Abstract
The thermal model of a satellite project is commonly referred to as a black art in the aerospace industry. The entire thermal design depends on the completion of an accurate thermal model of the satellite. In turn, the thermal model depends on the finalization of the satellites physique as well as its modes of operation. Many of these decisions are made only a few deadlines before the integration stages of the satellite. In the meantime, thermal engineers must abide by the laws of thermodynamics and materials science to predict potential problems in their design while faithfully developing their analytical model, which hopes to merely confirm the engineers’ intuition. This paper provides an overview of the thermal model of a satellite known as DINO. At this point in the development of DINO, the thermal model is beginning to manifest its strategy. With a sound strategy, the thermal design of DINO will ensure that all components will endure thermal environments well within their prescribed temperature limits.

1.0 Modeling Concepts
1.1 Focus
DINO stands for Deployment and Intelligent Nanosatellite Operations. As the name suggests, this satellites purpose is to exhibit deployment technology as well as intelligent operations. These processes are achieved by use of a network of components, which together are able to accomplish the desired task. In a sense, the satellite itself is just a collection of components connected in a certain way. These components consist of materials with desirable properties for their application. Electrical devices, for example, take advantage of materials with specific electrical properties. Alternatively, a structural component depends on the mechanical properties of the materials it employs to provide a stable satellite structure. All components of DINO have a certain utility whether it is of a structural, electrical, or optical nature. In order to perform this utility in a given environment, materials are selected carefully when designing the components’ hardware. The challenge for a thermal design is to consider the design limitations of each component, and control the thermal environment it will be subjected to so as to keep it safe from thermal damage for the duration of the satellites lifetime.
The goal sounds simple enough, but becomes more complex when considering the environment of DINO as a whole. The satellite orbits Earth and thus alternates between periods of direct sunlight exposure and periods in the shadow of Earth.
A closer look into the satellite also reveals electrical devices, which produce heat, that are being operated randomly rather than on a continual basis. In the overall

picture, the variable radiation exposure and internal heat generation makes for a challenge in creating an isothermal environment for the component onboard
DINO. An ideal thermal design for DINO would allow for a balance between the rate at which DINO dumps heat into cold space and the rate at which radiation heat and heat generated by onboard devices is being introduced to the satellite.
Before discussing current progress on overcoming these challenges, a brief background on some thermodynamic concepts as well as the theoretical analysis utilized will be given.
1.1
Thermodynamics Background
1.1.1 Temperature
The main thermal requirements are temperature ranges. Each team working on DINO depends on hardware to some extent in their respective designs. These hardware components are sometimes homogenous materials, and other times are composites of multiple materials. Depending on the thermal properties of all materials utilized in a component and the interfaces between them, a specific temperature range can be assigned so as to guarantee its desired performance. There are many factors which go into making such a guarantee and that will be covered shortly. First, it is appropriate to stress the significance of being able to generalize the thermal stability of a system by a single variable, namely temperature .
Temperature is an often-misconceived measurement. What temperature tells an engineer is whether there will be an exchange of thermal energy between

two subjects in contact. If the two objects are at the same temperature, there will be no heat exchange between them and they are said to be in thermal equilibrium.
This is a more specific version of the fundamental law of thermodynamics.
Originally formulated in 1931 by R.H. Fowler, the zeroth law of thermodynamics states: “If two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other (Cengel).” In today’s world this idea is almost intuitive.
What is often taken for granted is the idea that temperature is not a measurement of what is directly perceived through touch. There are other variables independent of temperature that contributes to how warm or cold and object feels. Consider the use of a glass thermometer in measuring boiling water.
The boiling water transfers thermal energy to the thermometer until it is at the same temperature as the water. Although it would be unwise to touch the boiling water directly, its no problem to grab the glass thermometer and read the temperature of the water. The water obviously would feel much hotter than the thermometer but they are at the same temperature. This problem must have troubled the human race until Anders Celsius devised a universal temperature scale in 1741. Perhaps a strong reason his scale caught on is because it was based on the most vital human resource, which also happens to have possibly the most obvious thermal side affects. Water can freeze or evaporate with a small fluctuation in temperature with respect to other common substances. Celsius observed this convenience and created a centigrade scale, meaning 100 grades,

between the freezing and evaporating points of water. According to the original scale: at 100

