The thermal subsystem is a vital and integral component of the MEROPE satellite project. The main task of the thermal team is to ensure a safe thermal environment in which the satellite can properly operate. The term "safe thermal environment" means that all components of MEROPE are within their optimal operating temperatures. Any significant variance from any of the component operating temperatures could result in a failure of the satellite mission. In order to contribute to the success of the mission, the thermal team must consider many factors in its subsystem design. Among the many factors to account for are the nature of the harsh outer space environment, the type of orbit that the satellite will be in, the various heat transfer mechanisms that may affect the temperature of the satellite, and the size, shape, weight, and configuration of the satellite. The thermal team must also have close contact with all other MEROPE teams to ensure that their designs comply with the existing thermal subsystem plan. Compiling all of this data into one successful thermal subsystem design is the task to the thermal team.

For the mission to succeed, the satellite must survive the rigors of the space environment. Space is one of the most brutal environments imaginable with temperatures ranging from 120 C (248 F) in the sunlight and -100 C (-212 F) in the Earth's shadow. Unfortunately, MEROPE cannot operate properly within this temperature range, and thus its thermal environment must be controlled. It is hard to imagine how extreme these temperatures are, since most of the habitable regions of the Earth have never reached these temperatures before. Not only do the temperatures in space themselves induce a burden upon the satellite, but the rapid fluxuations of these temperatures can also cause problems for the satellite. Within about an hour and a half, the satellite may experience both ends of the temperature spectrum.

MEROPE will be flying on a polar, sun-synchronous orbit, which means that the satellite will pass over the Earth at approximately the same local sun time each day. Since the exact period of this orbit is not yet known, the satellite may experience anywhere from 50% to 100% sun exposure for one full orbit. When exposed to the sun, the satellite will receive three types of solar loads (which are pictured in the graphic above), direct solar, reflected direct solar (albedo), and Earth-shine. Direct solar is the direct infrared radiation from the sun and is by far the most significant solar input that the satellite will receive. Albedo, which is only 35% as intense as direct solar, is a signifcant solar input since our orbit is relatively low. As indicated above, albedo is the direct solar infrared radiation that is reflected off of the Earth's surface. Earth-shine is the weak, and usually negligible infrared radiation that is emitted from the Earth, but does originate from the sun as direct solar and albedo do. When in the eclipse of the orbit, the satellite will not receive any external heat loads and must rely solely upon internal heat during this time.

In order to successfully control the temperatures on the satellite, our team must understand and utilize the mechanisms of heat transfer. Heat can be transferred or can "flow" through three different methods: conduction, convection, and radiation. A brief description of each is listed below.

Conduction

Conduction of heat through a solid conductor is analigous to water flowing through a hose. We all are generally familiar with heat conduction and have most likely experienced it often in our lives. For instance, if you were to touch the handle of a cast iron frying pan while it still on the burner of the stove, it undoubtedly was very hot. The heat that was incident at the burner was transferred to your hand, through the frying pan, via conduction. Conduction occurs when molecules at a higher energy state (temperature) deliver their energy to adjacent molecules at a lower energy state. These molecules in turn excite their neighboring molecules until the entire conductor is at equilibrium temperature or until the heat source is removed. Conduction is accelerated in those materials that contain high concentrations of "free electrons", thus making that material a good thermal conductor. Conduction, just like all heat transfer, can occur only if a temperature gradient exists within a particular heat path. This means that two surfaces in contact will only transfer heat between them if one of the surfaces is at a higher temperature.

Conduction is a an important component of the heat transfer mechanism that will occur on MEROPE. Heat will be conducted from various internal regions of the satellite to the radiators that are located on the external surface of the structure. For analysis purposes, the thermal team will define various nodes within the structure of the satellite. These nodes are simply unique surfaces within MEROPE that may prove advantageous to identify, such as the faces of the particular component that generates a lot of heat. For MEROPE's purposes, our team will quantify heat conduction three ways: conduction through surfaces of the equal thickness, conduction through surfaces of unequal thickness, and conduction through assembled interfaces, such as screw, bolt, or rivet joints. The graphic below illustrates the notation that is used in some of the following conduction equations.

For conduction through two arbitrary nodes of equal thickness, Node1 and Node2, a single relation is used:
Note: k=thermal conducitivity a particular material

For conduction through two arbirary nodes of unequal thickness, Node2 and Node3, a few equations are needed:

In which R1 and R2 are defined below:


If a node needs to be thermally isolated from another node, or from the rest of the satellite, a single relation can be used to determine how much heat can be taken from the particular node through a certain conducting rod.

