Department of Chemical Engineering & Materials Science
University of California Davis
Chemical Engineering Laboratory – ECH 155A
Heat Conduction in Solid Rods Experiment
Goals
1.
Determine the transient and steady state temperature profiles in solid rods heated in
one end by a constant temperature energy source.
2.
Compare experimental results with theoretically predicted temperature profiles.
Theoretical Background
A long, solid rod of uniform material and circular cross section, which is initially at a
uniform temperature equal to that of the ambient air, is suddenly heated at one end by a
constant temperature energy source. It is assumed that:
1.
All physical properties of the rods (e.g., thermal conductivity, density, heat capacity,
etc.) are independent of temperature.
2.
The rods are long.
3.
Heat is only conducted along the length of the rod; the temperature is uniform across
a radial crosssection.
4.
The film heat transfer coefficient is independent of axial position.
The conservation of energy then becomes
∂
T
∂
t
= α
∂
2
T
∂
x
2
 β
(T

T
a
)
(1)
Here, T denotes the temperature, which is a function of time, t, and the distance along the
rod, x. The thermal diffusivity is
α
and
β
is related to the heat transfer coefficient (see
Nomenclature).
The assumptions listed above can be transformed into the following initial and boundary
conditions:
1. Initially uniform temperature:
t
0
≤
T=T
a
for x
0
≥
2. Constant temperature energy source:
x=0
T=T
s
for t>0
3. Long Rod:
x=
∞
T=T
a
for t>0
Equation (1) can be solved subject to these boundary conditions to obtain the transient
temperature profiles
1
2
2
2
x
x
a
s
a
T
T
x
x
e
erfc
t
e
erfc
t
T
T
t
t
β
β
α
α
β
β
α
α


=
+
+


(2)
At long times, as t
→
, the steady state profiles can be obtained from Eq. (2).
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 Summer '11
 Kuhl
 Thermodynamics, Heat, Heat Transfer, Thermal conductivity, temperature energy source

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