C water freezes and at 0

C it will evaporate.
This trend of decreasing temperature with increasing warmth was reversed in 1887, by the International Commission on Weights and Measures who adopted the scale and reversed the order so that 100

C corresponded to the warmer temperature where water begins to evaporate and 0

C corresponds to the colder state of water where freezing takes place. As the world of science evolved, Lord
Kelvin mathematically projected the temperature corresponding to zero pressure with respect to 0

C. He determined this value to be –273.15

C. This corresponds to the absolute lowest possible temperature in the universe and corresponds to
0

K on the newly devised Kelvin scale. This scale became known as the absolute temperature scale. Both temperature scales will be utilized throughout the analysis of DINO depending on the circumstance.
In reality, temperature is a measurement of the average molecular kinetic energy of a substance. At every level from sub-atomic to molecular, particles in a system can vibrate, rotate, or translate. The particles in motion have mass and their motion can be quantified as a form of kinetic energy. The average energy of all motion is what temperature is a measurement of. With this in perspective it makes a bit more sense why heat transfer does not occur between objects with the same temperature. The particles of each object possess the same kinetic energy so there can be no transfer of momentum from one object to the other by direct contact.

The temperature of the components that make up DINO is vastly important, as it is the beginning and the end to the analysis. We are given initial temperatures, as well as temperature restrictions for each component, and in the end will provide the maximum and minimum temperatures each component will see for any possible mode of operation DINO could endure. In order to get from beginning to end, an analysis of heat transfer between all components is performed. Temperature differences drive heat transfer throughout the satellite and heat transfer leads to changes in temperature.
1.1.2 Temperature Change
As was just established, temperature is a measure of the internal kinetic energy of a system. Changes in this energy, or changes in temperature, are the result of transfers of this kinetic energy to and from the system. This type of energy transfer is called heat transfer. The driving force that activates heat transfer is temperature. In a system, kinetic energy is distributed throughout so as to reach equilibrium, at which point the system is said to be in steady state. In a steady state system, all components are in thermal equilibrium with each other and there is no transfer of heat. DINO will be in steady state only while it is stored in the payload of the shuttle that transports it to orbit. This is because the satellite is in a controlled environment while in the shuttle, allowing it to reach a uniform temperature. There are no temperature differences to drive the transfer of heat to or from the satellite. Once in orbit, however, the satellite is subjected to cold space as well as warm bodies such as the Sun and the Earth resulting in

periodic fluctuations of heat gain and loss while orbiting. Furthermore, electrical devices onboard DINO are activated, generating heat that is dumped into the satellite.
In order to predict temperatures of components onboard DINO, it is necessary to quantify how much is transferred as a result of temperature differences as well as how much heat is required to change the temperature of each component. A thermal engineer works in the macroscopic realm of thermodynamics. Meaning, the engineer is concerned with properties of materials rather than the microscopic processes that determine these properties.
1.1.3 Heat
Originally, heat was thought of as a massless substance called calorie . It was quantified with the Celsius temperature scale in mind. One calorie of heat is enough to raise the temperature of 1 gram of water by 1

C. 1000 calories are equivalent to a Calorie, as seen on the side of food and drink boxes today.
However, since discovering that heat transfer is literally the transfer of internal energy rather than the transfer of a massless substance, heat energy has been more conveniently quantified on the same scale as many other forms of energy, Joules or BTU’s (British Thermal Units).
Different materials of identical mass require different amounts of heat to change the temperature by 1

C. This is a result of the structure of the material. A rigid structure such as iron, for example, requires 4.5 Joules of heat to change the temperature of 1 gram of the substance by 1

C. Alternatively, liquid water

requires 41.9 Joules to change the temperature of 1 gram of water by 1

C. The amount of heat required to change the temperature of a specific material is a property of that material. This property is called specific heat , C p
. With knowledge of a materials specific heat, comes knowledge of how much heat is required to change its temperature. Equation 1 gives the relation for the change in temperature, as a result of heat transfer for a specific material.

