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Microsystems in Spacecraft Thermal Control 185

9.2.1 CONDUCTION
Conduction is the most common mode of heat transfer. In conduction, thermal energy
can be transferred through the medium from a region of high temperature to a region
of low temperature. The driving force for this type of heat transfer is a temperature
difference (temperature gradient), DT. Fourier’s law of conduction is the empirical
equation used to describe the conduction heat transfer. The law states that the rate of
heat transfer, Q, through a homogenous solid is directly proportional to the surface
area, A, (at right angles to the direction of heat flow) and to the temperature gradient,
dT/dx, along the path of heat flow. For the one-dimensional plane with temperature
distribution T ¼ f(x), the conduction rate equation is expressed as follows:

dT
Q ¼ kA (9:2)
dx
where Q: heat transfer rate (J sec 1 or W)
1
k: thermal conductivity (W m 1 K )
2
A: surface area (m )
T: temperature (K)
x: distance (m)

The minus sign is a consequence of the fact that heat is transferred in the
direction of decreasing temperature, that is, from the high-temperature region to
low-temperature region. The material property that describes heat conduction,
thermal conductivity, is typically dependent on the temperature of the material.
In most space applications, heat conduction in a continuous medium can be
properly described by Fourier’s law. The same law, however, is inadequate to
illustrate the heat transfer by conduction between two adjoined hardware surfaces.
Thermal conduction across a physical interface is considered as a special case. At a
microscopic level, such interfaces are rough and therefore significantly reduce
conduction. These interfacial resistances often dominate the rate of heat flow in
the process. An ‘‘interface heat conductance’’ is typically used to quantify this
affect and is relevant to many MEMS applications. To understand the general
concept of thermal conductance, C, Equation (9.2) can be rewritten for a plate of
given material and thickness, l/d as follows:

Q ¼ C DT (9:3)
kA
C ¼ (9:4)
d
where Q: heat transfer rate (J sec 1 or W)
1
C: thermal conductance (W K )
1
k: thermal conductivity (W m 1 K )
2
A: surface area (m )
DT: temperature difference between the two surfaces of the material (K)
d: thickness of the material (m).

© 2006 by Taylor & Francis Group, LLC