Hydrophobic surfaces, enabling flow slip past a solid boundary, can be effective for suppressing flow unsteadiness, as well as for heat transfer enhancement; both are important for heat exchanger applications. In the present work, a computational investigation of forced convection heat transfer in cross-flow past a hydrophobic circular cylinder is performed at a Reynolds number value of 300, for which flow past a non-hydrophobic cylinder is three-dimensional. Here, the cylinder surface is maintained at a constant temperature, whereas a Prandtl number of unity is considered. Surface hydrophobicity is modelled based on the Navier model. In a first step, slip conditions are implemented on the entire cylinder surface (full slip), for a nondimensional slip length b* = b/D = 0.20, b being the slip length and D the cylinder diameter. This results in a suppression of flow unsteadiness, as well as in a simultaneous heat transfer enhancement; the latter is quantified by the increase of the mean Nusselt number. Next, in order to reduce the extent of the hydrophobic region, and thus the associated cost, a partial slip setup is considered. This setup consists of alternating hydrophobic and non-hydrophobic strips along the spanwise direction, the width of which is selected considering the spanwise wavelength, λz, of three-dimensional flow. Further, following recent studies of the authors on two-dimensional flow, a non-hydrophobic region is considered around the average rear stagnation point (in the circumferential direction), for all hydrophobic strips. It is shown that the present setup can result in values of mean Nusselt number comparable to those attained with full slip. Overall, the present results illustrate that a proper implementation of partial hydrophobicity on the cylinder surface, along the circumferential and the spanwise direction, results in a suppression of wake unsteadiness and fluctuating forces, as well as in a simultaneous enhancement of heat transfer rates.

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