2019/07/04 by Michael MacDonald, MacDonald, Michael, Nicholas Hutchins +5
Engineering · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Heat Transfer Mechanisms #Nanofluid Flow and Heat Transfer
paper · pdf · doi:10.48550/arxiv.1907.02504
openalex publication_date 2019/07/04 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Heat and momentum transfer in wall-bounded turbulent flow, coupled with the\neffects of wall-roughness, is one of the outstanding questions in turbulence\nresearch. In the standard Rayleigh-B 'enard problem for natural thermal\nconvection, it is notoriously difficult to reach the so-called ultimate regime\nin which the near-wall boundary layers are turbulent. Following the analyses\nproposed by Kraichnan [Phys. Fluids vol 5., pp. 1374-1389 (1962)] and Grossmann\n& Lohse [Phys. Fluids vol. 23, pp. 045108 (2011)], we instead utilize recent\ndirect numerical simulations of forced convection over a rough wall in a\nminimal channel [MacDonald, Hutchins & Chung, J. Fluid Mech. vol. 861, pp.\n138--162 (2019)] to directly study these turbulent boundary layers. We focus on\nthe heat transport (in dimensionless form, the Nusselt number Nu) or\nequivalently the heat transfer coefficient (the Stanton number Ch).\nExtending the analyses of Kraichnan and Grossmann & Lohse, we assume\nlogarithmic temperature profiles with a roughness-induced shift to predict an\neffective scaling of Nu \∼ Ra0.42, where Ra is the dimensionless\ntemperature difference, corresponding to Ch \∼ Re-0.16, where Re is\nthe centerline Reynolds number. This is pronouncedly different from the\nskin-friction coefficient Cf, which in the fully rough turbulent regime is\nindependent of Re, due to the dominant pressure drag. In rough-wall\nturbulence the absence of the analog to pressure drag in the temperature\nadvection equation is the origin for the very different scaling properties of\nthe heat transfer as compared to the momentum transfer. This analysis suggests\nthat, unlike momentum transfer, the asymptotic ultimate regime, where Nu\∼\nRa1/2, will never be reached for heat transfer at finite Ra.\n