T

Q
IN / OUT
C
P
Equation 1
1.1.4 Heat Transfer
With the thermal analysis of DINO, the initial temperature of all components is known as being equal to the steady state temperature of the payload onboard the shuttle. From the moment the satellite is placed into orbit, and its instruments are initiated heat is being gained and lost by components on the satellite simultaneously. This begins a cycle of non-homogenous temperature distribution throughout the satellite that must be predicted continuously through the end of DINO’s lifetime. The amount of heat created by onboard devices can easily be predicted, as well as the magnitude of heat provided by celestial bodies.
However, this information along with equation 1 is inadequate it analyzing a complex network of components such as with DINO. Once one component onboard DINO gains or loses heat energy it begins exchanging energy with all components it is in contact with. If it gains heat, it immediately transfers enough of this heat so its neighboring components so as to maintain thermal equilibrium.

In effect, the satellite is constantly distributing heat so as to reach steady state. So in order to change the temperature of a single component, enough heat must be provided so as to change the temperature of all components in contact with it, and the components in contact with them and so on. This is where the calculation becomes tricky, and it becomes necessary to quantify how heat travels through
DINO as well as how it is deposited in equation 1.
As stated previously, heat transfer is a result of temperature. In practice, a temperature difference is required to drive heat from one point to another so it is a temperature difference that activates heat transfer. Since temperature differences drive heat transfer and the result of heat transfer is a change in temperature, heat transfer is calculated as a time rate. As the process of heat transfer progresses, the driving temperature difference decreases and the rate at which heat is transferred decreases accordingly.
The three mechanisms of heat transfer are conduction, radiation, and convection. Thermal conduction is heat transfer as a result of momentum transfer at a molecular level thru a medium. Radiation heat transfer is a result of electromagnetic waves driven by temperature differences between objects not in contact. Radiation heat transfer is a much faster process than the other mechanisms of heat transfer, as energy it is not hindered by a medium thru which to travel as in the case of conduction. Convection is a form of conduction in which case a moving fluid is in contact with an object. The rate of heat transfer in a convective process depends on the surface properties of the fixed object. In the case of DINO, convection is neglected as space can be considered a vacuum.

1.1.5
Heat Conduction
The most common form of heat transfer is thermal conduction. At a microscopic level it is the transfer of momentum through an object or between objects in contact. This type of heat transfer is what allows heat to be distributed through an object when applied at a specific point. The rate at which heat propagates from one point to another through a medium is given by equation 2.

Q
  kA dT dx
Equation 2
In 1822, J. Furier first expressed equation 2 quantifying the rate of heat transfer via conduction. It states that the time rate of heat transfer is equal to the product of the cross sectional area thru which heat is transferred, the thermal conductivity of the material in the direction of heat transfer, x, and the temperature gradient, dT/dx, which drives the process. Thermal conductivity, k, is a measure of how quickly heat can travel through a material. It depends mainly on the molecular structure of the material, but also on the instantaneous temperature of it. If the structure is rigid in all directions, then internal kinetic energy can travel with ease through the material. This explains in large part why metals, typically with rigid crystal structures, can more easily pass heat than say polymers, which have strong bonds in one direction along chains but have weak vander-waals bonds between chains. The thermal conductivity of a material also varies with the temperature of the material. If there is already a relatively large amount of kinetic energy stored by the structure of a given material, its ability to

