MAE 310 Heat Transfer Fundamentals Lecture 24 MAE 310 Outline Heat Transfer Between Gray Surfaces Gray Surface Emission and absorption Diffuse gray model Two surface enclosure Examples MAE 310 Real Surfaces Thermodynamic equilibrium Real Surface Black body T T T 4 MAE 310 T 4 T 4 T 4 Real Surfaces Monochromatic hemispherical emissivity Eb I b blackbody T E T Eb T T 1 real body Total hemispherical emissivity Wavelength E T T Eb T T 1 MAE 310 Gray Surfaces Gray surfaces or gray bodies Eb I b blackbody T T real body T gray body Wavelength MAE 310 Monochromatic hemispherical emissivity is independent of wavelength Gray Surfaces Emissive power of gray surface T T E T T Eb d 0 E T T T 4 T Const MAE 310 E T T 4 Emission and Absorption of Gray Surfaces Gray body in thermodynamic equilibrium Only part of the energy is absorbed T 4 T 4 The rest is scattered From energy balance T 4 T 4 T 4 MAE 310 dA Kirchoff s law Diffuse Absorber and Diffuse Reflector dA Diffuse absorber Absorption is independent of the direction of incident radiation MAE 310 dA Diffuse reflector Apparent intensity of the reflected radiation is uniform in all directions 1 Diffuse Gray Model 1 Monochromatic hemispherical emissivity is independent of wavelength gray body E T T 4 2 A gray body is a diffuse emitter 3 A gray body is a diffuse absorber 4 A gray body is a diffuse reflector 5 A gray body is opaque MAE 310 1 Diffuse Gray Model Two Surface Enclosure Consider a two surface enclosure A2 T2 2 q2 q1 2 q1 q1 2 q2 q1 A1 T1 1 MAE 310 Diffuse Gray Model Two Surface Enclosure Consider a two surface enclosure J1 G1 radiosity G1 1 T 4 1 J1 1G1 1 T14 J1 1 1 G1 1 T14 J1 1 1 G1 1 T14 J1 1 T14 G1 1 1 G1 A1 A1 1 T14 J1 q1 A1 J1 G1 1 1 MAE 310 Diffuse Gray Model Two Surface Enclosure Two surface enclosure A2 T2 2 q1 1 A1 T14 J1 1 1 q1 2 A1F12 J1 q2 2 A2 T24 J 2 1 2 q2 1 A2 F21J 2 A1F12 J 2 q1 2 q1 2 q2 1 A1F12 J1 J 2 q1 q1 2 q2 A1 T1 1 q1 2 MAE 310 T14 T24 1 1 1 1 2 A1 1 A1 F12 A2 2 Diffuse Gray Model Two Surface Enclosure Two surface enclosure A2 T2 2 R1 T 4 1 A1 T1 1 1 1 A1 1 R3 R2 1 2 A2 2 1 A1 F12 q1 2 q1 2 T14 T24 1 1 1 1 2 A1 1 A1 F12 A2 2 MAE 310 q1 2 U1 U 2 R1 R2 R3 T24 Two Surface Enclosure Example Two surface enclosure example A1 T1 1 A2 T2 2 q1 2 q1 2 q1 2 T14 T24 1 1 1 1 2 A1 1 A1 F12 A2 2 1 2 A T14 T24 1 1 1 1 MAE 310 A T14 T24 1 1 1 2 1 2 Two Surface Enclosure Example Two surface enclosure limiting the view factor A1 T1 1 A2 T2 2 q1 2 T14 T24 1 1 1 1 2 A1 1 A1 F12 A2 2 F12 0 q1 2 A1F12 T14 T24 MAE 310 Two Surface Enclosure Example Rates Radiation cont Heat Transfer Rates q1 2 Irradiation Special case of surface exposed to large surroundings of uniform temperature Tsur G Gsur Tsur4 T14 T24 1 1 1 1 2 A1 1 A1 F12 A2 2 A2 F12 1 If the net radiation heat flux from the q1 2 surface due to exchange with the surroundings is Eb Ts G Ts4 Tsur4 qrad 1 7 A1 1 T14 T24 1 1 1 q1 2 A1 1 T14 T24 MAE 310 Two Surface Enclosure Example q1 2 A1 T1 1 1 A2 T2 2 2 Radiation shielding q1 2 q1 2 T14 T24 1 s 1 s 1 1 1 1 1 2 A1 1 A1 F1s As s As s As Fs 2 A2 2 A T14 T24 1 1 2 2 1 MAE 310 A T14 T24 1 1 1 2 s Two Surface Enclosure Example A1 T1 1 A2 T2 2 No shielding q1 2 A T14 T24 1 1 1 1 Shielding q1 2 2 s Special case s 1 MAE 310 2 A T14 T24 1 1 2 2 1 q1 2 A T14 T24 1 1 2 2 1 2 1