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

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## Abstract

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

*A*Projected area

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

- \(\bar{{C}}_\mathrm{D} \)
Mean drag coefficient

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

- \(\bar{{C}}_\mathrm{L}\)
Mean lift coefficient

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

- \(c_\mathrm{p} \)
Specific pressure

*D*Cylinder diameter

- \(F_\mathrm{D}\)
Drag force

- \(F_\mathrm{L}\)
Lift force

*G*Gap space between the cylinders

*k*Conductivity

*n*Surface vertical vector

*Nu*Nusselt number

- \(\overline{Nu} \)
Mean Nusselt number

- \(p_\infty \)
Free-stream pressure

*p*Pressure

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

*r*Radial coordinate

*R*Cylinder radius

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

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

*t*Time

*T*Temperature

- \(T_\infty \)
Free-stream temperature

*u*Streamwise velocity

- \(\bar{{u}}\)
Time-averaged streamwise velocity

*U*Free-stream velocity

- \(u_\mathrm{{rms}} \)
Root-mean-square of the streamwise velocity

*v*Vertical velocity

- \(\bar{{v}}\)
Time-averaged vertical velocity

- \(v_\mathrm{{rms}} \)
Root-mean-square of the vertical velocity

*x*Streamwise dimension of coordinates

*y*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

## Subscripts

- 1
Upstream cylinder

- 2
Downstream cylinder

- \(\max \)
Maximum

- \(\min \)
Minimum

- s
Surface of the cylinder

- \(\infty \)
Free-stream

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