
Thermal FAQ, Volume 2
 Natural (free) Convection:
 The convection coefficient hc is a complicated function of fluid flow,
thermal properties of the fluid, and the geometry of the system. Good
ENGINEERING JUDGMENT is required to cool effectively with natural convection.
Without going into any of the underlying equations, the natural convection
coefficient can be approximated by:
hc = .52 * C * ( (Tw  Tair) / L ) **.25
where:
L 
is characteristic length 
C 
is the configuration factor 
Tw 
is the wall temperature 
Tair 
is the air temperature 
For a vertical plate, L is the length of the plate and C is .56.
For a horizontal plate, L is given by:
L = 2 * length * width / (length+width)
For a horizontal plate facing up, C is .52; a plate facing down is
.26. Units for these constants are BTUs, hrs, feet, F.
 Nodes
 In order to develop a thermal network and solve it using numerical
techniques, it is necessary to subdivide the thermal system into a number
of finite subvolumes called nodes. The thermal properties of each node
are concentrated at the central nodal point of each subvolume. Each node
represents a capacitance and has a temperature.
The temperature assigned to a node represents the average mass temperature
of the subvolume. The thermal capacitance assigned to a node is computed
from the specific heat of the material evaluated at the temperature
of the node. Because a node represents a lumping of parameters to a
single point in space, the temperature distribution through the subvolume
is linear. In a homogeneous material, the temperature at a point other
than the nodal point may be approximated by interpolation between adjacent
nodal points where the temperatures are known.
The error introduced by dividing the system into finite sized nodes
rather than an infinite number of nodes depends on numerous considerations:
material properties, boundary conditions, node size, node center placement,
and time increment in transient calculations.
Typically a node is associated with a finite thermal mass (thermal
capacitance) and a temperature which varies as a result of changes
in the environment. These nodes are called diffusion nodes (mass
nodes). The temperatures predicted by these nodes represent a "lump" of
finite mass. In thermal modeling it is usually expedient to hold some
aspect of the system constant. This portion of the thermal system is
called a boundary condition. The boundary conditions drive the
thermal system. The system does not drive the boundary. Examples are:
Deep space for spacecraft modeling; A baseplate of an electronic box
for board modeling. The nodes used to model these conditions are called boundary
nodes . Constant temperatures are usually assigned to these
nodes however they can also be made to vary. Very often it is important
to know the surface temperature of a material. Remember, diffusion
nodes predict a "lump average" temperature. A two dimensional node
can be made to represent the surface. It has no thickness and therefore
has no thermal mass. These nodes can also represent interfaces between
nodes. These nodes are called arithmetic nodes (massless
nodes).
 Oscillating Coolant Heat Exchange:
 The Oscillating Coolant Heat Exchanger has recently been awarded 2
patents. This device behaves like a mechanically driven heat pipe, however
it is not limited by the operational constraints that often limit the
usefulness of heat pipes. The device has not been applied commercially
to date.
 Phase Change thermal control:
 Method by which a material's heat of transition is used to advantage.
This could include, but is not limited to, boiling water or melting wax.
 Planetary (earth) IR:

Perihelion 
Aphelion 
Mean 
234+/7 W/m^{2} 
234+/7 W/m^{2} 
234+/7 W/m^{2}
72 to 76 Btu/ft^{2}hr 
 Peltier Effect:
 When a current flows through a thermocouple junction, heat will either
be absorbed or evolved depending on the direction of current flow. This
effect is independent of joule IR heating.
 Parallel Conductors
 Thermal modeling term. Many times a conductor representing a complicated
geometry can be evaluated on a piecewise basis, then recombined into
one conductor value. One or more parallel conduction paths between nodes
may be summed to create one conductor value by the following equation;
G(tot) = G1 + G2 + G3 +...+Gn
 Radial Conductors
 Thermal modeling term. For conductors between nodes which are circular
sections, the equation shown below should be used.
 Radiation Conductors
 A thermal modeling term. The value of a radiation conductor is input
in units of energy per unit time per degree**4. It is be computed as:
G = A * e(eff) * F(ij) * s
or
G = A * F(ij) * s
where;
G 
value of the conductor 
A 
area of the surface i 
e(eff) 
emittance (dimensionless) 
s 
StefanBoltzmann Constant (energy/length2timedeg4) 
F(ij) 
black body view factor from surface i to j (dimensionless) 
F(ij) 
gray body view factor from surface i to j (area) 
The emittance e, is a measure of how well a body can radiate energy
as compared with a black body. Emittance is the ratio of total emissive
power of a real surface at temperature T to the total emissive power
of a black surface at the same temperature. The emittance of surfaces
is a function of several things including the material, surface condition,
and temperature. The emittance may be altered by polishing, roughing,
painting, etc.<
The view factor F(ij) is a function of the geometry of the system
only. Many computer programs have been developed to compute the view
factors between complex geometry's; however view factors between some
surfaces with simple geometry's can be hand calculated. The methods
and equations are found in several heat transfer texts.
