MARYLAND. Fundamentals of heat transfer Radiative equilibrium Surface properties Non-ideal effects. Conduction Thermal system components

Size: px

Start display at page:

Download "MARYLAND. Fundamentals of heat transfer Radiative equilibrium Surface properties Non-ideal effects. Conduction Thermal system components"

Osborn McLaughlin
5 years ago
Views:

1 Fundamentals of heat transfer Radiative equilibrium Surface properties Non-ideal effects Internal power generation Environmental temperatures Conduction Thermal system components 2003 David L. Akin - All rights reserved

2 Classical Methods of Heat Transfer Convection Heat transferred to cooler surrounding gas, which creates currents to remove hot gas and supply new cool gas Don t (in general) have surrounding gas or gravity for convective currents Conduction Direct heat transfer between touching components Primary heat flow mechanism internal to vehicle Radiation Heat transferred by infrared radiation Only mechanism for dumping heat external to vehicle

3 Ideal Radiative Heat Transfer Planck s equation gives energy emitted in a specific frequency by a black body as a function of temperature e lb = 2 2phC 0 È Ê l 5 exp -hc ˆ 0 Í Á -1 Î Ë lkt (Don t worry, we won t actually use this equation for anything ) Stefan-Boltzmann equation integrates Planck s equation over entire spectrum P rad =st 4 s = 5.67x10-8 W m 2 K 4 ( Stefan-Boltzmann Constant )

4 Thermodynamic Equilibrium First Law of Thermodynamics Q -W = du dt heat in -heat out = work done internally Heat in = incident energy absorbed Heat out = radiated energy Work done internally = internal power used (negative work in this sense - adds to total heat in the system)

5 Radiative Equilibrium Temperature Assume a spherical black body of radius r Heat in due to intercepted solar flux Q in = I s p r 2 Heat out due to radiation (from total surface area) Q out = 4p r 2 st 4 For equilibrium, set equal I s p r 2 = 4p r 2 st 4 fi I s = 4sT 4 Ê T eq = I ˆ s Á Ë 4s 1 AU: I s =1394 W/m 2 ; T eq =280 K 1 4

6 Effect of Distance on Equilibrium Temp Black Body Equilibrium Temperature ( K) Distance from Sun (AU)

7 Shape and Radiative Equilibrium A shape absorbs energy only via illuminated faces A shape radiates energy via all surface area Basic assumption made is that black bodies are intrinsically isothermal (perfect and instantaneous conduction of heat internally to all faces)

8 Effect of Shape on Black Body Temps Black Body Equilibrium Temperature ( K) Spherical Black Body Adiabatic Black Wall Double-Sided Wall Distance from Sun (AU)

9 Incident Radiation on Non-Ideal Bodies Kirchkoff s Law for total incident energy flux on solid bodies: Q Incident = Q absorbed + Q reflected + Q transmitted Q absorbed Q Incident + Q reflected Q Incident + Q transmitted Q Incident =1 a Q absorbed Q Incident ; where a =absorptance (or absorptivity) r =reflectance (or reflectivity) t =transmittance (or transmissivity) r Q reflected Q Incident ; t Q transmitted Q Incident

10 Non-Ideal Radiative Equilibrium Temp Assume a spherical black body of radius r Heat in due to intercepted solar flux Q in = I s ap r 2 Heat out due to radiation (from total surface area) Q out = 4p r 2 est 4 For equilibrium, set equal (e = emissivity - efficiency of surface at radiating heat) I s apr 2 = 4p r 2 est 4 fi I s = 4 e a st 4 Ê T eq = Á a Ë e I s ˆ 4s 1 4

11 Effect of Surface Coating on Temperature Black Ni, Cr, Cu Black Paint 0.7 a = absorptivity Polished Metals Aluminum Paint White Paint Teq=560 K (a/e=4) Teq=471 K (a/e=2) Teq=396 K (a/e=1) Teq=333 K (a/e=0.5) Teq=280 K (a/e=0.25) 0 Optical Surface Reflector e = emissivity

12 Non-Ideal Radiative Heat Transfer Full form of the Stefan-Boltzmann equation ( ) P rad =esa T 4 4 -T env where T env =environmental temperature (=4 K for space) Also take into account power used internally I s a A s + P int =esa ( rad T T ) env

13 Example: AERCam/SPRINT 30 cm diameter sphere a=0.2; e=0.8 P int =200W T env =280 K (cargo bay below; Earth above) Analysis cases: Free space w/o sun Free space w/sun Earth orbit w/o sun Earth orbit w/sun

14 AERCam/SPRINT Analysis (Free Space) A s = m 2 ; A rad = m 2 Free space, no sun Ê Á 200W P int = esa rad T 4 fi T = Á Ê W Á Á Ë Ë m 2 K 4 ˆ m 2 ( ) ˆ 1 4 = 354 K

15 AERCam/SPRINT Analysis (Free Space) A s = m 2 ; A rad = m 2 Free space with sun Ê I s a A s + P int = esa rad T 4 fi T = I sa A s + P int Á Ë esa rad 1 ˆ 4 = 362 K

16 AERCam/SPRINT Analysis (LEO Cargo Bay) T env =280 K LEO cargo bay, no sun P int =esa rad T 4 4 ( - T env ) fi T = Ê Á Á 200W Á Ê W ˆ Á Á m 2 Ë Ë m 2 K 4 ( ) + (280 K)4 ˆ 1 4 = 384 K LEO cargo bay with sun I s a A s + P int =esa rad T T env ( ) fi T = I sa A s + P int Ê Á Ë esa rad 14 ˆ 4 + T env = 391 K

17 Radiative Insulation I s T insulation T wall Thin sheet (mylar/kapton with surface coatings) used to isolate panel from solar flux Panel reaches equilibrium with radiation from sheet and from itself reflected from sheet Sheet reaches equilibrium with radiation from sun and panel, and from itself reflected off panel

18 Multi-Layer Insulation (MLI) I s Multiple insulation layers to cut down on radiative transfer Gets computationally intensive quickly Highly effective means of insulation Biggest problem is existence of conductive leak paths (physical connections to insulated components)

19 1D Conduction Basic law of one-dimensional heat conduction (Fourier 1822) where K=thermal conductivity (W/m K) A=area Q = -KA dt dx dt/dx=thermal gradient

20 3D Conduction General differential equation for heat flow in a solid 2 T r,t where ( ) + g(r g(r,t)=internally generated heat r=density (kg/m 3 ) r,t) K = rc K c=specific heat (J/kg K) K/rc=thermal diffusivity T( r,t) t

21 Simple Analytical Conduction Model Heat flowing from (i-1) into (i) T i-1 T i T i+1 Q = -KA T - T i i-1 in Dx Heat flowing from (i) into (i+1) Q out = -KA T i+1 -T i Dx Heat remaining in cell Q out -Q in = rc K T i ( j +1) - T i ( j) Dt

22 Heat Pipe Schematic

23 Shuttle Thermal Control Components

24 Shuttle Thermal Control System Schematic

25 ISS Radiator Assembly

Thermal Systems Design MARYLAND. Fundamentals of heat transfer Radiative equilibrium Surface properties Non-ideal effects

Thermal Systems Design MARYLAND. Fundamentals of heat transfer Radiative equilibrium Surface properties Non-ideal effects Fundamentals of heat transfer Radiative equilibrium Surface properties Non-ideal effects Internal power generation Environmental temperatures Conduction Thermal system components 2002 David L. Akin - All