Q = heat taken from node, in watts
A = cross-sectional area of conducting rod
L = length of conducting rod

Convection

Convection is the second fundamental mode of heat transfer and is slightly more complicated than conduction. Heat is transferred between a solid and a fluid (either a gas or liquid) via convection if, just as in conduction, a temperature gradient occurs. While a complete understanding of convection requires the knowledge of fluid mechanics, one can think of hot air rising to the top of a room as an example of convective heat transfer. The hotter air is less dense than the cooler surrounding air, and thus the hot air displaces upward relative to the cooler air. This is an example of natural convection ,one of two types of convection, and is possible mainly through the interaction of gravity with existing fluid density differences. Forced convection, a second type of convection, occurs when fluid is delivered to a solid by an external source in order to facilliate convective heat transfer. Although convection is vitally important to heat transfer analysis on Earth, the effects of convection can be neglected when analyzing heat transfer mechanisms on MEROPE due to the fact that the outer space environment is essentially a vacuum.

Radiation

The final mode of heat transfer is radiation and is the second type of heat flow that MEROPE will experience in orbit. Radiation is the only mechanism of heat transfer in which a medium is not needed in order to transport heat between two elements. In fact, radiative heat transfer is maximized when it occurs in a vacuum environment. Radiation is transferred from one body to another by photons that travel at the speed of light via electromagnetic waves. If it weren't for radiation, the suns rays would never reach Earth and life on this planet would get very cold. Although radiation is optimized in vacuum environments such as outer space, this heat transfer mode occurs quite frequently on Earth. There are many examples of radiative heat transfer on Earth, such as radiator heaters, microwave ovens, and even simple black surfaces. For instance, if you have ever stood on black asphalt on a hot summer day, you probably noticed that heat seemed to rise from beneath you. This is because as the sun heats up the blacktop it absorbs the radiation from the sun and it radiates its own heat due to its increased temperature. All things that exist above a temperature of 0 K (which is basically everything one can think of) emits a certain amount of radiation. The amount of radiation an object emits (and absorbs) is affected by its geometry, surface condition, relative position with respect to other thermally significant objects, and as mentioned before, its overall temperature.

The factors affecting radiative heat transfer become very important when analyzing heat transfer mechanisms on MEROPE. When studying radiation of various components on the satellite, one of the first things to consider is the surface condition of the components. The two main variables that describe a component's surface condition with respect to radiation are emissivity and absorptivity. These two variables are a measure of a surface's ability to emit radiation and a surface's ability to absorb radiation, respectively. A perfect black-body radiator has emissivity and absorptivity values that are close to unity. All other surface finishes have values that are less than that of a perfect black-body. Next, our thermal team must determine the relative view factors for all components on MEROPE. A view factor is a measure of how well two surfaces "see" each other and their relative oriention to one another. Finally, the components' various temperatures is factored into the analysis and can be obtained from previous heat transfer computations. The main equation for quantifying radiation for analysis purposes is a variation of the Stefan-Boltzmann law of radiation and is defined as the rate at which a perfect black body emits radiative heat. This equation can be used to determine the amount of radiant heat transfer that occurs between two arbitrary surfaces; surfaces 1 and 2.

q(1-2) = radiant power delivered from surface 1 to surface 2
E(b1) = total emission of radiation per unit surface area from surface 1
A(1) = surface area of surface 1
F(1-2) = view factor from surface 1 to surface 2

Note: A view factor is a value that quantifies the relative size, geometry, and location of two arbitrary surfaces.

This relation can be modified in order to account for surfaces that aren't perfect blackbodies. Emissive and absorptive properties are taken into account when modifying this law.

