# Analysis of heat and fluid flow around two co-rotating side-by-side cylinders

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## Abstract

Analysis of the heat and fluid flow around two co-rotating side-by-side cylinders is the subject of this numerical study which is done at constant Reynolds and Prandtl numbers of 200 and 7.0, respectively. Both cylinders rotate in the counterclockwise direction with an identical rotating speed (RS) in the range from 0 to 4. On the other hand, several gap spaces between the rotating cylinders such as G/D = 1.5, 2.0, and 3.0 are considered in the present study. The obtained results are validated against the available data in the open literature. Many different results have been reported in this investigation. It is observed that co-rotating the cylinders deforms the wake region downstream of both cylinders which the vortex strength of the lower cylinder against the rotation is stronger than that of the upper cylinder. On the other hand, co-rotating the cylinders develops a negative lift force on both cylinders. Finally, it was concluded that rotating the side-by-side cylinders reduces the heat transfer rate between the fluid flow and cylinders in general. At whole RS and G/D values, the heat transfer rate of the upper cylinder is realized to be less than that of the lower cylinder.

## Keywords

Forced convection co-rotating cylinders side-by-side cylinders fluid rotating zone## Nomenclature

- Symbol
Description

- \( A \)
area

- \( C_{D} \)
drag coefficient

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

- \( C_{L} \)
lift coefficient

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

- \( C_{p} \)
pressure coefficient

- \( c_{p} \)
specific pressure

- \( D \)
cylinder diameter

- \( F_{D} \)
drag force

- \( F_{L} \)
lift force

- \( G \)
gap space between the cylinders

- \( k \)
conductivity

- \( n \)
surface vertical vector

- \( Nu \)
Nusselt number

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

- \( p \)
pressure

- \( \Pr \)
Prandtl number (= \( \frac{{\mu c_{p} }}{k} \))

- \( r \)
radial coordinate

- \( R \)
cylinder radius

- \( \text{Re} \)
Reynolds number (= \( \frac{\rho UD}{k} \))

- \( RS \)
non-dimensional rotating speed (= \( \frac{{\omega_{o} D}}{2U} \))

- \( t \)
time

- \( T \)
temperature

- \( u \)
streamwise velocity

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

- \( U \)
free-stream velocity

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

- \( \overrightarrow {V} \)
velocity vector

- \( v \)
vertical velocity

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

- \( v_{rms} \)
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

- \( \omega_{o} \)
rotating speed

- \( \omega \)
vorticity

- \( \tau \)
cyclic period of vortex shedding

## Subscripts

- \( 1 \)
upper cylinder

- \( 2 \)
lower cylinder

- \( s \)
surface of the cylinder

- \( \infty \)
free-stream

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