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Tham khảo tài liệu 'a heat transfer textbook - third edition episode 2 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 414 Natural convection in single-phase fluids and during film condensation 8.3 Variable-properties problem Sparrow and Gregg 8.7 provide an extended discussion of the influence of physical property variations on predicted values of Nu. They found that while fl for gases should be evaluated at T all other properties should be evaluated at Tr where Tr Tw - C Tw - Tn 8.28 and where C 0.38 for gases. Most books recommend that a simple mean between Tw and or C 0.50 be used. A simple mean seldom differs much from the more precise result above of course. It has also been shown by Barrow and Sitharamarao 8.8 that when fl AT is no longer 1 the Squire-Eckert formula should be corrected as follows Nu Nusq-Ek 1 3flAT O flAT 2 1 4 8.29 This same correction can be applied to the Churchill-Chu correlation or to other expressions for Nu. Since fl 1 . for an ideal gas eqn. 8.29 gives only about a 1.5 correction for a 330 K plate heating 300 K air. Note on the validity of the boundary layer approximations The boundary layer approximations are sometimes put to a rather severe test in natural convection problems. Thermal b.l. thicknesses are often fairly large and the usual analyses that take the b.l. to be thin can be significantly in error. This is particularly true as Gr becomes small. Figure 8.5 includes three pictures that illustrate this. These pictures are interferograms or in the case of Fig. 8.5c data deduced from interferograms . An interferogram is a photograph made in a kind of lighting that causes regions of uniform density to appear as alternating light and dark bands. Figure 8.5a was made at the University of Kentucky by G.S. Wang and R. Eichhorn. The Grashof number based on the radius of the leading edge is 2250 in this case. This is low enough to result in a b.l. that is larger than the radius near the leading edge. Figure 8.5b and c are from Kraus s classic study of natural convection visualization methods 8.9 . Figure 8.5c shows that at Gr 585 the b.l. assumptions .
