Annular fin

FIG. 11-30ii Efficiencies for annular fins of constant thickness,... 

The complete study of annular ftns is essential in order to calculate the amount of conduction in the plate fin. A schematic diagram of annular fins is given in Fig. 9.8. 

The temperature distribution within the annular fin is given by the differential equation... 

Sparrow E.M., Miller G.B., Jonsson V.K. (1962) Radiative effectiveness of annular-finned space radiators, including mutual irradiation between radiator elements. Journal of Aerospace Science 20(0), 1291-1299. 

Problem A thin annular fin in a vacuum is enclosed in insulation so that there is no heat transfer on one face and around its outside edge. The disk is of thickness b, has an inner radius r , an outer radius r , and a thermal conductivity k. Energy is supplied to the inner edge, say from a solid rod of radius r, that fits the central hole, and this keeps the inner edge at a temperature T . 

Batra D. Rao T. R, (2000) Analysis of an annular finned pyrolyzer-II. Energy Convers. Manage, 41, 573-83. 

Fig. 2.12 Annular fin on a tube (outer radius ro) with profile function y = y(r)...

For thin annular fins, as in Fig. 2.12, with r as the radial coordinate we obtain... 

The chosen height h of the fin using this condition gives the maximum heat flow for a set fin volume Vt. A similar calculation for annular fins with different profile functions is available in A. Ullmann and H. Kalman [2.12]. 

For the frequently used annular fins of constant thickness f, y(r) = <5f/2 has to be put into (2.70) for the profile function. The fin efficiency r/f is dependent on two dimensionless groups mh according to (2.78) and the radius ratio (r0+h)/r0 = 1+ h/r0, cf. Fig. 2.12. This yields a complicated expression containing modified Bessel functions. F. Brandt [2.13] found the rather accurate approximation equation... 

Frequently square, rectangular or hexagonal disk fins are attached to tubes, whereby several tubes can also be joined together by the use of sheets of fins through which the tubes pass, Fig. 2.15. In these fins the temperature does not only depend on one coordinate, but two-dimensional temperature fields must be reckoned with. As a first approach, the efficiency r]f of these disk fins can be calculated from (2.81) or (2.82) for an annular fin with the same surface area. Then for a rectangular fin as in Fig. 2.15 we get... 

A brass tube with outer diameter d = 25 mm is exposed to an air stream flowing across it perpendicular to its axis, the heat transfer coefficient is a = 90W/m2K. The tube has annular fins made of brass (Af = 126W/Km) attached to it, which have a thickness of Sf = 1.5mm and are h = 20mm high. The surface temperature of the tube and the air temperature can be taken to be constant. 

Ullmann, A. Kalman, H. Efficiency and optimized dimensions of annular fins of different cross-section shapes. Int. J. Heat Mass Transfer 32 (1989) 1105-1110... 

E. M. Sparrow, G. B. Miller, and V. K. Jonsson, Radiative Effectiveness of Annular-Finned Space Radiators, including Mutual Irradiation between Radiator Elements, J. Aerospace Sci., 29(11), pp. 1291-1299,1962. 

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