Thermal FAQ, Volume 2

Volume 1. A B C D E F G H I J K L M
Volume 2. N O P Q R S T U V W X Y Z

PCAnalyze TAK 2000 Thermal Connection

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


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.

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/m2 234+/-7 W/m2 234+/-7 W/m2
72 to 76 Btu/ft2-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 piece-wise 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(i-j) * s
G = A * F(i-j) * s


G value of the conductor
A area of the surface i
e(eff) emittance (dimensionless)
s Stefan-Boltzmann Constant (energy/length2-time-deg4)
F(i-j) black body view factor from surface i to j (dimensionless)
F(i-j) 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(i-j) 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(i-j) is the product of the geometric shape factor F(i-j) and a factor which allows for departures from black body conditions (i.e. reflections). For example, for two parallel flat plates:

F(1-2) = F(2-1) = 1

F(1-2) = [ 1 / ( 1/e1 + 1/e2 -1) ] x F(1-2)

The effective emittance e* between two surfaces may be used to compute the gray body view factor with the following equation;

F(i-j) = e* x F(i-j)

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
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.

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/m2 1323 W/m2 1367 W/m2
433 Btu/ft2-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.

Stefan-Boltzman constant:
5.6697E-08 W/m2-K4
5.6697E-12 W/cm2-K4
1.355E-12 cal/cm2-K4-sec
1.714E-09 Btu/ft2-hr-R4

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 boiling-point 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

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 non-linear 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.

That portion of the electromagnetic spectrum below blue light (380 nanometers).

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