The Proceedings of the Eighth International Conference on Creationism (2018)

lithosphere. However it does reproduce Stein and Stein’s results by an alternative numerical method, which demonstrates the success of our verification exercise. As a verification of mesh convergence in our calculations we have repeated them on another spreadsheet with finer discretization, viz. Δ z = 475 m and Δ t = 2,500 years; to preserve the same μ value halving Δ z requires a 4 times smaller value of Δ t . This calculation is continued to a simulated time of 10 Ma. The only differences visible in the spreadsheets at 10 Ma are in the heat fluxes, being of order 1 in the fourth significant figure for the surface heat flux and 4 in the second significant figure in the bottom heat flux; since the latter is very small (~10 -5 Wm -2 ), these differences are insignificant. 2. Accelerated heat conduction The half space and GDH1 model calculations were repeated with drastically higher thermal conductivity and correspondingly shorter timesteps in order to show the effect of seeking to cool the lithosphere in a biblically-compatible time scale simply by accelerating the heat conduction process. Thermal conductivity is increased by a purely illustrative factor 10 9 , while the timestep is reduced by the same factor. To maintain the same ocean floor profile the uniform spreading rate is also accelerated by a factor of 10 9 . Given that the computational mesh is kept as before (Δ z = 950 m), this means that the combination кΔ t and hence μ are also the same. Not surprisingly, therefore, the temperature field and shrinkage are identical to those obtained in the uniformitarian case, while surface heat fluxes are 10 9 times larger than before at corresponding points in time; however the total simulated time is now only 0.2 of a year (about 73 days) instead of 200 million years. Thus the total surface heat load of 4.58×10 14 Jm -2 is deposited into the above-surface environment in only 73 days, an average surface heat flux exceeding 70 MWm -2 (The net heat loss, which gives rise to the vertical shrinkage, is only 2.68×10 14 Jm -2 , the difference being accounted for by heat transfer into the plate from the hotter region below). The above high rate of heat loss could not be sustained naturally by the earth’s oceans. Since even blackbody radiation from a free surface at 1,450ºC can only remove 500 kWm -2 , this enhanced conduction scenario demands an extraordinary surface cooling mechanism in addition to the postulated extraordinarily efficient heat conduction within the cooling lithosphere. The “enhanced thermal conduction hypothesis” is considered further in the discussion section below. 3. A uniform heat sink The attraction of postulating an internal heat sink to cool the lithosphere is that the above-surface environment is only subject to modest heat loads; it does not necessarily “know” about exceptional sub-surface processes. Furthermore there have been suggestions in the creation science literature of an expansion of space during the Flood as a way of providing volume cooling (see Humphreys 2000, pp.369-374, and Humphreys 2005, pp.67-74); in models of the kind investigated here such a process would be manifested as a heat sink. We therefore repeat the calculations of the previous section Worraker and Ward ◀ Ocean floor cooling ▶ 2018 ICC 678 Figure 2. Plot of the surface heat flux for the half spacemodel and theGDH1 model of Stein and Stein (1992), taken from our spreadsheet calculations with Δ z = 950 metres and Δ t = 10 4 years such that the dimensionless timestep μ =0.2841. By construction the curves are identical up to t =8.0 Ma. The results are graphically indistinguishable from those presented in Stein and Stein’s (1992) Fig. 1a. Given the considerable scatter on the data points in their plot, the GDH1 model becomes distinguishable from the half space model at about 120 Ma. Figure 3. Plot of the ocean depth profiles for the half space model and the GDH1 model of Stein and Stein (1992), taken from our spreadsheet calculations with the same mesh size and timestep as in Fig. 1. These model plots are practically the same as those in Stein and Stein’s Fig. 1b, and it is clear that the models give divergent results at an earlier time for ocean depth than for surface heat flux. The curves are slightly lower here compared with those in Fig. 1 because the ridge depth there was 2.5 km vs. 2.6 km here. Figure 4. Temperature profiles through the depth of the plate from our spreadsheet calculations of the GDH1 model (Stein and Stein 1992). Note that by 200 Ma the profile is practically straight – by this time the system has almost reached its asymptotic steady state condition.