Untitled - Aerobib - Universidad Politécnica de Madrid

2.4. THERMAL CONDUCTIVITY 55
2000
1800
10 7 µ (gr cm −1 s −1 )
1600
1400
1200
H 2
− CO
H 2
− N 2
H 2
− CO 2
H 2
− N 2
O
H 2
− O 2
1000
800
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
X
H2
Figure 2.7: Viscosity for some gas mixture as function of composition.
Considering a surface element dσ, see Fig. 2.5, not parallel to any of the coordinate
planes and whose orientation is defined by unit vector ¯n, it is easily demonstrated
that heat flux Q through dσ per unit surface and per unit time is
Q = ¯q · ¯n = ∑ i
q i n i . (2.55)
Therefore, once the flux vector at a point is known, this determines heat transfer
through any surface element passing through it.
Kinetic Theory of Gases shows that within a dilute gas heat flux originates only
from molecular energy transfer when dσ moves at a velocity ¯v of the gas at the point.
Such transfer originates from the motion of molecular agitation and from diffusion
between species forming the gas if it is a mixture. When such transfer is calculated
one obtain the expression 27
¯q = −λ∇T + ρ ∑ i
Y i h i¯v di + M m RT ∑ i
∑
j
Y j D T i
M i M j D ij
(¯v di − ¯v dj ) , (2.56)
where λ is the thermal conductivity of the gas and h i is the total specific enthalpy
of species A i . Since diffusion fluxes of the species are produced by differences in
composition, pressure and temperature, it results according to (2.56) that this three
causes also produce heat transfer. In general, contributions from the third term in the
27 See Ref. [2], p. 498.