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Handbook of Thermal Science and Engineering pp 691–758Cite as

Natural Convection in Rotating Flows

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Abstract

The effect of rotation is shown to have a significant impact on the natural convection in pure fluids as well as in porous media. In isothermal systems, this effect is limited to the effect of the Coriolis acceleration on the flow. It is shown that Taylor–Proudman columns and geostrophic flows exist in both pure fluids as well as porous media subject to rotation. Results of linear stability analysis for natural convection in a rotating fluid layer heated from below are presented, identifying the unique features corresponding to this problem as compared to the same problem without rotation. In nonisothermal porous systems, the effect of rotation is expected in natural convection. Then the rotation may affect the flow through two distinct mechanisms, namely thermal buoyancy caused by centrifugal forces and the Coriolis force (or a combination of both). Since natural convection may be driven also by the gravity force, and the orientation of the buoyancy force with respect to the imposed thermal gradient has a distinctive impact on the resulting convection, a significant number of combinations of different cases arise in the investigation of the rotation effects in nonisothermal porous systems. Results pertaining to some of these cases are presented.

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Abbreviations

X ∗ :

Position vector from the origin located on the axis of rotation to any point in the flow domain in Cartesian coordinates, equals \( {x}_{\ast }{\widehat{\boldsymbol{e}}}_x+{y}_{\ast }{\widehat{\boldsymbol{e}}}_y+{z}_{\ast }{\widehat{\boldsymbol{e}}}_z \)

t ∗ :

Time

V ∗ :

Velocity vector, equals \( {u}_{\ast }{\widehat{\boldsymbol{e}}}_x+{v}_{\ast }{\widehat{\boldsymbol{e}}}_y+{w}_{\ast }{\widehat{\boldsymbol{e}}}_z \)

ω ∗ :

Angular velocity of rotation

T ∗ :

Temperature

p ∗ :

Pressure

ρ ∗ :

Fluid density

ρ o :

A constant reference value of the density

μ o :

Dynamic viscosity (assumed constant)

α o :

Thermal diffusivity, equals ko/ρocp

β T∗ :

Thermal expansion coefficient assumed constant, equals −1/ρo(∂ρ∗/∂T∗)

\( {\widehat{\boldsymbol{e}}}_x \),\( {\widehat{\boldsymbol{e}}}_y \),\( {\widehat{\boldsymbol{e}}}_z \):

Unit vectors in the x∗ , y∗, and z∗ directions, respectively

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Authors and Affiliations

  1. Department of Mechanical Engineering, Northern Arizona University, Flagstaff, AZ, USA

    Peter Vadasz

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  1. Peter Vadasz
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Corresponding author

Correspondence to Peter Vadasz .

Section Editor information

  1. Armour College of Engineering, Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, Illinois, USA

    Sumanta Acharya

  2. Gas Technology Institute, Des Plaines, Illinois, USA

    Yaroslav Chudnovsky

  3. Universidade Federal do Rio de Janeiro - UFRJ, Rio de Janeiro, Rio de Janeiro, Brazil

    Renato Machado Cotta

  4. Department of Mechanical Engineering, Louisiana State University, Baton Rouge, Louisiana, USA

    Ram Devireddy

  5. Mechanical and Aerospace Engineering, University of California Los Angeles, Los Angeles, California, USA

    Vijay K. Dhir

  6. Cekmeköy Campus, Özyegin University, Çekmeköy - Istanbul, Turkey

    M. Pinar Mengüç

  7. Department of Mechanical and Industrial Engineering, Faculty of Applied Science + Engineering, University of Toronto, Centre for Advanced Coating Technologies, Toronto, Ontario, Canada

    Javad Mostaghimi

  8. Department of Mechanical Engineering, University of California, Riverside, California, USA

    Kambiz Vafai

  9. Herff College of Engineering,Department of Mechanical Engineering, The University of Memphis, Memphis, Tennessee, USA

    Sumanta Acharya

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Vadasz, P. (2018). Natural Convection in Rotating Flows. In: Handbook of Thermal Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-26695-4_11

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