tailieunhanh - Computational Fluid Mechanics and Heat Transfer Third Edition_15

Tham khảo tài liệu 'computational fluid mechanics and heat transfer third edition_15', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Kirchhoff s law 535 Figure Heat transfer between two infinite parallel plates. ond integral divided by ƠT4. Hence etna E1 T1 o-T14 - a1 T1 T2 ơĩị Vy J _ X emitted by plate 1 absorbed by plate 1 We see that the total absorptance depends on T2 as well as T1. Why does total absorptance depend on both temperatures The dependence on T1 is simply because A1 is a property of plate 1 that may be temperature dependent. The dependence on T2 is because the spectrum of radiation from plate 2 depends on the temperature of plate 2 according to Planck s law as was shown in Fig. . As a typical example consider solar radiation incident on a warm roof painted black. From Table we see that E is on the order of . It turns out that a is just about the same. If we repaint the roof white E will not change noticeably. However much of the energy arriving from the sun is carried in visible wavelengths owing to the sun s very high temperature about 5800 K .3 Our eyes tell us that white paint reflects sunlight very strongly in these wavelengths and indeed this is the case 80 to 90 of the sunlight is reflected. The absorptance of 3Ninety percent of the sun s energy is on wavelengths between and ụm see Figure . For a black object at 300 K 90 of the radiant energy is between and 42 ụm in the infrared. 536 Radiative heat transfer white paint to energy from the sun is only to much less than 8 for the energy it emits which is mainly at infrared wavelengths. For both paints eqn. applies. However in this situation eqn. is only accurate for the black paint. The gray body approximation Let us consider our facing plates again. If plate 1 is painted with white paint and plate 2 is at a temperature near plate 1 say T1 400 K and T2 300 K to be specific then the incoming radiation from plate 2 has a wavelength distribution not too dissimilar to plate 1. We might be very comfortable approximating 81 a1. The net heat