Substrate wettability induced alterations in convective heat transfer characteristics in microchannel flows: An order parameter approach

In this paper, we analyze the consequences of substrate wettability on the convective heat transfer characteristics in microchannel flows. However, in sharp contrast to other reported studies, we do not presume a slip-length a priori, but take an explicit accounting of the substrate wettability through an order parameter consideration. The order parameter formalism also allows us to consider co-existences of bulk and interfacial phases and takes the consequent thermo-physical property variations aptly into account. Our results reveal explicit dependence of the heat transfer characteristics, such as the thermal entrance length and the Nusselt number, on the equilibrium contact angle. Further, we present an analysis that theoretically justifies the role of wettability by decomposing the thermophysical properties and flow variables into a base part and a wettability-dependant part, with rigorous justification from a perturbation-based analysis of the order parameter evolution equations. These considerations, along with our simulation predictions, reveal that the effect of substrate wettability on bulk thermal characteristics of microchannel transport is primarily advection-dominated, although a combined advection–diffusion mechanism controls the corresponding interfacial transport in the near-wall regime. Our results bring out an explicit dependence of the heat transfer characteristics on the substrate wettability, and in particular, reveal a trend of decreasing Nusselt number with increasing value of the contact angle.