tailieunhanh - A HEAT TRANSFER TEXTBOOK - THIRD EDITION Episode 1 Part 8

Tham khảo tài liệu 'a heat transfer textbook - third edition episode 1 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | a Eight examples of externally finned tubing. 1 and 2 Typical commercial circular fins of constant thickness 3 and 41 Serrated circular fins and dimpled spirally-wound circular fins both intended to improve convection. 5 Spirally-wound copper coils outside and inside. 6 and 81 Bristle fins spirally wound and machined from base metal. 7 A spirally indented tube to improve convection as well as to increase surface area. bl An array of commercial internally finned tubing photo courtesy of Noranda Metal Industries Inc. Figure Some of the many varieties of finned tubes. 164 Fin design 165 Figure The Stegosaurus with what might have been cooling fins etching by Daniel Rosner . ing condensing or other natural convection situations and will not be strictly accurate even in forced convection. The tip may or may not exchange heat with the surroundings through a heat transfer coefficient hL which would generally differ from h. The length of the fin is L its uniform cross-sectional area is A and its circumferential perimeter is P. The characteristic dimension of the fin in the transverse direction normal to the x-axis is taken to be A P. Thus for a circular cylindrical fin A P n radius 2 2n radius radius 2 . We define a Biot number for conduction in the transverse direction based on this dimension and require that it be small h A P Bifin 1 k This condition means that the transverse variation of T at any axial position x is much less than Tsurface - T . Thus T - T x only and the 166 Analysis of heat conduction and some steady one-dimensional problems Figure The analysis of a one-dimensional fin. heat flow can be treated as one-dimensional. An energy balance on the thin slice of the fin shown in Fig. gives X. dT kA dx . .dT x Sx kA d h PSx T - Tn x 0 x but dT dx x Sx - dT dx x d2T d2 T - Tn --------- T Sx dx2 dx2 so d2 T - Tn _ hP J 1 A T T n dx2 kA