Page 386 - Mechanical Engineers' Handbook (Volume 4)

1 Thermal Modeling 375
54.185 0.547
ln 3.132
Y P
H
and M is a gas parameter used to account for rarefied gas effects
M
where is an accommodation parameter (approximately equal to 2.4 for air and clean
metals), is the mean free path of the molecules (equal to approximately 0.06 m for air
at atmospheric pressure and 15 C), and is a fluid property parameter (equal to approxi-
mately 54.7 for air and other diatomic gases).
Equations (8a) and (8b) can be added and, in accordance with Eq. (7b), the contact
resistance becomes
R 0.95 k g A 1
m
P

1.25k
co
s
H Y M a (9)
1.3 Convective Heat Transfer
The Heat-Transfer Coefficient
Convective thermal transport from a surface to a fluid in motion can be related to the heat
transfer coefficient, h, the surface–to–fluid temperature difference, and the ‘‘wetted’’ surface
area, S, in the form
q hS(T T ) (W) (10)
s
fl
The differences between convection to a rapidly moving fluid, a slowly flowing or
stagnant fluid, as well as variations in the convective heat-transfer rate among various fluids,
are reflected in the values of h. For a particular geometry and flow regime, h may be found
from available empirical correlations and/or theoretical relations. Use of Eq. (10) makes it
possible to define the convective thermal resistance as
1
R cv (K/W) (11)
hS

Dimensionless Parameters
Common dimensionless quantities that are used in the correlation of heat-transfer data are
the Nusselt number, Nu, which relates the convective heat-transfer coefficient to the conduc-
tion in the fluid where the subscript, fl, pertains to a fluid property,
h hL
Nu
k /L k fl
fl
the Prandtl number, Pr, which is a fluid property parameter relating the diffusion of mo-
mentum to the conduction of heat,

c
p
Pr
k
the Grashof number, Gr, which accounts for the bouyancy effect produced by the volumetric
expansion of the fluid,
3
2
gL
T
Gr
2