Since the satellite cannot survive the extreme temperatures that space presents; thermal control is needed in order for the spacecraft to survive. Considering the size, dimensions, internal heat dissipation, and MEROPE budget, the thermal team will utilize a passive thermal control system, rather than an active thermal control system. The difference between a passive and active system is that a passive system does not utilize power or any type of working fluid in order control the temperature of the spacecraft. Instead we must take advantage of internal heat conduction and body-mounted radiators in order to control the amount of heat that exists on MEROPE. The first thing to focus upon in a passive thermal subsystem design is how the operating temperature ranges of each of the components compare to the temperature extremes that are expected for the satellite. The thermal team has calculated that the satellite would operate between 65 C (149 F) and -35 C (-95 F) without any type of thermal protection. An example of some of the operating temperature ranges on MEROPE are listed below:
 
 

Component	Minimum Temp.	Maximum Temp.
Batteries	0	40
Processor	-40	85
Transmitter	-35	80
Transceiver	-40	80
Memory chip	-40	80
Other chips	-40	85
Geiger tube	-40	75
TNC	-40	85
500 volt HVPS	-20	65

Note: All temperatures are in degrees Celsius
 
  Based upon these operating limits, the thermal system will be designed to have the spacecraft operate between 0 C and 40 C to ensure that all components are within their safe, functioning temperature limits. Comparing this to the unprotected operating temperature range of the satellite, thermal protection and a radiator system is needed. With this established, the radiator area that is needed in order to maintain the satellite at the given temperature limits must be calculated. In doing this, we must also determine the type of surface finish that the outer and inner structure must have so that the efficiency of the radiator is optimized. Next, we must calculate new temperature extremes taking into account the size, dimensions, and surface finish of the radiator area. If these extremes are still out of our designed temperature range, we may need to thermally protect the entire satellite or just certain select components. These are preliminary consideration and their scope cannot be determined until further analysis is performed.

The next stage of the thermal subsystem design is to begin to analyze in detail the many conduction and radiation paths that exist on MEROPE. Calculating the environmental solar loads and internal heat generation must also accompany this analysis. Once all of the heat transfer paths are quanitified and catelogued and the various heat loads are computed, our team can then begin to calculate the estimated temperatures for all components of MEROPE at different times of the orbit (this temperature data will be posted on this site once it has been gathered). Designing for a worse-case hot condition of 100% sun exposure and a worse-case cold condition of less than 50% sun-exposure, the thermal team will then assess the need for thermal protection. We will use multi-layered thermal insulation and thermal tape when thermal protection for the satellite or certain components are needed. If we must thermally isolate a certain component, (this would be done if it is deemed that the satellite as a whole will not operate within a given component's operating temperature range), we will use thermal insulation and various other thermal stand-offs in order to maintain the component's temperature within its given temperature range. Upon implementing the proper thermal protection for MEROPE, new temperatures for all components throughout the orbit will be computed. These values will be the temperatures that we will expect during the flight of MEROPE. Themistors will be placed on all vital components to monitor and compare their temperature readings to those that were calculated for the final thermal subsystem design.

However, before flight, we will work with the Integration and Test team to develop a thermal vacuum test to be performed on an engineering prototype. This test will be used to compare and verify the expected temperatures of MEROPE and its components. A thermal vacuum test is performed in an oxygen-free chamber that is subject to cyclic hot and cold conditions that are designed to simulate the actual orbit that the satellite must endure. If temperature readings vary too greatly from expected values, or if the engineering prototype fails in any way thermally, the thermal subsystem must be reworked or partially redesigned. Once the prototype passes a thermal vacuum test, the satellite is thermally ready for its actual flight.

While MEROPE is in flight, the thermal team is responsible for monitoring the thermistor readings and fine-tuning the system based upon gathered data. Telemetry data for in-flight temperatures will be posted here as soon as that data becomes available. Another task for the thermal team after launch is to observe any problem areas of the thermal subsystem during flight and make adjustments for Montana's second pico satellite, MEROPE II.

The themal team has received valuable aid and mentorship from a variety of industry sources. Without their help, MEROPE's thermal team could not successfully design a spacecraft thermal subsystem.

Lockheed Martin Corporation

The thermal team has received valuable industry mentorship from Brenda Constanzo, a thermal engineer working for the Palt Alto, CA division of the Lockheed Martin Corporation. Her help has been very important thus far as our team is performing the main stages of thermal subsystem work. We wish to thank her and Lockheed Martin for providing us with invaluable industry aid. We appreciate all the help that Brenda has provided and look forward to working further with her as we proceed toward to final stages of our design.

Sheldahl

Sheldahl is a corporation based in Minnesota that provides various thermal control materials for spacecraft thermal design. The thermal team has been working with the Sheldahl corporation to obtain multi-layered insulation and thermal tape for thermal protection of our satellite. We are very grateful for the assistance that Sheldahl had provided and we look forward to working further with them once our subsystem design has reached its final stages.