Figure 4 plots the fully developed Nusselt number averaged over the composite interface, Nu_{fd}, versus the solid fraction $\varphi $ for aspect ratios of *H*/*d* = 1, 1.5, 2, 4, 6, 10, and 100, when the lower plate is textured with isothermal ridges and the upper one is smooth and adiabatic. The dashed curve corresponds to smooth plates with Nusselt number Nu_{fd,}_{s} = 4.86. The results obey the expected asymptotic behavior as $\varphi \u21921$, with $Nufd\u2192Nufd,s$, irrespective of the aspect ratio. Additionally, as $\varphi \u21920,\u2009Nufd$ tends to zero because the available area for heat transfer vanishes. Moreover, for a given $\varphi $ (excluding the aforementioned limits) as *H*/*d* → 0 and $H/d\u2192\u221e,\u2009Nufd$ tends to zero and to Nu_{fd,}_{s}, respectively. This is because for *H*/*d* → 0 heat is mainly advected by the part of the flow above the shear-free meniscus as opposed to the relatively stagnant liquid above the ridges degrading the heat transfer. In the other limit, as *H*/*d* → *∞* the difference between the temperature of the ridge and the mean temperature of the composite interface becomes significantly smaller than the difference between the temperature of the ridge and the bulk temperature of the flow.