The gray body view factor F(ij) is the product of the geometric
shape factor F(ij) and a factor which allows for departures from black
body conditions (i.e. reflections). For example, for two parallel flat
plates:
F(12) = F(21) = 1
F(12) = [ 1 / ( 1/e1 + 1/e2 1) ] x F(12)
The effective emittance e* between two surfaces may be used to compute
the gray body view factor with the following equation;
F(ij) = e* x F(ij)
The error induced by the use of e* is the result of neglecting secondary
reflections from surfaces other than the two for which the effective
emittance was determined.
 Resistance Temperature Characteristic:
 A relationship between a thermistor's resistance and the temperature.
 Resistance (thermal):
 The resistance to the flow of heat.
Resistance = 1 / Conductance
 Series Conductors
 Thermal modeling term. Series conduction paths between nodes may be
combined to create one conductor value by the following equation:
G(tot) = 1 / (1/G1 + 1/G2 +...+1/Gn) = R1 + R2 + ... + Rn
 Second Surface Mirror:
 The metal deposit provides the absorptance property. Silver and aluminum
are the most popular metals and are often used on 2.0 and 5.0 (50 and
125 microns) FEP, also referred to as FOSR, (Flexible Optical Surface
Reflector). This combination of materials obtains low absorptance over
emittance ratios for low operating temperatures.
An interesting combination of materials such as 5 mil (125 microns)
FEP and chromium can produce a "black" mirror.
Metal Deposits 
Solar Absorptance 
Silver 
.06  .09 
Aluminum 
.10  .14 
Copper 
.20  .30 
Germanium 
.50  .70 
Inconel 
.60  .70 
Chromium 
.70  .80 
FEP Thickness
Inches 
Emittance 
0.0005 
0.4 
0.001 
0.5 
0.002 
0.6 
0.005 
0.77 
0.010 
0.85 


 Set Point:
 The temperature at which a controller is set to control a system.
 SI:
 System Internationale. The name given to the standard metric system
of units.
 Solar constant:
 In space, normal to the sun line.
Perihelion 
Aphelion 
Mean 
1414 W/m^{2} 
1323 W/m^{2} 
1367 W/m^{2}
433 Btu/ft^{2}hr 
 Specific Gravity:
 The ratio of mass of any material to the mass of the same volume of
pure water at 4°C.
 Specific Heat:
 The ratio of thermal energy required to raise the temperature of a
body 1° to the thermal energy required to raise an equal mass of
water 1°. Typical
values.
 StefanBoltzman constant:
 5.6697E08 W/m^{2}K^{4}
5.6697E12 W/cm^{2}K^{4}
1.355E12 cal/cm^{2}K^{4}sec
1.714E09 Btu/ft^{2}hrR^{4}
 Super Cooling:
 The cooling of a liquid below its freezing temperature without the
formation of the solid phase.
 Super Heating:
 1. The heating of a liquid above its boiling temperature e without
the formation of the gaseous phase. 2. The heating of the gaseous phase
considerably above the boilingpoint temperature to improve the thermodynamic
efficiency of a system.
 TAK 2000:
 Thermal Analysis
Kit 2000, a most excellent thermal analysis program.
 Thermal Coefficient of Resistance:
 The change in resistance of a semiconductor per unit change in temperature
over a specific range of temperature.
 Thermoelectric Cooler:
 A solid state refrigerator based on the Peltier effect. Typically
very small; on the order of 1x1 inch. A single stage devices can create
a 37C temperature differential between hot and cold sides. A three stage
devices can create a 60C temperature differential. Use ranges from beer
coolers to spacecraft.
 Thermal Conductivity:
 The ability of a substance to conduct heat. Mathematically, the ratio
of heat flow to the rate of temperature change in the particular substance.
 Thermal Control:
 Thermal control is the engineered approach to control the thermophysical
aspects of a system. Typically, temperature is controlled but sometimes
heat flow is the controlled parameter.
Reasons for thermal control include:
 Preclude catastrophic thermal failure
 Increase some performance characteristic
 Increase reliability
Reliability concerns have taken on new importance as a result of various
studies that show a strong correlation between electronic equipment failures
and:
 High temperatures
 Thermal cycling
 Thermal Gradient:
 The distribution of a differential temperature through a body or across
a surface.
 Thermal model
 First and fore most a thermal model is tool. It is used to build the
knowledge base of the thermal engineer. This knowledge enable the engineer
to create a design that meet the requirements.
This could be accomplished (and sometimes is) with physical models
and prototypes. The time and expense of this approach is often prohibitive.
Another approach is to construct a computer based, mathematical model
of a thermal system. Such a model can be run through multiple conditions
or configurations in seconds or minutes. Parametric (sensitivity) studies
can also be quickly performed. Expense is incurred chiefly during the
initial construction of the model not the running of the model
 Thermistors
 Negative temperature coefficient thermistors are used to measure temperatures
below 150C. They have sensitivities of several hundred ohm per 1C. Their
cost range from $1 to $20. Their various configurations range from glass
beads to stainless steel probes. Drawback is the nonlinear response.
 Transpiration cooling
 Transpiration
cooling requires a liquid or gas coolant that flows through the surface
of a severely heated component and exits the component from the heated
surface through small pores in the surface. The coolant will both reduce
the convective part of any heating and also removes heat from the surface
in a very efficient way. Transpiration cooling is presently used in local
regions of commercial turbine and rocket engines.
 Ultraviolet:
 That portion of the electromagnetic spectrum below blue light (380
nanometers).
