ME 259 Heat Transfer Lecture Slides V

1. ME 259Heat TransferLecture Slides V Dr. Gregory A. Kallio Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology California State University, Chico ME 259

2. Radiation Heat Transfer ME 259

3. Introduction to Thermal Radiation • Recall definition: process by which heat flows between surfaces at different temperatures via the emission of electromagnetic (EM) waves • Notes: • transport does not require the presence of matter • energy transfer depends upon Ts4 • all surfaces with Ts > 0 K continuously emit EM radiation due to electron activity • emission from solids and liquids is a surface phenomenon, since interior radiation is absorbed by adjoining molecules • emission from gases is a volumetric phenomenon • thermal radiation is characterized by its spectral and directional nature ME 259

4. Summary of Radiative Fluxes • Total emissive power(E) - total radiation emitted by a surface in all directions: • Total irradiation (G) - total radiation incident upon a surface from all directions: • Total radiosity (J)- total radiation leaving a surface due to emission and reflected irradiation in all directions: ME 259

5. Blackbody Radiation • A blackbody is an ideal surface which • absorbs all incident radiation, regardless of wavelength and direction • emits radiation equally in all directions at the maximum rate for a given temperature and wavelength • Since a blackbody is a perfect absorber and emitter, it serves as a standard against which all real surfaces are compared • The closest approximation to a blackbody is a cavity with a small aperture whose inner surface is at a uniform temperature ME 259

6. The Planck Distribution • Planck determined the spectral distribution of blackbody emission: • where h is the Planck constant, co is the speed of light, and k is the Boltzmann constant • the distribution displays a maximum value at • Total emissive power from a blackbody is found by integrating the Planck distribution over all wavelengths; this yields the familiar Stefan-Boltzmann law: ME 259

7. Band Emission • The fraction of total emission from a blackbody at temperature T within a certain wavelength interval (band) is expressed by • The results of this integration are tabulated in Table 12.1 as function of T • The fraction of emitted radiation between any two wavelengths 1and 2 may be found by ME 259

8. Emissivity • The spectral, hemispherical emissivity of a surface at temperature T is • The total, hemispherical emissivity is found by integrating the spectral emissive power over all wavelengths: • Measurements have been performed to determine these properties for many different materials and surface coatings (Figures 12.18-12.20, Tables A.11, A.12) ME 259

9. Absorptivity • The spectral, hemispherical absorptivity of a surface is • The total, hemispherical absorptivity is found by integrating the absorbed spectral irradiation over all wavelengths: • Measurements have been performed to determine these properties for many different materials and surface coatings (Figure 12.23, Table A.12) ME 259

10. Reflectivity • The spectral, hemispherical reflectivity of a surface is • The total, hemispherical reflectivity is found by integrating the reflected spectral irradiation over all wavelengths: • Measurements have been performed to determine these properties for many different materials and surface coatings (Figure 12.23) ME 259

11. Transmissivity • The spectral, hemispherical transmissivity of a surface is • The total, hemispherical transmissivity is found by integrating the transmitted spectral irradiation over all wavelengths: • Measurements have been performed to determine these properties for many different materials and surface coatings (Figure 12.24, Table A.12) ME 259

12. Kirchhoff’s Radiation Law • The ability of a diffuse surface to emit radiation at a particular  is equal to its ability to absorb radiation at  , or • This law can be proved by applying a surface energy balance to a body inside an evacuated isothermal enclosure (see section 12.6) • The only restriction to the above law is that the surfaces involved must be diffuse or that the irradiation must be diffuse (independent of direction) • If  and  are independent of  (known as a gray surface), then the total hemispherical values will also be equal: ME 259

13. Environmental Radiation • The emissive power at the sun’s surface is approximately 6.25107 W/m2 and its spectral distribution approximates that of a blackbody at 5800 K. • The irradiation normal to the sun’s rays just outside the earth’s atmosphere is 1353 W/m2, known as the solar constant • The irradiation that reaches the earth’s surface is reduced by atmospheric absorption and scattering; the maximum value is around 1000 W/m2. • Absorption is primarily due to ozone (O3), H2O, O2, CO2, and fine particles or droplets. ME 259

14. Effective Sky Temperature • In the absence of an atmosphere, the sky (i.e., space) has an effective temperature near 0 K; the atmosphere significantly increases the effective sky temperature, defined by • where • therefore, • for low cloud cover, ME 259

15. Typical Engineering Approx-imations to Radiation Problems • Diffuse surface – a surface for which all radiation properties are independent of direction • Gray surface – a surface for which emissivity and absorptivity are independent of wavelength, thus  =  • Nonparticipating medium – a medium that has no effect on radiation transfer between surfaces (i.e., negligible absorption, emission, and scattering) ME 259

16. Radiation Exchange Between Surfaces • Assumptions: • surfaces are diffuse and gray for the spectrum of radiation considered • surfaces are separated by a nonparticipating medium • surfaces are opaque unless specified otherwise • surfaces are isothermal, or can be subdivided such that each “subsurface” is isothermal • We know that • EM waves travel in straight lines (rays) and in all possible directions from a diffuse surface • geometric orientation of surfaces affects net radiation transfer ME 259

17. The View Factor, Fij • The view factor (or shape factor), Fij , is a geometric quantity that represents the fraction of radiation leaving a surface i that is intercepted by a surface j : • mathematically, • The view factor between each pair of surfaces in a radiation system must be known before the net radiation heat transfer can be calculated ME 259

18. View Factor Integrals • Consider two differential surfaces: • For diffuse surfaces, it can be shown that • Since Fij = qij / AiJi, we have ME 259

19. Evaluation of View Factors • There exist several approaches to determining the view factor between two surfaces: 1) Direct integration - analytical or numerical evaluation of the view factor integrals 2) Statistical determination - Monte Carlo sampling method 3) View factor algebra - repeated application of special view factor “rules” 4) Crossed-strings method - for 2-D geometries • Direct integration has been applied to many common geometries - these are presented in Tables 13.1, 13.2, and Figures 13.4-13.6 ME 259

20. View Factor Rules • Reciprocity - it is evident from the view factor integrals that • Summation for Enclosures - the sum of all view factors from one surface to all other surfaces inside an enclosure must be unity: ME 259

21. View Factor Rules, cont. • Subdivision of Surfaces • if the receiving surface (j) is subdivided, • if the emitting surface (i) is subdivided, ME 259

22. Radiation Exchange Between Two Surfaces • Radiation circuit: • Heat transfer: ME 259

23. Radiation Exchange Between Three Surfaces in an Enclosure ME 259