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Internally Heated Convection and Rayleigh-Bénard Convection

  • Book
  • © 2016

Overview

Authors:
  1. David Goluskin

    1. Mathematics Department, University of Michigan, Ann Arbor, USA

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  • Provides the first review of theoretical results on various convection models beyond the canonical Rayleigh-Bénard model
  • Advances the emerging view of parallels between varied occurrences of convection
  • Stands as the first concise book on internally heated convection and the first full literature review on the subject in nearly 30 years
  • Poses several open problems poised to generate important findings
  • Aids understanding with unique diagrams and visualizations

Part of the book series: SpringerBriefs in Applied Sciences and Technology (BRIEFSAPPLSCIENCES)

Part of the book sub series: SpringerBriefs in Thermal Engineering and Applied Science (BRIEFSTHERMAL)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. A Family of Convective Models

    • David Goluskin
    Pages 1-26

  3. Stabilities and Bounds

    • David Goluskin
    Pages 27-48

  4. Internally Heated Convection Experiments and Simulations

    • David Goluskin
    Pages 49-64
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Keywords

About this book

This Brief describes six basic models of buoyancy-driven convection in a fluid layer: three configurations of internally heated convection and three configurations of Rayleigh-Bénard convection. The author discusses the main quantities that characterize heat transport in each model, along with the constraints on these quantities. This presentation is the first to place the various models in a unified framework, and similarities and differences between the cases are highlighted. Necessary and sufficient conditions for convective motion are given. For the internally heated cases only, parameter-dependent lower bounds on the mean fluid temperature are proven, and results of past simulations and laboratory experiments are summarized and reanalyzed. The author poses several open questions for future study.

Authors and Affiliations

  • Mathematics Department, University of Michigan, Ann Arbor, USA

    David Goluskin

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