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Handbook of Thermal Science and Engineering pp 647–690Cite as

Heat Transfer in Rotating Flows

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Abstract

Convective heat transfer in rotating flows is of great technical and scientific importance. Two kinds of configurations, namely, bodies of revolution spinning in a fluid and rotor-stator disk systems, are considered in this chapter. In many cases, not only centrifugal but also Coriolis force contributions play a significant role, and the boundary layer flow is essentially three dimensional. In this case, the rotating flow and heat transfer cannot be described by a simple change of the reference frame and very complex and unexpected phenomena can be found. A substantial difficulty is given by the fact that the number of input parameters is typically rather large in case of rotating systems subjected to an outer forced flow. Then, not only the rotational Reynolds number and the Prandtl number are important for the resulting heat transfer but also the translational Reynolds number and further input variables like angle of incidence or partial admission factors. In this chapter, experimental, theoretical, and recent numerical methods are reviewed. The following discussion is limited to an incompressible Newtonian fluid. Selected results of current research projects are discussed, too. The phenomena arising from natural convection or heat transfer in a rotating fluid heated from below might be found in Chap. 16, “Natural Convection in Rotating Flows.”

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Abbreviations

a:

Annular domain parameter

a :

Potential flow parameter

a T :

Thermal diffusivity

A ijk :

Tensor (Taylor series for velocity)

B :

Angular velocity ratio

C :

(Correlation) constant

C cr :

Correlation constant (Landau model)

Cf:

Friction coefficient

C M :

Moment coefficient

d :

Diameter

D :

Sphere or nozzle diameter

f :

Function

F:

Self-similar function

g :

Acceleration due to gravity

G :

Dimensionless cavity height

G:

Self-similar function (azimuthal component)

Gr:

Grashof number

h :

Heat transfer coefficient

h:

Cavity height

h m :

Mean heat transfer coefficient

H:

Self-similar function

K :

Heat transfer correlation constant

L :

Characteristic length

m :

Correlation exponent

m cr :

Correlation exponent (Landau model)

n*:

Exponent for temperature distribution function

N :

Velocity ratio (potential flow)

Nu:

Nusselt number

Num:

Mean Nusselt number

p :

Pressure

P:

Self-similar function (pressure)

Pr:

Prandtl number

q i :

Heat flux component in i-direction

\( {\dot{q}}_w \) :

Heat flux

r :

Radial coordinate

R :

Radius

R cr :

Critical ratio between Reynolds numbers (Landau model)

Rm:

Curvature parameter

Re:

Reynolds number

Reh:

Reynolds number based on cavity height h

ReL:

Reynolds number based on length scale L

Reu:

Inflow or translational Reynolds number

Reδ:

Reynolds number based on boundary layer thickness

Reω:

Rotational Reynolds number

Reω,r:

Local rotational Reynolds number

Ro:

Rosby number

Sc:

Schmidt number

Sh:

Sherwood number

t :

Time

T :

Temperature

Ta:

Taylor number

u :

Velocity (component)

u i :

Velocity component in i-direction

U :

Characteristic velocity

x :

Coordinate

x i :

Coordinate in i-direction

y :

Coordinate

z :

Axial coordinate

α :

Angle

β :

Angle of attack, incidence

β T :

Thermal expansion coefficient

δ :

Boundary layer thickness

ε :

Gap width

ζ :

Self-similar variable

ζ:

Normal coordinate

λ :

Thermal conductivity

Ʌ:

Order parameter (Landau model)

μ :

Dynamic viscosity

ν :

Kinematic viscosity

ρ :

Density

φ :

Azimuthal angle

Ψ:

Control parameter (Landau model)

τ :

Shear stress

ω :

Angular velocity (disk)

Ω:

Angular velocity (flow)

cr:

Critical

f :

Film

i :

i-direction (i = 1, 2, 3)

j :

j-direction (j = 1, 2, 3)

lam:

Laminar

m nc :

Mean

nc:

Natural convection

r :

Radial

tur:

Turbulent

tr:

Transition

w :

Wall

z :

Axial

0:

Reference, nominal

∞:

Infinity, ambient, bulk

ΔT:

Temperature difference

Δui:

Laplace operator for velocity component ui

F′:

Derivative of self-similar function F

\( \overline{f} \) :

Normal component of f

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Acknowledgments

The author gratefully acknowledges the Deutsche Forschungsgemeinschaft DFG for its strong financial support of his research projects devoted to heat transfer in rotating disk systems.

The efforts and contributions of the many students involved in the author’s research projects are appreciated. In particular, the work of Christian Helcig is acknowledged.

Among the many scientists and workers on the field, the author would like to deeply acknowledge the fruitful discussions with Igor V. Shevchuk.

The editorial assistance of the staff at Springer and the interests of the editor of the book, Professor Kulacki, are also gratefully appreciated.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Muenster University of Applied Sciences, Steinfurt, Germany

    Stefan aus der Wiesche

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  1. Stefan aus der Wiesche
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Corresponding author

Correspondence to Stefan aus der Wiesche .

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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aus der Wiesche, S. (2018). Heat Transfer in Rotating Flows. In: Handbook of Thermal Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-26695-4_12

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