The Taylor Wave Configuration during Boiling from a Flat Plate

DURING the development of the hydrodynamic theory of the peak and minimum pool boiling heat flux there have lingered certain questions about the Taylor wavelength in the liquidvapor interface and the spacing of the grid of jets or bubble release nodes. Zuber [i] originally used the most susceptible twodimensional Taylor wavelength. L,, in his analysis. He envisioned that the vapor jets, which become Helmholtz unstable at the peak heat flux. were spaced on a square grid of dimensions 1, x %2. His arrangement is shown in Fig. la. He envisioned that the minimum heat flux occurred when the cyclic release of bubbles from the peaks of such a grid reached its minimum stable frequency. There are two problems with this formulation. One is the use of& instead of the correct three-dimensional wavelength. The other lies in counting the wave peaks for a particular grid. Let us consider the latter problem first. If two-dimensional waves are superposed orthogonally they will actually yield the configuration shown in Fig. 1 b. We see that there should be an additional peak in the center. Thus Zubefs original conceptualization would appear to be correct only for a square grid of dimensions AZ/$! as shown in Fig. lb. Recently Sernas [2] derived the expression for the length of a true three-dimensional Taylor wave. He found that the interface took the form shown in Fig. 1 c with a three dimensional wave of length, ,I, = ,%I,. This result is extremely fortuitous because it shows that the square grid corresponding with Zuber’s assumption actually has peaks distributed just as he assumed they were-on a wavelength equal to A2 (see Fig. ic). There exists one piece of experimental evidence to support this outcome for a flat plate. It is shown in the authors’ closure of [3] that Hosler and Westwater’s photographic results [4] give a wavelength almost exact& equal to ,i, or I,/$?!. Thus it is correct to assume (as Zuber did) that there is one Helmholtz unstable jet per 1: at the peak heat flux and 7’1