LSU 06/21/2 004
Thermal Issues 1
Payload Thermal Issues &
Calculations
LSU 06/21/2 004
Thermal Issues 2
Thermal Requirements
• All payload components can function properly only within particular temperature ranges
• Operating temperature range (narrowest)
– In this temperature range the component will perform to within specified parameters
• Non-Operation temperature range (wider)
– Component will not perform within specs, but will do so when returned to operating temperature range
• Survival temperature range (widest)
– If this range is exceeded component will never return to proper operation
LSU 06/21/2 004
Thermal Issues 3
Thermal Control Plan
• Systems and procedures for satisfying the thermal
requirements
• Show that thermal system (i.e. heaters, insulation,
surface treatment) is sufficient to avoid excursions
beyond survival temperature range
• Show critical components remain mostly in the
operating temperature range
LSU 06/21/2 004
Thermal Issues 4
Determining Temperature Ranges
• Start with OEM (original equipment manufacturer) datasheet on product
– Datasheets usually specify only operating temperature range – Definition of “operating” may vary from manufacturer to
manufacturer for similar components
• Look for information on how operating parameters change as a function of temperature
– Your operating requirement may be more stringent than the manufacturer
• Find similar products and verify that temperature ranges are similar
• Search for papers reporting results from performance testing of product
LSU 06/21/2 004
Thermal Issues 5
Survival Temperature Range
• Survival temperature range will be the most
difficult to quantify
• Range limits may be due to different effects
– Softening or loss of temper
– Differential coefficients of expansion can lead to excessive shear
• Contact manufacturer and ask for their
measurements or opinion
LSU 06/21/2 004
Thermal Issues 6
Heat Transfer
• The payload will gain or lose heat energy through three fundamental heat transfer mechanisms
• Convection is the process by which heat is transferred by the mass movement of molecules (i.e. generally a fluid of some sort) from one place to another.
• Conduction is the process by which heat is transferred by the collision of “hot” fast moving molecules with “cold” slow moving molecules, speeding (heating) these slow molecules up.
LSU 06/21/2 004
Thermal Issues 7
Convection
• Requires a temperature difference and a working fluid to transfer energy
Qconv = h A ( T1 – T2 )
• The temperature of the surface is T1 and the temperature of the fluid is T2 in Ko
• The surface area exposed to convection is given by A in m2 • The coefficient h depends on the properties of the fluid.
– 5 to 6 W/(m2 Ko ) for normal pressure & calm winds
– 0.4 W/(m2 Ko ) or so for low pressure
• In the space environment, where air pressure is at a
LSU 06/21/2 004
Thermal Issues 8
Conduction
• Requires a temperature gradient (dT/dx) and some kind of material to convey the energy
Qcond = k A ( dT / dx)
• The surface area exposed to conduction is given by A in m2
• The coefficient k is the thermal conductivity of the material.
– 0.01 W/(m2 Ko ) for styrofoam
– 0.04 W/(m2 Ko ) for rock wool, cork, fiberglass
– 205 W/(m2 Ko ) for aluminium
• Need to integrate the gradient over the geometry of the conductor.
– Q = k A ((T1-T2)/L) for a rod of area A and length L
– Q = 4 k r (r + x) ((T1-T2)/x) for a spherical shell of radius r and
LSU 06/21/2 004
Thermal Issues 9
Radiation
• Requires a temperature difference between two bodies, but no matter is needed to transfer the heat
Qrad = A ( T14 – T24 )
• The Stefan-Boltzmann constant, , value is 5.67 x 10-8 W/m2 K4
• The surface area involved in radiative heat transfer is given by A in m2
• The coefficient is the emissivity of the material.
– Varies from 0 to 1
– Equal to the aborptivity ( )at the same wavelength
– A good emitter is also a good absorper
– A good reflector is a bad emitter
LSU 06/21/2 004
Thermal Issues 10
Emissivity & Absorptivity 1
• Kirchoff’s Law of Thermal Radiation:
At thermal
equilibrium, the emissivity of a body (or surface)
equals its absorptivity
• A material with high reflectivity (e.g. silver) would
have a low absorptivity AND a low emissivity
– Vacuum bottles are “silver” coated to stop radiative emission
– Survival “space” blankets use the same principle
• Kirchoff’s Law requires an integral over all
wavelengths
LSU 06/21/2 004
Thermal Issues 11
Emissivity & Absorptivity 2
• Manufacturers define absorption and emission parameters over specific (different) wavelength ranges
– Solar Absorptance ( s ): absorptivity for 0.3 to 2.5 micron wavelengths
– Normal Emittance ( n ): emissivity for 5 to 50 micron wavelengths
• The Sun, Earth and deep space are all at different temperatures and, therefore, emit power over different wavelengths
– A blackbody at the Sun’s temperature (~6,000 Ko) would emit between about 0.3
and 3 microns and at the Earth’s temperature (~290 Ko) would emit between
about 3 and 50 microns
• For space we want to absorb little of the Sun’s power and transfer much of the payload heat to deep space. • Want a material with low s and
high n .
