Condensation heat transfer in a sessile droplet at varying Biot number and contact angle

Dropwise condensation has been identified as a promising heat transfer mechanism because it can yield heat fluxes up to an order of magnitude higher than typically found in filmwise condensation. Models for dropwise condensation generally assume a statistical distribution of droplet sizes and integrate heat transfer over the droplet size spectrum, considering droplet curvature effects on saturation temperature, conduction thermal resistance, and interfacial resistance. Most earlier studies have assumed a constant heat transfer factor (f = O(1)) to account for the conduction contribution to total thermal resistance. However, f varies with droplet Biot number (Bi) and contact angle (θ). Formulations for f with broad ranges of applicability are not currently available. In this study, finite element simulations are performed to determine f and corresponding numerical uncertainties for 0.0001 ⩽ Bi ⩽ 1000 and 10° ⩽ θ ⩽ 170°. This spans the active droplet size range considered in most droplet condensation studies (e.g., for water condensing at Patm on a surface 10 K below the ambient temperature, active droplets have 0.0005 < Bi < 300). An explicit correlation is proposed for f and is validated with published results. The proposed correlation can facilitate modeling and analysis of dropwise condensation.