Penetrative internally heated convection in two and three dimensions

D. Goluskin, Erwin van der Poel

Research output: Contribution to journalArticleAcademicpeer-review

29 Citations (Scopus)


Convection of an internally heated fluid, confined between top and bottom plates of equal temperature, is studied by direct numerical simulation in two and three dimensions. The unstably stratified upper region drives convection that penetrates into the stably stratified lower region. The fraction of produced heat escaping across the bottom plate, which is one half without convection, initially decreases as convection strengthens. Entering the turbulent regime, this decrease reverses in two dimensions but continues monotonically in three dimensions. The mean fluid temperature, which grows proportionally to the heating rate (H) without convection, grows proportionally to H4=5 when convection is strong in both two and three dimensions. The ratio of the heating rate to the fluid temperature is likened to the Nusselt number of Rayleigh–Bénard convection. Simulations are reported for Prandtl numbers between 0.1 and 10 and for Rayleigh numbers (defined in terms of the heating rate) up to 5 1010.
Original languageEnglish
Pages (from-to)R6-1-R6-13
Number of pages13
JournalJournal of fluid mechanics
Publication statusPublished - 24 Feb 2016


  • METIS-316100
  • IR-100118


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