Liquid Argon Maximm Convective Heat Flux vs. Liquid Depth

Abstract

In order to help answer questions about the magnitude of heat flux to the liquid argon in a liquid argon calorimeter which could cause boiling (bubbles), calculations estimating the heat flux which can be removed by free convection were made in February, 1988. These calculations are intended to be an estimate of the heat flux above which boiling would occur. No formal writeup was made of these calculations, although the graph dated 3 Feb 88 and revised (adding low-velocity forced convection lines) 19 Feb 88 was presented in several meetings and widely distributed. With this description of the calculations, copies of the original graph and calculations are being added to the D0 Engineering Note files. The liquid argon surface is in equilibrium with argon vapor at a pressure of 1.3 bar, so the surface is at 89.70 K. The liquid is entirely at this surface temperature throughout the bulk of the volume, except locally where it is warmed by a solid surface at a higher temperature than the bulk liquid. This surface temperature is taken to be the boiling temperature of argon at the pressure corresponding to 1.3 bar plus the liquid head; hence it is a function of depth below the surface. The free and forced convection correlations used are 'from Kreith, 'Heat Transfer', for heated flat plates in a large (i.e., no other objects nearby enough to disturb the flow) uniform volume of fluid. Heat flux is a function of plate size, really length along the flow path (since a boundary layer increases in thickness starting from the leading edge of the plate), and orientation (i.e., vertical or horizontal). The maximum heat flux which can be carried away by free convection (i.e., the heat flux above which boiling occurs) is .001 W/sq.cm. at 4 inches below the surface and 0.1 to 0.2 W/sq.cm. 15 feet below the surface. Forced convection over a 1 cm plate with a fluid velocity of 1 cm/sec, or a 10 cm plate at 10 cm/sec, is about like free convection. The line for much higher heat flux is 10 cm/sec flow over a 1 cm plate.