It has recently been proposed by Andraka el al. of Sandia National Laboratories, Albuquerque, in Sodium Reflux Pool-Boiler Solar Receiver On-Sun Test Results (SAND89-2773, June 1992), that the heat flux from a parabolic dish solar concentrator could be delivered effectively to a Stirling engine by a liquid-metal pool boiler. The sketch below shows a cross-section of the pool boiler receiver assembly. Solar flux is absorbed on the concave side of a hemispherical absorber dome, boiling molten sodium metal on the convex side of the dome. The sodium vapor condenses on the engine heater tube as shown near the top of the figure. Condensing sodium transfers its latent heat to the engine working fluid that circulates inside the tube. Calculations indicate that a maximum heat flux of 75 W/cm2

Question

delivered by the solar concentrator to the absorber dome is to be expected. After the receiver had been tested for about 50 hours, a small spot on the absorber dome suddenly melted and the receiver failed. Is it possible that the critical flux for the boiling sodium was exceeded? Use the following properties for the sodium:





GIVEN



FIND

(a) Whether the critical heat flux could have been exceeded

ASSUMPTIONS

? To first order, the absorber dome can be treated as flat, horizontal surface

PROPERTIES AND CONSTANTS

As given in the problem statement, the pertinent properties of the sodium vapor and liquid are

Answer 1

The critical heat flux can be calculated from Equation (9.4)



For the property values listed above we have



If we use Lienhard and Dhir’s recommendation that the factor ?/24 be replaced by 0.149, the critical heat flux would be



which exceeds the expected maximum flux. Therefore, exceeding the critical heat flux is a possible factor in the failure of the receiver.