Radiation Heat Transfer

Transcription

1 Applied Heat Transfer Part Three Dr. Ahmad RAMAZANI S.A. Associate Professor Sharif University of Technology انتقال حرارت کاربردی احمد رمضانی سعادت ا بادی Autumn, 1385 (2006) (Applications) Building Dryer Dryer Combustion Chamber (Applications) (Applications) Aerospatiale and aeronautic

2 Heat exchange between nonblackbodies Irradiation Radiosity Isolated surface Infinite parallel surfaces Convex object in a large enclosure Apparent emissivity of a cavity Radiation shields Gas radiation Beer law Radiation network for an absorbing and transmitting medium Radiation exchange with specular surfaces Radiation exchange with transmitting, reflecting, and absorbing media Apparent emissivity of cavity with transparent cover Formulation for numerical solution Parallel plates Constant heat flux and surrounding shields Combined convection and radiation Solar radiation Greenhouse effect Radiation properties of the environment Insolation Langley (a meterological unit) Albedo Effect of radiation on temperature measurement Radiation heat-transfer coefficient Light speed =

3 Electromagnetic Spectrum (Kirchhoff s law) Incident radiation Reflection P=Transmissivity α=absorpitivity or emissivty τ= reflactivity Embedded sample by a blackbody at equilibrium emitted energy = absorbed energy dividing two relations q i =radiant flux arriving at surface of enclosure E= emissive power Absorptivity = emissive power of a body at a given Tem. emissive power of a black body at the same Tem. = ε = E E b

4 Black Body Emissive Power as Function of Wavelength and Temperature The Fraction of The fraction of energy radiated between 0 = and lambda Dividing both side by T 5

5 : Greenhouse Effect Radiant energy emitted between= lambda1 and 2

6 (Shape Factor) Total Incident radiation between0.2 and 3.5 Micrometer All radiated energy from A 1 arrives at A 2 (F 12 =1) but only a fraction (F 21 ) of radiated from A 2 arrive at A 1 Fraction of Incident radiation Transmitted between0.2 and 3.5 Micrometer A 2 Q 12 =Q 21 =F 21 A 2 E b2 (Shape Factor) (Emission Radiation and The solid angle ) F 12 = Fraction of energy leaving surface 1 which reaches surface 2 E b1 A 1 F 12 = the energy leaving surface 1 and arriving at surface 2 Definition of Plane angle Emission of Radiation from differential surface da 1 into a solid angle dω subtended by da n at point on da 1 Definition of solid angle Projection of da 1 normal to the direction of radiation

7 (Shape Factor).. (Shape Factor) I b =Intensity= The radiation emitted per unit area and per unit of solid angle in a certain specified direction (Shape Factor Con.) I b 1 da 1 cosφ dω = So that energy leaving sourface dq E 1 2 b1 = I 1 b (cos φ da cos φ cos φ da da )( dω ) = ( E 2 / Π r 2 ) b da 1 which arrives at / Π )(cos φ da )( da 1 1 n da / r 2 2 is : ) = I b = E b / Π

8 (Shape factor for a small area element and a disk) Considering the radiation from the small area of da 1 to the flat disk A 2, as shown in Fig The element of area da 2 is chosen as circular ring of Thus da 2 =2πxdx (Shape factor for a small area and a disk)

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11 (Shape Factor Con.) (Shape Factor Example) 500 o C 0.5 m 1000 o C 0.5 m 1 m 0.5 m For bodies that cannot see themselves For concave curved surface which can see themselves

12 for Real Surface (Real surface Behavior) (Absorbed energy by a real surface) Example ε = α λ λ Heat exchange between non-blackbodies

13 Heat exchange between non-blackbodies (con.) Heat exchange between non-blackbodies (Con.) q A r = q A r Heat exchange between non-blackbodies (Con.) Heat exchange between non-blackbodies (Con.)

14 Heat exchange between non-blackbodies (Con.) Heat exchange between non-blackbodies (Con.) Heat exchange between non-blackbodies (Con.) Infinite parallel surfaces

15 Infinite concentric cylinder

16 (Radiation Shields) (Radiation Shields) If n shields with same emissivity have been used, then 2n +2 surface resistance (each of them equal to (1-epsilon)/epsilon) and n+1 space resistances (all of them equal to unity because shape factor is 1) would be exist in system.

17 (Radiation Shield Application) : Gas Radiation Consider that radiation with intensity of I λ impinges on the gas layer of thickness dx the decrease in intensity resulting from absorption in layers is assumed to be proportional to thickness of the layer and the intensity of radiation at the point. Thus (Gas Radiation) (Gas Radiation for Water and Carbon dioxide) Monochromic Transmissivity Method of Hottel and Egbert (or Mean Beam length) for calculation of Gas Emittances for carbon dioxide and water: Real calculations for gas absorptivity and Emissivity could be difficult so Hottel and Egbert using different sources and presented Figs and 8.35 for calculation of gas emittances for carbon dioxide and water vapor. In these figures L e is a Characteristic dimension called MEAN BEAM Length Pc is partial pressure of considered gas For some system L e is presented in table 8-3.

18 (Gas Radiation) (Gas Radiation) (Gas Radiation) (Gas Radiation) C c = Correction Coefficient For non pure Carbon Dioxide from figure 8-37 C w = Correction Coefficient For non pure Water Vapor from figure 8-37 ε = Additional Correction from figure 8-38

19 (Gas Radiation) Emissivity facture Correction for pressure other than 1 atm for CO 2 (C c ) (Gas Radiation) Emissivity facture Correction for pressure other than 1 atm for H 2 O (C w ) (Gas Radiation) Additional Emissivity facture Correction, ε, for Mixture of CO 2 and Water Vapor (Gas Radiation Heat Exchange with Black Enclosure)

20 (Gas Radiation Heat Exchange with Black Enclosure Con.) (Gas Radiation Heat Exchange with Two different temperature Black Enclosures ) Energy balance on plate 1 Energy balance on plate 2 (Gas Radiation) (Gas Radiation Heat Exchange with Black Enclosure Con.) (Gas Radiation Heat Exchange with Black Enclosure: Example)

21 (Gas Radiation Heat Exchange with Black Enclosure: Example Con.) Radiation heat transfer by multiple reflections Radiation heat transfer by multiple reflections (Con.) Radiation in absorbing and transmitting media

22 Radiation in absorbing and transmitting media (Con.) Radiation in absorbing and transmitting media (Con.) Radiation in absorbing and transmitting media (Con.) Two-layer transmitting medium

23 Two-layer transmitting medium (Con.) Two-layer transmitting medium Two-layer transmitting medium (Con.) Two-layer transmitting medium (Con.)

24 Two-layer transmitting medium (Con.) Specular surfaces Specular surfaces (Con.) Specular-diffuse surfaces

25 Specular-diffuse surfaces (Con.) Specular-diffuse surfaces (Con.) Specular-diffuse surfaces (Con.) Specular-diffuse surfaces (Con.)

26 Specular-diffuse surfaces (Con.) Specular-diffuse surfaces (Con.) System with two specular-diffuse surfaces Transmitting, reflecting, and absorbing media

27 Transmitting, reflecting, and absorbing media (Con.) Transmitting, reflecting, and absorbing media (Con.) Infinite parallel planes separated by TRANSMITTING SPECULAR-DIFFUSE PLANE Apparent emissivity of cavity WITH TRANSPARENT COVER

28 Convection Greenhouse Effect Radiation network for an absorbing and transmitting medium Radiation exchange with specular surfaces Radiation exchange with transmitting, reflecting, and absorbing media Apparent emissivity of cavity with transparent cover

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