pass excess kinetic energy is hampered. Thus thermal conductivity is higher for rigid structures and decreases with temperature.
In order to apply this equation to the satellite, DINO is broken up into discrete rectangular elements. Each element, called a node in modeling the satellite, has a temperature that is assigned at its center of mass. Of interest to the thermal model of DINO, is the rate at which heat can conduct from node to node.
If the nodes are of the same material, then equation 2 can be applied directly with the temperature gradient determined by the temperature difference and the distance between the centers of each node. If the nodes are different materials, the average rate of heat conduction is calculated depending on the temperature gradient from the center of each node to the interface between them.
Creating a thermal conduction model of DINO is the fundamental step in the overall analysis. By breaking the satellite up into nodes, a network of potential heat paths and depositories is established. The accuracy of this model depends on its resolution, as determined by selecting nodes. The temperature of a node is an average of the mass it represents. Therefore decreasing the size of the nodes and thus increasing the number of nodes representing the physical satellite results in an accurate representation of thermal activity throughout the satellite.
Each node represents a quantity of mass that can gain or lose energy with interfacing nodes according to equation 2. In so doing, the temperature of this node changes with the relation shown in equation 1. The next step in building the thermal model of DINO is including all sources of heat transfer to and from the satellite.

1.1.6 Thermal Radiation
Heat transfer to and from the satellite is a result of radiation heat transfer.
It is also a mechanism that allows heat transfer between nodes as with conduction.
In practice it is calculated as if it were driven by a temperature difference between surfaces that are in view of one another. In reality radiation transfer is a combination of radiation being emitted from a surface as result of its temperature, and energy incident on a surface that was emitted by others.
Joseph Stefan first quantified the rate at which heat is transferred via radiation in 1879. Stefan discovered that the energy at which a blackbody emits radiation is the product of the Boltzmann constant,

, and the temperature of the emitting surface to the fourth power. This law became known as the Stefan-
Boltzmann equation and is included as equation 3.
E
 
T
4
Equation 3
The Stefan-Boltzmann equation assumes an ideal surface known as a blackbody, in which heat is radiated at a maximum rate. A real surface, however, has a color which limits the wavelength at which heat is radiated, as well as a rough surface which alters the direction in which radiation is emitted. To account for these variables, the total amount of radiation emitted from a given surface at a specific temperature is found by multiplying a constant by the Stefan-Boltzmann equation known as emissivity,

. Emissivity is a property that determines what fraction of thermal energy is radiated by a surface with respect to an ideal

blackbody. So, if the surface property and temperature of a material are known, the amount of heat lost thru radiation can be quantified.
Once the radiation is emitted from a surface, it propagates thru space to any and all surfaces in its direct path. These surfaces then absorb components of the incident radiation that are normal to their respective surfaces. Similar to the case of emission, real surfaces are not ideal blackbodies and can only absorb a fraction of the radiation it is incident to. For this reason the fraction of incident radiation that is absorbed is taken into account by a surface property called absorbtivity. In the practice of calculating heat transfer via radiation, the processes of absorbing and emitting radiation are combined and the driving factor for heat exchange becomes the temperature difference between surfaces in direct view. In order to calculate heat transfer in this way, all surfaces of DINO must be contained in a closed system. The benefit is that in the end all emitted radiation is accounted for as it is absorbed by other surfaces that are part of the closed system.
For the interior of the satellite, a closed network is already provided for in which to calculate heat radiation as a function of the temperature difference between surfaces. The difficulty lies in taking into account the geometry of the system of surfaces. Each surface can see a finite number of other surfaces in its direct view. Since the surface is also emitting a finite amount of radiation, it is necessary to determine how much of the emitted radiation will run into each surface in its view. Furthermore, the angle at which the radiation impacts each surface must be known to determine how much of it will be absorbed. These geometrical factors are taken into account by use of what is known as a view

factor. The view factor is a constant reflecting the orientation between any pair of surfaces that can transfer radiation. It is a fraction that tells how much of the emitted radiation from surface ‘i’ will strike surface ‘j’ squarely and is denoted by
F i-j
. Each surface element has an associated view factor with each surface it
‘sees.’ Summing all view factors together for each surface yields the value 1.0, indicating the successful distribution of 100% of its emitted radiation.
For a closed system consisting of N surface nodes, the relation used to quantify radiation heat transfer from each surface ‘i’ and all other surfaces it sees,
‘j’ is given by equation 4. It is obtained by utilizing Stefan-Boltzmann’s relation in adding the radiation loss of surface ‘i’ to the absorbed radiation from surfaces
‘j’. The summation is performed for every surface in the closed system. j
N 

