Acta Mechanica

, Volume 229, Issue 4, pp 1783–1802 | Cite as

Convective heat transfer and fluid flow of two counter-rotating cylinders in tandem arrangement

  • Mohsen Darvishyadegari
  • Rahim Hassanzadeh
Original Paper


This paper discusses the forced convective heat transfer and fluid flow around two counter-rotating cylinders in tandem arrangement at a constant Reynolds number of 200. The upstream and downstream cylinders rotate in counterclockwise and clockwise directions, respectively, with an identical non-dimensional rotating speed (RS) in the range of \(0\le \hbox {RS}\le 4\). Computations are carried out at various non-dimensional gap spaces between the cylinders such as the \({G{/}D}=1.5\), 2.0, and 3.0. It is found that counter-rotating the tandem cylinders deforms the wake region downstream of both cylinders in which the vortex strength of the upstream cylinder is realized to be stronger at larger gap spaces. On the other hand, it is stated that the instabilities of the shear layer of both cylinders become maximum and minimum at \(\hbox {RS}=1\) and \(\hbox {RS}=2\), respectively. Examination of the Nusselt number distributions on the cylinders indicates that at the high RS values, more or less, all points on the each individual cylinder have identical roles in the heat dissipation rate. Finally, it is concluded that the maximum heat transfer occurs at \(\hbox {RS}=1\) for both cylinders.

List of symbols


Projected area

\(C_\mathrm{D} \)

Drag coefficient (\({=}\,\frac{F_\mathrm{D}}{0.5\rho U^{2}A})\)

\(\bar{{C}}_\mathrm{D} \)

Mean drag coefficient


Lift coefficient (\({=}\,\frac{F_\mathrm{L}}{0.5\rho U^{2}A})\)


Mean lift coefficient

\(C_\mathrm{p} \)

Pressure coefficient (\({=}\,\frac{p-p_\infty }{0.5\rho U^{2}})\)

\(c_\mathrm{p} \)

Specific pressure


Cylinder diameter


Drag force


Lift force


Gap space between the cylinders




Surface vertical vector


Nusselt number

\(\overline{Nu} \)

Mean Nusselt number

\(p_\infty \)

Free-stream pressure




Prandtl number (\({=}\,\frac{\mu c_\mathrm{p}}{k})\)


Radial coordinate


Cylinder radius


Reynolds number (\({=}\,\frac{\rho UD}{\mu })\)


Non-dimensional rotational speed \(({=}\,\frac{\omega D}{2U})\)





\(T_\infty \)

Free-stream temperature


Streamwise velocity


Time-averaged streamwise velocity


Free-stream velocity

\(u_\mathrm{{rms}} \)

Root-mean-square of the streamwise velocity


Vertical velocity


Time-averaged vertical velocity

\(v_\mathrm{{rms}} \)

Root-mean-square of the vertical velocity


Streamwise dimension of coordinates


Vertical dimension of coordinates

Greek symbols

\(\mu \)

Dynamic viscosity of the fluid

\(\upsilon \)

Kinematic viscosity of the fluid

\(\rho \)

Density of the fluid

\(\alpha \)

Angular location

\(\omega \)

Rotating speed

\(\xi \)

Element size



Upstream cylinder


Downstream cylinder

\(\max \)


\(\min \)



Surface of the cylinder

\(\infty \)



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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUrmia University of TechnologyUrmiaIran

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