conduction 1 dimension 08
TRANSCRIPT
One Dimensional,
Steady state Conduction
The Conduction Rate Equation
x
TkAQx
T1
T2
T(x)
x
Qx
Thermal
Conductivity
Gradient Temperature
Surface Area
Range of thermal conductivity for various states of matter at normal
temperatures and pressure
Temperature dependence
of the thermal conductivity
of selected solid
Temperature
dependence of the
thermal conductivity of
selected gases at
normal pressure
Temperature dependence
of the thermal conductivity
of selected nonmetallic
liquids under saturated
condition
Thermal Conductivity Measurement Apparatus
Heat Diffusion Equation
t
T
k
c
k
q
z
T
y
T
x
T p2
2
2
2
2
2
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.
Thermal Resistance
kA
L
Q
TTR
x
ss
condt
2,1,
,
Thermal resistance for conduction
hAQ
TTR s
convt
1,
Thermal resistance for convection
The Composite Wall
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,
Find the heat transfer per unit area through the
composite wall sketched. Assume one dimensional heat
flow
The cylinder
Lk
rrR condt
2
)ln( 12,
Thermal resistance for conduction (cylinder)
rLhR convt
2
1,
Thermal resistance for convection (cylinder)
The cylinder