1

Q i
 j
 j
N 

1
A i
F i
 j

(
 i
T i
4   i
 j
T j
4
) Equation 4
For the interior of DINO, this process is straightforward as all surface nodes see other real surfaces. In the case of surface nodes on the exterior of
DINO, the system must be modified so as to create a closed system for which equation 4 can be applied. This is accomplished by constructing an imaginary
‘space box’ around the satellite to orbit with the satellite at all times. The sides of the box are transparent, massless, and at a temperature equal to the cold space they represent, 0

K. The fact that the space surfaces are massless means that they cannot absorb heat energy and thus their temperature cannot change. Since the temperature of each of the space nodes is constantly zero, they cannot emit radiation and the satellite surfaces which see them can only lose heat to space.

Before explaining the significance of the space box being transparent, it is first important to explain celestial sources of thermal radiaton.
1.1.7 Celestial Heat Source
As shown, all warm bodies emit radiation as a function of their surface properties. This means all bodies in space that the satellite can see emit radiation that can be potentially absorbed by the satellite. The sources taken into account by the thermal model are the Sun and Earth. Other sources emit heat that is absorbed by the satellite at such a small scale that they can be neglected. The heat provided by the sun is incident on the exterior surfaces of DINO in two ways.
The first is direct solar radiation and the second is referred to as albedo. Albedo is the reflection of solar radiation by Earth. Also, the earth itself emits radiation that can be absorbed by the satellite.
All together the sources of radiation from celestial bodies includes: Direct
Solar, Albedo, and Earthshine. With the current state of science, it is impossible to predict exactly how much radiation each body emits as a function of time.
However average values of the magnitude of thermal radiation emitted by each have been measured historically and are readily available. The maximum average heat flux given off by each over the course of a year is taken as the maximum heat orbit. Likewise, the minimum of each constitutes the coldest possible orbit DINO will endure. Earthshine and Direct Solar radiation heat transfer to the satellite is given as a heat flux, while Albedo is given as a fraction of direct solar that is reflected from earth. All that is needed to determine the exact amount of heat

transfer is the view factor between each surface node on the exterior of DINO and the celestial bodies for each point in orbit. When the satellite is behind earth it can only absorb earthshine as the sun is not in its view. When in view of the Sun, the surfaces which see the earth are absorbing earthshine and albedo while the surfaces that see the sun are absorbing direct solar. Equations 5-7 show the calculations involved for evaluation heat transfer from celestial bodies for exterior surfaces of DINO.

Q
Sun
 j

A j
 j
F
Sun
 j

DS
H / L
Equation 5

Q
Albedo
 j

A j
 j
F
Earth
 j

DS
H / L
R
H / L
Equation 6

Q
Earth
 j

A j
 j
F
Earth
 j

E
H / L
Equation 7
In equations 5-7, the rate at which heat is absorbed from celestial bodies depends on the view factor between each surface and the bodies in question, the surfaces ability to absorb incident radiation, and the rate at which each body emits thermal radiation. The variables DS, E, and R correspond to direct solar, earthshine, and the fraction of direct solar reflected by the earth respectively.
2.0 Analysis
2.1 Thermal Model
The thermal model for DINO is still being developed at the time of this paper.
However, the underlying concepts have been presented in the preceding discussion.
Basically the thermal model is formulated by first breaking the satellite up into a

