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Estimated temperature-dependent interfacial heat transfer coefficient during gas cooling based on firefly algorithm and finite element method

  • Xiaowei Wang
  • Huiping LiEmail author
  • Lianfang He
  • Zhichao Li
  • Zhaozhi Wang
Original
  • 21 Downloads

Abstract

The interfacial heat transfer coefficient (IHTC) is one of the most important thermal-physical parameters in heat conduction problem. To solve the IHTC in gas cooling, a 304 stainless steel sample is heated up to 800 °C by an induction heating device and then cooled by a high-pressure gas source. The IHTC between the high-pressure gas and the sample is evaluated by ZFA-FEM (normal distribution method, firefly algorithm (FA) and finite element method (FEM)) and ZGFA-FEM (normal distribution method, global optimization factor (G), firefly algorithm and finite element method) according to the temperature curve attained in the experiment. The research results show that, these IHTCs attained in the solution of IHCP according to those temperature curves of CFD simulation and the experiment are consistent, and the trend of IHTC attained in the experiment is consistent with that in the literature. The group scale of fireflies in ZGFA is much smaller than that in ZFA. Only 20 fireflies in ZGFA can ensure all fireflies move to the optimal position due to global optimization factor used in ZGFA. The convergence, iteration and CPU time of ZGFA are better than ZFA.

Nomenclature

λ

Thermal conductivity of sample [W/m∙°C]

cp

Constant pressure specific heat of sample [J/Kg∙°C]

ρ

Density of sample [kg/m3]

t

Time [s]

n

Outer normal of boundary surface

Hk

Convection coefficient [W/m2∙°C]

Hs

Radiation coefficient [W/m2∙°C]

H

Interfacial heat transfer coefficient (IHTC) [W/m2∙°C]

T

Temperature of quenching part [°C]

Tw

Temperature of boundary [°C]

Tc

Temperature of external environment [°C]

T0

Initial temperature [°C]

r, z

Cylindrical coordinates [m]

E

Convergence accuracy

fitness

The cost function for solving the IHCP

Tk

The experimental temperature in the k time step

\( {T}_i^{\prime } \)

The temperature calculated by ZFA and ZGFA

I0

Source of light intensity

I(d)

Light intensity

xi, xj

Position of firefly

d, dij

Distance between different fireflies

γ

Light absorption coefficient

Tmax

Maximum iterations

iter

Iterations

\( {v}_i^k \) and \( {v}_i^{k-1} \)

Current and previous velocity of the ith particle

\( pbest-{x}_i^{k-1} \)

Self-cognition in PSO

\( gbest-{x}_i^{k-1} \)

Social cognition in PSO

global − xi

Social cognition in FA

c1, c2

Accelerating factors in PSO

a and b

Accelerating factors in ZGFA

global

Global best position

∆t

Time step

Maxt

Maximum time step

Notes

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (51575324), Taishan Scholarship of Climbing Plan (tspd20161006) and Shandong university of science and technology Postgraduate technology innovation project SDKDYC180241.

Compliance with ethical standards

Conflict of interest

The authors declared that they have no conflicts of interest to this work.

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Copyright information

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

Authors and Affiliations

  • Xiaowei Wang
    • 1
  • Huiping Li
    • 1
    Email author
  • Lianfang He
    • 1
  • Zhichao Li
    • 1
  • Zhaozhi Wang
    • 1
  1. 1.School of Materials Science and EngineeringShandong University of Science and TechnologyQingdaoPeople’s Republic of China

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