conduction 1 dimension 08
TRANSCRIPT
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One Dimensional,
Steady state Conduction
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The Conduction Rate Equation
x
TkAQx
T1
T2
T(x)
x
Qx
Thermal
Conductivity
Gradient Temperature
Surface Area
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Range of thermal conductivity for various states of matter at normal
temperatures and pressure
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Temperature dependence
of the thermal conductivity
of selected solid
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Temperature
dependence of the
thermal conductivity of
selected gases at
normal pressure
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Temperature dependence
of the thermal conductivity
of selected nonmetallic
liquids under saturated
condition
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Thermal Conductivity Measurement Apparatus
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Heat Diffusion Equation
t
T
k
c
k
q
z
T
y
T
x
T p2
2
2
2
2
2
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The plane wall
For one dimensional conduction in a plane wall,
temperature is a function of the x coordinate only and
heat transferred exclusively in this direction.
For one dimensional, steady state conduction in
plane wall with no heat generation , the heat flux is a
constant, independent of x.
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Thermal Resistance
kA
L
Q
TTR
x
ss
condt
2,1,
,
Thermal resistance for conduction
hAQ
TTR s
convt
1,
Thermal resistance for convection
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The Composite Wall
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Example
A leading manufacturer of household appliances is proposing a self
cleaning oven design that involves use of a composite window
separating the oven cavity from the room air. The composite is to
consist of two high temperature plastics (A and B) of thicknesses
LA = 2LB and thermal conductivities kA = 0.15 W/M and kB = 0.08
W/m.K, During the self cleaning process, the oven wall and air
temperatures Tw and Ta are 400 °C while the room air temperature
T is 25 °C. The inside convection and radiation heat transfer
coefficient hi and hr as well as the outside convection coefficient
ho are each approximately 25 W/m2 K. What is the minimum
window thickness, L = LA +LB, needed to ensure a temperature is
50 °C or less at the outer surface of the window?
This temperature must not be exceeded for safety reasons,
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Find the heat transfer per unit area through the
composite wall sketched. Assume one dimensional heat
flow
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The cylinder
Lk
rrR condt
2
)ln( 12,
Thermal resistance for conduction (cylinder)
rLhR convt
2
1,
Thermal resistance for convection (cylinder)
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The cylinder
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