collection of nodes. Each node represents the mass and thermal energy content of a real component onboard DINO. The first step in creating the thermal model is to connect these nodes with conductors. The conductors represent the rate at which heat can transfer between nodes via thermal conduction or thermal radiation. The rate depends on the speed at which heat can propagate between each node pair, as well as the amount of heat required by each node to change in temperature. Once this
‘frame’ of conductors is complete, and all possible heat paths are characterized the heat sources can be included in the model. The heat sources include radiation heat transfer to and from the satellite as well as the heat generated by electrical devices onboard DINO. Depending on the magnitude of these heat sources (and leaks in the case of energy lost due to thermal radiation to cold space), which are determined in large part by the possible orbits DINO can follow, each node will endure a maximum and minimum temperature. If this temperature range does not agree with the required temperature limits for the real components performance, thermal control devices must be introduced to the system to maintain thermal equilibrium.
The thermal model is constructed using autoCAD based software. Details of this process are not included in this discussion although it follows the theoretical calculations outlined above. The reasoning is that shortly before submission of this paper, the software that was utilized in building the thermal model was lost. It was centralized on a computer that crashed in early March of 2004. This provided an opportunity to upgrade the software to something that was more efficient and provided more useful output data. In result we changed our analysis software from a combination of several independent programs to a single program, which performs all

necessary calculations. This newer software, which is currently being utilized, is called Thermal Desktop and works from an autoCAD foundation. One of the most attractive features is the ability to work with SOLIDWORKS files. Importing directly from SOLIDWORKS allows the thermal team to skip a very laborious step hinted at above. Previously, the physical satellite was reconstructed on a node-bynode basis by defining the coordinates of each node with respect to a coordinate system fixed at the center of DINO and then calculating the view factors between each node. By importing SOLIDWORKS drawings of the physical satellite, this laborious process can be eliminated all together as Thermal Desktop does all the work of calculating the geometric qualities between nodes.
2.2 Thermal Control
With the completion of the thermal model of DINO maximum and minimum temperatures that each node will be expected to endure in its lifetime will be provided. In all there are several thousand nodes, with tens of thousands of potential paths for heat to travel throughout the satellite. Verifying the model becomes a difficult but necessary process. However, since the model is being developed simultaneously with the development of the physical satellite, the use of thermal control devices must be anticipated. The following provides and overview of the types of thermal devices that will be utilized. The specifics of these devices cannot be determined until the thermal model is complete and tested for accuracy. This process will also be discussed, as the testing process itself depends on the employment of thermal devices.

2.2.1 Temperature Sensors
Once the satellite is in orbit, knowledge of temperatures at specific points in DINO is almost useless. We can monitor the temperature of devices directly, and if they begin to overheat we can turn them off. Likewise if a device is turned off and is beginning to run cold we can turn it on. Otherwise, the temperature of devices that cannot be turned on or off is redundant. Therefore, only the electrical device temperatures will be measured will DINO is in orbit. For this, highly accurate temperature sensors with low cost will be utilized. Specifically, transducers assembled by Analog Digital (Model # AD590) have been selected for this task. The transducers can be embedded directly onto integrated circuits, or can be glued to surfaces with an adhesive. They require a voltage input between 4 and 30V, and output a current proportional to the absolute temperature they measure. The output current corresponds to 1

A per degree Kelvin.
Circuitry which will power these devices and collect their output data is currently being designed by the Command and Data Handling team of DINO.
Another type of temperature sensor will be used in testing the thermal model. Testing will occur in a thermal vacuum. Details relating to the testing process have not been considered at this point in the thermal design process, however the procedure for collecting data from the testing process has been planned to some extent. In testing the model, the actual heat transfer rates between each point on the satellite will be compared to the heat transfer rates as predicted by the thermal model. Therefore, the criteria for selecting temperature

sensors is different than for the highly accurate transducers selected for direct measurement of devices. Also, it is desired to have a large number of test points meaning the cost of potential temperature sensors is a limiting factor. After considering many temperature sensor types it was determined that T-type thermocouples would be the best option. They are inexpensive, self-powered, and accurate over a wide temperature range. The placement of these thermocouples depends on the results of the thermal model of DINO. As the thermal model reaches completion, theoretical heat transfer rates will be known between all nodes of DINO. Some will be more extreme than others, and the accuracy of specific heat paths will be essential to verify. Therefore, until the model is complete it is impossible to predict how many thermocouples will be utilized as well as where they will be adhered to the satellite. However, obtaining the sensors must be complete before the thermal model is. The thermocouples are only to be used in testing the model, so will not be wired through the onboard computers. They will be wired to an external computer for data collection. Due to the lack of information regarding how many thermocouples will be used, and the required length for data collection, they will be assembled by Space Grant rather than purchased. Based on the maximum number of thermocouples as well as the average length of wiring required to network all thermocouples to an external computer, a specific length of thermocouple wire will be obtained. The thermocouples will be made from this wire.
2.2.2 Surface Control

