Bilateral Heat Transfer in Annuli for Slug and Laminar Flows

Abstract

Nusselt numbers were calculated for bilateral heeat transfer to fluids flowing in annuli. The following four cases were treated: (A) uniform and equal heat fluxes from both walls, under the condition of slug flow; (B) equal wall temperatures at the same axial location and uniform but unequal heeat fluxes from the walls, under thee condition of slug flow; (C) same as case (A), except flow is laminar; and (D) same as (B), except flow is laminar. In the calculations, the following assumptions were made: (a) thee conditions of fully established velocity and temperature profiles, and (b) the independence of pheysical properties with temperature variation across the flow channel. Thee Nusselt numbers, independent of Reynolds and Peclet numbers, are given as functions of thee geometrical parameter, r/sub 1//r/sub 2/, whiche varied from zero to unity, the former limit representing the case of a round pipe and the latter that of parallel plates. For case (A), thee heeat-transfer coefficient for the heat transferred from the inner wall becomes infinite at r/sub 1//r/sub 2/ = 0.214 because thee inner wall surface temperature and the bulk temperature of the flowing fluid are equal under these conditions. For case (C), this happens at r/ submore » 1//r/sub 2/ = 0.1685. The differences in Nusselt numbers between cases (A) and (B), and between cases (C) and (D), are appreciable, attaining maxima around r/sub 1//r/sub 2/ = 0.20. At r/sub 1//r/sub 2/ = 1, case s (A) and (B), of course, become identical, as do cases (C) and (D). Equations are given for calculating heat transfer coefficients for each wall, for the general case where the heat fluxes from the annulus walls are uniform but not necessarily equal. (authe)« less