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Chapter 2
Introduction to Conduction
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A rate equation that allows determination of the conduction heat flux
from knowledge of the temperature distribution in a medium
Fourier’s Law
•
Its most general (vector) form for multidimensional conduction is:
→
→
′′
=  ∇
q
k
T
Implications:
–
Heat transfer is in the direction of decreasing temperature
(basis for minus sign).
–
Direction of heat transfer is perpendicular to lines of constant
temperature (isotherms).
–
Heat flux vector may be resolved into orthogonal components
(2.22)
φ
→
→
→
→
∂
∂
∂
′′
= 


∂
∂
∂
T
T
T
q
k
i
k
j
k
k
r
r
z
′′
r
q
′′
q
′′
z
q
•
Cylindrical Coordinates:
( 29
, ,
T r
z
sin
θ
θ φ
→
→
→
→
∂
∂
∂
′′
= 


∂
∂
∂
T
T
T
q
k
i
k
j
k
k
r
r
r
(2.25)
′′
r
q
′′
q
′′
q
•
Spherical Coordinates:
( 29
, ,
T r
φ θ
•
Cartesian Coordinates:
( 29
, ,
T x y z
→
→
→
→
∂
∂
∂
′′
= 


∂
∂
∂
T
T
T
q
k
i
k
j
k
k
x
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This note was uploaded on 02/01/2012 for the course MECH ENG 225 taught by Professor Koylu during the Spring '11 term at Missouri S&T.
 Spring '11
 Koylu

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