The untreated exterior surfaces of DINO allow for a quantifiable amount of radiation heat transfer as determined by equation 3 in conjunction with the specific surface properties of absorbtivity and emissivity. Ideally, all components onboard DINO will endure an isothermal environment in which the temperature remains constant and within their required operating limits. This requires a balance between the amount of heat introduced to the satellite by heat generating devices and radiating celestial bodies with the heat that is lost to space as a result of radiation. The strategy thus taken in achieving this balance is to take advantage of the properties of surfaces exposed to space, and actually manipulating these properties as necessary by use of paints and insulation blankets.
2.2.2.1 Surface Paints
Surface paints are effective means to change the emissivity or absorbtivity properties of a surface. Bright colored paints result in low radiation transfer as they correspond to longer wavelengths of radiation that can pass through the surface. Likewise, dark colored paints increase the rate at which radiations as thermal energy propagates into or out of the surface at low wavelengths. Therefore, if the thermal model predicts a component will be too hot with respect to its operating temperatures, the surface can be painted a dark color so that it ejects more heat into space.
However, this also means that if the surface sees a warm body such as the sun it will absorb more heat further perpetuating the problem. For this

reason, surfaces that are designed for maximum radiation transfer are located on the faces of the satellite that will not see the bright sun in orbit.
Therefore, surface treatment is not a good solution for components that will contain an excess amount of heat. For components that are likely to be too cold, however, surface paint is an effective way to isolate the component from the volatile radiation transfer with space.
An example of where paint will be a useful control method for a surface on DINO is the zenith face of DINO, which houses the batteries that power DINO. The primary concern is that these batteries will become too cold at some point in the orbit. For this reason, the surface will be painted a bright color. Until the thermal model is complete the assumption is that the surface will be painted white so that the ability to absorb or emit thermal radiation approaches zero. Upon completion of the thermal model, it is possible that a small amount of heat must be rejected or added to the zenith panel to maintain the batteries within their operating limits, in which case the exact color of the paint will be slightly darker such as gold.
2.2.2.2 Radiator
As stated above it is risky to treat an external surface of DINO with a dark color of paint. If the surface is intended to dump excess heat into space, it must be located on a face of the satellite that will not be exposed to the hot sun. The only face where this is possible is the nadir

face of DINO. This face is constantly exposed only to Earthshine and
Albedo. Therefore, a radiator will be placed on this face. The purpose of a radiator is to simply take advantage of a highly emissive surface so as to eject heat from the satellite. It will be sized based on how much heat must be ejected, as determined by equations 4, 6, and 7. No new material will be required to dedicate a surface as a radiator with the exception of black surface paint. This radiator will not be the only radiator onboard DINO.
The body mounted solar panels will also act as radiators as the highly absorbent surfaces will eject heat when not exposed to the Sun for which they are designed.
2.2.2.3 Multi-Layer Insulation
Not all surfaces can be treated by the application of paint. The structure of DINO is designed so as to contain a minimum amount of mass, so as to provide enough strength with minimum cost in terms of weight. Therefore the frame is not a solid, but more accurately described as grid. There are thus ‘holes’ which allow radiation transfer between internal surfaces of DINO and cold space. It is in the interest of the thermal design to block these holes so that interior surfaces do not have to be treated with paint to minimize radiation transfer. This is accomplished by using multi-layer insulation (MLI) blankets. The blankets are composed of several layers of material so as to minimize the amount of radiation energy that can transfer to and from the satellite.

