
generation
heat
of
Rate
+
at
surface
at the
conduction
heat
of
Rate
at
surface
the
at
conduction
heat
of
Rate
z
z
z
or,
&&
&
QQ
G
E
t
zz
z
−+
=
+Δ
Δ
Δ
element
element
But the change in the energy content of the element and the rate of heat
generation within the element can be expressed as
Δ
Δ
ΔΔ
EE
E
m
C
T
T
C
A
z
T
tt
t
tt t
element
=−
=
Δ
T
−
=
−
++
+
()
ρ
and
&
Gg
Vg
A
element
element
==
z
Δ
Substituting,
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat

Click to edit the document details