Heat transfer correlations for ordinary fluids do not apply to liquid metals. With ordinary fluids the molecular conductivity of heat is negligible compared with the eddy conductivity as a means of transporting heat in the turbulent core. However with liquid metals this is no longer true, owing to their extremely large molecular conductivities.Martinelli (1) was the first to take this factor into account in developing a heat transfer relation for low Prandtl number fluids flowing within tubes. Lyon ( 2 ) made similar assumptions, but followed a different development, and presented his results in the form of a simpler equation. Other investigators have assumed constant wall temperature instead of uniform heat flux and have developed correlations for liquid metal heat transfer in flow between parallel plates and in annuli, as well as in tubes ( 3 ) . In addition, a number of experimental liquid metal heat transfer studies have been made, as reviewed by Lubarsky and Kaufman (4).In the present paper a method similar to that employed by Lyon has been used for an analytical investigation of the heat transfer to a liquid metal in parallel flow through a bundle of tubes. Constant heat flux was employed, and the outer boundary was approximated by a circle of equal area. A simultaneous investigation of this problem was made independently by D y e r and Tu different values of the parameters and with the integrations performed at different stages in the development. A further and more significant difference in the two developments was in the assumption of the velocity distribution. In both studies the model of an annulus was used taking the flow from the inner wall to the point of maximum flow. However Dwyer and Tu used the recent correlations of Rothfus, Walker, and Whan ( 6 ) , whereas in the present paper the velocity distribution assumed by Bailey (7) was used. The results of the present investigation show Nusselt numbers from 7 to 30% higher than those obtained by Dwyer and Tu in the pitch-to-diameter ratio range of 1.375 to 2.2.
METHODIt is postulated that the physical properties of the fluid are constant, that the system i s operating under steady state conditions with no end effects, and that there is uniform radial heat flux at the tube wall. This means that in the region being considered the velocity and temperature profiles are fully established so that atlax is constant at all points.Three of the tubes in an infinite array with uniform triangular pitch are shown in Figure 1 A heat balance around a cylindrical shell of inner radius r gives 9 = 27r pc, ( a t / a x ) p rudr ( 7 )Combining Equations ( 7 ) and (6) and substituting the result in (5), then substituting that result in (4), and fipally substituting that result and ( 2 ) in ( I ) , one gets h = (r," -r:) a u,"
With the view to determining whether or not gas entrained in the sodium coolant couldThe effect of gas entrainment on the coolant flow rate and on coolant temperatureThe effect of gas entrainment on the coolant heat transfer coefficient and film tem-Equations were derived to serve in estimating the thermal-hydraulic effect of the gas entrainment, and calculations performed therewith to obtain information on conditions corresponding to the Core A under operation in the Fermi Reactor.The results of the present examination reveal that in the Fermi Reactor a n amount of gas almost inconceivable as a practical possibility must be entrained before the coolant or the fuel surface would be heated to the boiling point of sodium. cause overheating of a fast reactor core, the following items were studied:(1)(2) rise. perature drop.
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