Study on heat transfer characteristics of a circular tube with polygonal twisted elements


This paper reported experimental and numerical simulation investigations on heat transfer characteristics of polygonal twisted elements in the constant wall temperature with Reynolds number (Re) ranging from 200 to 1800. In this study, the results revealed that the entransy efficiency (η) increased with the polygonal twisted element’s edge number increasing. Moreover, the highest entransy efficiency η of the quadruple-edge continuous twisted element (QEC) heat exchange tube was 93.97%. Besides, the field synergy performance also showed a positive correlation with the element edge number. A maximum increase of 57% was observed in the field synergy number (Fc) of the QEC insert as compared with the plain tube while the performance evaluation criteria (PEC) had little relationship with the element edge number. In the case of the interlaced twisted elements, both the PEC value and the entransy efficiency η were lower than the corresponding continuous ones. In addition, the Fc values were not apparent, of which the maximum difference was only 7% in the two cases(continuous twisted element and interlaced twisted element). In Re= 1800, when the d/D(the ratio of the twisted element diameter to the inner diameter of the tube) of the QEC heat exchange tube increased, the PEC values and Fc values both increased significantly. The maximum PEC value was 1.62 and the maximum Fc values was 202% higher than the plain tube. Subsequently, the entransy efficiency η got the maximum value in the range of d/D = 0.375-0.75. The maximum entransy efficiency was 91.07%.

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Specific heat at constant pressure, J/kg K

c v :

Specific heat at constant volume, J/kg K


Inner diameter, mm


Diameter of twisted unit, mm


Entransy, J ⋅ K

f :

Resistance coefficient

f I :

Resistance coefficient of interlaced twisted element

f C :

Resistance coefficient of continuous twisted element

fI/fC :

Relative resistance ratio


Pitch of twisted unit, mm

h m :

Thermal conductivity, W/m2K


Thermal Convective heat transfer coefficient, W/m K


Length of tube, mm


Mass flow rate, kg/h

N u :

Nusselt number, hD/λ

N u I :

Nusselt number of interlaced twisted element

N u C :

Nusselt number of continuous twisted element

NuI/NuC :

Relative Nusselt number ratio


Prandtl number, μCp/k


Pressure of fluid, Pa

Q :

Constant volume heat capacity, W

q :

Heat flux, W/m2

R e :

Reynolds number, ρUD/μ


Surface area, m2


Temperature of fluid, k

\(\overline u\) :

Average velocity of fluid m/s


Twisted ratio


Pressure drop


Convective heat transfer temperature


Thickness of twisted unit,mm


Entransy efficiency


Density, kg/m3


Dynamic viscosity, kg/m⋅s


Plain tube








High temperature


Interlaced twisted element




Low temperature




Continuous twisted element




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Correspondence to Zhang Aoyu.

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Zongyong, W., Aoyu, Z. & Huibo, M. Study on heat transfer characteristics of a circular tube with polygonal twisted elements. Heat Mass Transfer 56, 2107–2120 (2020).

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  • Twisted element
  • PEC value
  • Entransy efficiency
  • Field synergy
  • Simulation method