Internally Heated Convection and Rayleigh-Bénard Convection

  title={Internally Heated Convection and Rayleigh-B{\'e}nard Convection},
  author={David Goluskin},
This work reviews basic features of both Rayleigh-B\'enard (RB) convection and internally heated (IH) convection, along with findings on IH convection from laboratory experiments and numerical simulations. In the first chapter, six canonical models of convection are described: three configurations of IH convection driven by constant and uniform volumetric heating, and three configurations of RB convection driven by the boundary conditions. The IH models are distinguished by differing pairs of… 

Penetrative internally heated convection in two and three dimensions

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

Analytical bounds on the heat transport in internally heated convection

Abstract We obtain an analytical bound on the non-dimensional mean vertical convective heat flux $\langle w T \rangle$ between two parallel boundaries driven by uniform internal heating. We consider

Internally heated Darcy-Brinkman-Bénard ferro-thermal-convection in a ferrofluid saturated porous layer: The influence of boundaries

This paper theoretically investigates the effects of different velocity, temperature and magnetic potential boundary conditions on the linear stability criteria of three models of internally heated

Model for classical and ultimate regimes of radiatively driven turbulent convection

Abstract In a standard Rayleigh–Bénard experiment, a layer of fluid is confined between two horizontal plates and the convection regime is controlled by the temperature difference between the hot

Convective dynamics with mixed temperature boundary conditions: Why thermal relaxation matters and how to accelerate it

Astrophysical simulations of convection frequently impose different thermal boundary conditions at the top and the bottom of the domain in an effort to more accurately model natural systems. In this

Heat transfer in rapidly rotating convection with heterogeneous thermal boundary conditions

Convection in the metallic cores of terrestrial planets is likely to be subjected to lateral variations in heat flux through the outer boundary imposed by creeping flow in the overlying silicate

Convection in an internally heated stratified heterogeneous reservoir

The Earth’s mantle is chemically heterogeneous and probably includes primordial material that has not been affected by melting and attendant depletion of heat-producing radioactive elements. One

Rigorous scaling laws for internally heated convection at infinite Prandtl number

We prove rigorous scaling laws for measures of the vertical heat transport enhancement in two models of convection driven by uniform internal heating at infinite Prandtl number. In the first model, a

Thermal forcing and ‘classical’ and ‘ultimate’ regimes of Rayleigh–Bénard convection

The fundamental challenge to characterize and quantify thermal transport in the strongly nonlinear regime of Rayleigh–Bénard convection – the buoyancy-driven flow of a horizontal layer of fluid

Internally heated convection of viscoplastic fluids in enclosures using a lattice Boltzmann method

Thermal convection driven by an internal heat source in a two-dimensional enclosure filled with viscoplastic fluids is investigated numerically. Two vertical side walls of the cavity are isotherms



Penetrative internally heated convection in two and three dimensions

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

Long wavelength thermal convection between non-conducting boundaries

A numerical investigation of thermal convection in a heat-generating fluid layer

Finite difference solutions of the equations governing thermal convection driven by uniform volumetric energy sources are presented for two-dimensional flows in a rectangular domain. The boundary

Convection driven by internal heating

Convection in horizontal layers with internal heat generation. Theory

  • P. Roberts
  • Physics, Environmental Science
    Journal of Fluid Mechanics
  • 1967
A theoretical study has been made of an experiment by Tritton & Zarraga (1967) in which eonvective motions were generated in a horizontal layer of water (cooled from above) by the application of

Bounds on Rayleigh–Bénard convection with imperfectly conducting plates

We investigate the influence of the thermal properties of the boundaries in turbulent Rayleigh–Bénard convection on analytical upper bounds on convective heat transport. We model imperfectly

Turbulent Thermal Convection in an Enclosure With Internal Heat Generation

Numerical results are presented for turbulent thermal convection, driven by uniform volumetric energy sources for two-dimensional flows in a rectangular enclosure. Rigid adiabatic sides and a rigid

Steady, three-dimensional, internally heated convection

Numerical calculations have been carried out of steady, symmetric, three‐dimensional modes of convection in internally heated, infinite Prandtl number, Boussinesq fluids at a Rayleigh number of

Nonlinear Rayleigh–Bénard convection between poorly conducting boundaries

The convective instability of a layer of fluid heated from below is studied on the assumption that the flux of heat through the boundaries is unaffected by the motion in the layer. It is shown that

Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile

An investigation is carried out to determine the conditions marking the onset of convective motion in a horizontal fluid layer in which a negative temperature gradient occurs somewhere within the