Natural-convection heat transfer from regularly ribbed vertical surfaces: Homogenization-based simulations towards a correlation for the Nusselt number

Abstract

Free-convection heat transfer from vertical surfaces is widely encountered in engineering applications, yet the role played by surface alterations in the heat transfer process and their practical effectiveness are still points of confusion. In this work, buoyancy-driven flows over periodically ribbed vertical plates of different surface micro-textures are investigated, mainly based on an asymptotic homogenization model through which the expensive resolution of the velocity and thermal fields within the inter-rib regions is bypassed, by imposing equivalent effective boundary conditions at a virtual plane surface. Efficiency of the homogenized simulations in detecting macroscopic behavior of the Nusselt number is first assessed, compared with full feature-resolving simulations in which the effects of complex flow patterns, near and within wall corrugations, on the local Nusselt number are captured. Second, the validated model is used to construct a database of numerical results describing deviations of the average Nusselt number over different ribbed surfaces, relative to a corresponding smooth surface. Under the conditions investigated, it is found that surface roughening generally deteriorates heat transfer from vertical surfaces, with slight enhancement for geometries characterized by low thermal slip, for example, rectangular ribs of narrow inter-rib spaces. Finally, a multiple-regression analysis is conducted to formulate a correlation describing effects of the thermal-slip coefficient, the number of ribs, and the Grashof number on the surface-averaged Nusselt number; accuracy of the proposed correlation is attested via further validation. This paper aims to call attention of the heat transfer society to the ability of the homogenization approach to considerably alleviate the computational requirements for relevant simulations and, thus, to significantly accelerate parametric optimization studies.