A comparison of the wall heat transfer rates determined from the temperature field is presented next. The dimensionless form of the heat flux, namely the Nusselt number has been determined on the present study. For reasons discussed below, heat fluxes have been computed over one as well as two roll widths at the wall. The wall heat flux is simply the gradient of the field temperature in the near–wall region. It is possible to define a Nusselt number for each hot and cold walls. The average Nusselt number can be computed from the slope of the S-shaped curve shown in Figure 4.26. For comparison, the benchmark result for Nusselt number has been taken from Gebhart et al.[89] This reference value is on a wide variety of experiments reported in the literature and has an uncertainty level of
Figure 4.29 shows the local Nusselt number variation with the coordinate over one roll for the three thinning algorithms. Both the hot and cold walls have been considered. The view angle is 90 degrees and so the roll formation is visible in this projection. The roll being inclined, the Nusselt number variation on the two walls are of opposite orientation. The three thinning algorithms qualitatively reproduce these trends. The Nusselt number profile predicted by the automatic thinning algorithm can be seen to be the smoothest of the three. Differences among the three algorithms can be seen to have increased in Figure 4.26, compared to the errors reported in Table 2. This is because the Nusselt number calculated form the three algorithms are within of one another.
Table 3: Fractional Distribution of Error over a Horizontal Plane
coordinate over one roll for the three thinning algorithms. Both the hot and cold walls have been considered. The view angle is 90 degrees and so the roll formation is visible in this projection. The roll being inclined, the Nusselt number variation on the two walls are of opposite orientation. The three thinning algorithms qualitatively reproduce these trends. The Nusselt number profile predicted by the automatic thinning algorithm can be seen to be the smoothest of the three. Differences among the three algorithms can be seen to have increased in Figure 4.26, compared to the errors reported in Table 2. This is because the Nusselt number calculated form the three algorithms are within 
of one another.
Error over a Horizontal Plane