– Sherwin Williams white paint has
LSU 06/21/2 004
Thermal Issues 12
Steady State Solution
• In a steady state all heat flows are constant and nothing changes in the system
• Sum of all heat generators is equal to the sum of all heat losses ( Qin = Qout )
• Example flow of heat
through a payload box wall
– Assume vacuum so no convection
– Input heat ( Qin ) generated by electronics flows through wall by
conduction and is then radiated to space.
Qcond = Qin or kA ( T1 – T2 ) / L = Qin (1)
Qrad = Qin or A (T24 – Ts4 ) = Qin (2)
– Use eq. 2 to determine T2 and then use eq. 1 to determine T1
• But real systems are never this simple
LSU 06/21/2 004
Thermal Issues 13
Balloon Environment is Complex
• Multiple heat sources
– Direct solar input (Qsun), Sun
reflection (Qalbedo), IR from Earth
(QIR), Experiment power (Qpower)
• Multiple heat sinks
– Radiation to space (Qr,space),
Radiation to Earth (Qr,Earth),
Convection to atmosphere (Qc)
• Equation must be solved by iteration to get the external temperature
• Then conduct heat through insulation to get internal temperature
LSU 06/21/2 004
Thermal Issues 14
Solar Input Is Very Important
• Nominal Solar Constant value is 1370 W / m2
• Varies ~2% over year due to Earth orbit eccentricity • Much larger variation due to solar inclination angle
– Depends upon latitude, time of year & time of day
• Albedo is reflection of sun from Earth surface or clouds
– Fraction of solar input depending on surface conditions under payload
LSU 06/21/2 004
Thermal Issues 15
Other Important Parameters
• IR radiation from the Earth is absorbed by the payload
– Flux in range 160 to 260 W/m2, over wavelength range ~5 to 50
microns, depending on surface conditions
– Radiation is absorbed in proportion of Normal Emittance ( n )
• Heat is lost via radiation to Earth and deep space
– Earth temperature is 290 Ko and deep space is 4 Ko
• There is also convective heat loss to the residual atmosphere
– Atmosphere temperature ~260 Ko
• For a 8 cm radius, white painted sphere at 100,000 feet above Palestine, TX on 5/21 at 7 am local time with 1 W interior power:
Qsun = 9.5 W, Qalbedo = 3.7 W, QIR = 1.6 W
LSU 06/21/2 004
Thermal Issues 16
Application for BalloonSat
• Can probably neglect heat loss due to convection and radiation to Earth
– Simplifies the equation you need to solve
• Need to determine if the solar inclination angle will be important for your payload geometry
– e.g. a sphere will absorb about the same solar radiation regardless of time of day and latitude
• Spend some time convincing yourself that you know values for your payload surface s and n and your insulation k.
• Biggest problem will be to estimate albedo and Earth IR input
LSU 06/21/2 004
Thermal Issues 17
References
• “HyperPhysics” web based physics concepts, calculators and examples by Carl R. Nave, Department of Physics & Astronomy, Georgia State University
– Home page at http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#hph
– Thermodynamics at http://hyperphysics.phy-astr.gsu.edu/hbase/heacon.html#heacon
– Heat Transfer at http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html#c1 – Vacuum Flask at http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/vacfla.html#c1 – Thermal Conductivity Table at http://hyperphysics.phy-astr.gsu.edu/hbase/tables/thrcn.html#c1
• Table of Solar Absorptance and Normal Emmittance for various materials by Dr. Andrew Marsh and Caroline Raines of Square One research and the Welsh
School of Architecture at Cardiff University.
– http://www.squ1.com/index.php?http://www.squ1.com/materials/abs-emmit.html • Sun, Moon Altitude, Azimuth table generator from the U.S. Naval Observatory