MLI blankets are composed of an outer ‘pillowcase’ made of a material such as Mylar that has low emissivity. Inside this pillowcase are a number of net-spacers. In space, which is assumed a perfect vacuum, the MLI blankets expand similar to a marshmallow in a vacuum. Ideally the layers do not make contact with each other, and thus the only way heat can transfer between the outer Mylar layers is by radiation. This explains why the inner layers are a net material, as they have minimum surface area in which to make contact with each other. The number of layers between the outer Mylar layers is determined by the thermal model and depends on how much heat transfer can safely occur between the outer surface and space as determined by the temperature of surfaces the MLI blanket hopes to protect.
2.2.3
Controlling Heat Distribution
So far the manner in which heat transfer to and from the satellite via radiation will be controlled has been discussed. Bright paints and MLI will block radiation transfer for most of the satellite. However the body mounted solar panels and the radiator will still allow for radiation heat transfer. In order to take advantage of the ability of these surfaces to absorb and eject heat into space, the excess heat must be transferred readily to or from these surfaces.
This is accomplished by taking advantage of the structural design of DINO.
2.2.3.1 Cold Plates

Cold plates will be used when it is desired to transfer heat from one part of the satellite to another. For example, the body mounted solar panels are mounted such that while one side of DINO is exposed to the bright sun the other is exposed to cold space. On the Sunny side, the solar panels are absorbing thermal radiation at a rapid pace. In contrast, the satellite is dumping heat thru solar panels on the cold side of the satellite.
This is a problem as the panels are held in place by the satellite frame. On the interior of this frame, sensitive electronic instruments are mounted.
Therefore, it is undesirable for the solar panels to dump variable amounts of heat into the frame as the heat will ultimately affect the other devices mounted to it. Furthermore, the effectiveness of solar panels decreases as their temperature increases. Therefore, highly conductive plates will connect the backs of panels mounted across from each other. The result is that the heat accumulated on the sunny side solar panel will be distributed to the cold panel on the opposite side of the satellite. The size of the plates will be determined with the completion of the thermal model, as it depends on how much heat must be conducted.
2.2.3.2 Washers
In other cases, it is desirable to hinder the conduction of heat between a device and the components it is mounted to. Consider a device that is mounted in a box to the frame of the satellite by screws. Depending on the pressure between the two surfaces, and the material of the surfaces,

heat transfers freely between the component box and the frame. If that part of the satellites frame is located such that it is subject to a wide range of temperatures it may be desirable to hinder the potential conduction of heat between the frame and the component box further. This can be accomplished by decreasing the interface area between the two objects. A simple method for doing this is to insert insulative washers around the screws that hold the assembly together. Heat is still being transferred thru the screws, but the overall heat conduction between the box and the frame can be significantly reduced. Again, results of the thermal model are required to predict if washers are potential problem solvers in the thermal model of DINO.
2.2.3.3 Heaters
A possible thermal control device that has not been discussed thus far but could be utilized onboard DINO is a heater. Heaters are simple, and only require a current source and a resistive element. It is likely that heaters will be used with some of the more sensitive devices onboard. As the transducer temperature sensors are accurate and will enable real-time temperature sensing of devices, heaters may become the only active control devices utilized by the thermal team. If a device approaches the cold end of its operating limits, current could be run through a heater so as to provide a specific amount of heat to keep the device warm.
3.0
Conclusion

The process of attaining thermal control of DINO has thus far been a work in progress. At this point in the thermal design of DINO, the overall strategy has been determined as well as device selection. As the physical satellite becomes more complete, as will the thermal model. As the thermal model becomes complete, the usage of thermal devices can be finalized, as well as their sizes and dimensions. Until this point, the thermal engineers can only anticipate and prepare for potential problems in the physical design of DINO.

References
1.
Cengel, Yunus A. “Introduction to Thermodynamics and Heat Transfer” The
McGraw-Hill Companies, Inc 1997
2.
Smith, William F. “Foundation of Materials Science and Engineering” The
McGraw-Hill Companies, Inc 1993
3.
Oxtoby, Freeman, Block “Chemistry Science of Change” Saunders College
Publishing, 1998
4.
Wertz, James R. and Larson, Wiley J. “Space Mission Analysis and Design”
Microcosm Press, 1999