Bilateral Heat Transfer to Liquid Metals Flowing Turbulently Through Annuli

The results of an analytical study of bilateral heat transfer to liquid metals flowing turbulently through annuli are reported. The study was based on the assumptions of 1) uniform, though not necessarily equal, heat fluxes from the walls, 2) fully-established temperature and velocity profiles, and 3) no effect of transverse temperature variations on the physical properties of the liquid metal. The fraction, ξ, of the total heat delivered to the flowing stream which comes from the inner wall was varied from zero to unity. Also two special situations were treated: (A) equal heat fluxes from both walls, and (B) uniform but unequal heat fluxes at the walls, with equal wall temperatures at a given axial position along the channel. The results are presented in the form of Nusselt numbers for r₂/r₁ values from 1 to 7, Peclet numbers for 10² to 10⁴, and ξ values from 0 to 1. The coefficient for the heat transferred from the inner wall goes to infinity at a certain value of ξ, which depends only on the ratio r₂/r₁. The same thing occurs for the coefficient for the outer walls, except at a different values of ξ. The interesting observation was made that at Pe = 6700, the Nusselt numbers for the following situations are all equal to about 35: 1) flow in a pipe, 2) flow between parallel plates with equal heat fluxes from both plates, 3) flow in any annulus with equal heat fluxes from the walls, with reference to the heat transferred from the outer wall, 4) flow in any annulus with a uniform heat flux from each wall and having equal wall temperatures at a given axial position, with reference to the heat transferred from the outer wall.