Heat and Mass Transfer

, Volume 55, Issue 11, pp 3117–3131 | Cite as

Research on heat transfer enhancement and flow characteristic of heat exchange surface in cosine style runner

  • Yongliang Zhang
  • Xilong ZhangEmail author
  • Min Li
  • Zunmin Liu


The steady state heat transfer and flow resistance performance in cosine style runners with different amplitudes are studied numerically and experimentally in this paper. The results show that: When the Reynolds numbers (Re) range from 1210 to 5080, the core volume goodness factor (ηohstdα) is used to compare the overall heat transfer performance of the two runners, and the ηohstdα value in the cosine style runner is 7–25% larger than that of the equal cross section runner, so that the cosine style runner has better overall heat transfer enhancement performance. When the amplitudes (2A) range from 5 to 9 mm, with the decrease of amplitude, the overall heat transfer performance is getting better. At the same amplitude, the convective heat transfer performance gradually increases as the inlet height (Fh) decreases; with the increase of Re, the thickness of the thermal and velocity boundary layers are both decreasing. Based on the field synergy principle, the heat transfer enhancement mechanisms with different parameters are evaluated, and we conclude that the smaller the amplitude is, its field synergy is better.



Surface area [m2]; Amplitude [mm]


Specific heat capacity [J/kg·K]


Hydraulic diameter [mm]


Fluid pumping power per unit surface area [W/m2]


Inlet height [mm]


Heat transfer coefficient [W/m2·K]


Fin length [mm]


Pressure difference [Pa]


Average value of the heat flux [W]


Fin pitch [mm]


Temperature [K]


Fin thickness [mm]


Temperature difference [K]


Velocity [m/s]



Fanning friction factor


Proportionality constant in Newton’s second law of motion, gc = 1


Colburn factor


Nusselt number


Prandtl number


Reynolds number

Greek letters


Ratio of total heat transfer area to the total volume of an exchanger [m2/m3]


Average field synergy angle [°]


Local field synergy angle [°]


Air density [kg/m3]


Heat conductivity [W/m·K]


Dynamic viscosity [Pa·s]


Extended surface efficiency on one fluid side of the extended surface heat exchanger, dimensionless


Ratio of free flow area to frontal area, dimensionless



Inlet air


Outlet air


Inlet water


Outlet water






Average value


Maximum value





Financial support is provided by the National Science Foundation of China (51874187, 51806114), China Postdoctoral Fund (2016 M602170, 2017 T100508), Key research and development plan of Shandong Province (2017GSF20113, 2018GSF121002), Shandong Province Natural Science Foundation (ZR2018MEE002, ZR2017PD011).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yongliang Zhang
    • 1
  • Xilong Zhang
    • 1
    Email author
  • Min Li
    • 1
  • Zunmin Liu
    • 1
  1. 1.School of Mechanical and Automotive EngineeringQingdao University of TechnologyQingdaoChina

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