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

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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.

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Abbreviations

λ :

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

c p :

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

ρ :

Density of sample [kg/m3]

t :

Time [s]

n :

Outer normal of boundary surface

H k :

Convection coefficient [W/m2∙°C]

H s :

Radiation coefficient [W/m2∙°C]

H :

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

T :

Temperature of quenching part [°C]

T w :

Temperature of boundary [°C]

T c :

Temperature of external environment [°C]

T 0 :

Initial temperature [°C]

r, z :

Cylindrical coordinates [m]

E :

Convergence accuracy

fitness :

The cost function for solving the IHCP

T k :

The experimental temperature in the k time step

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

The temperature calculated by ZFA and ZGFA

I 0 :

Source of light intensity

I(d) :

Light intensity

x i, x j :

Position of firefly

d, d ij :

Distance between different fireflies

γ :

Light absorption coefficient

T max :

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 − x i :

Social cognition in FA

c 1, c 2 :

Accelerating factors in PSO

a and b :

Accelerating factors in ZGFA

global :

Global best position

∆t :

Time step

Max t :

Maximum time step

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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.

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Authors and Affiliations

  1. School of Materials Science and Engineering, Shandong University of Science and Technology, 579 Qianwangang Road, Huangdao, Qingdao, Shandong Province, 266590, People’s Republic of China

    Xiaowei Wang, Huiping Li, Lianfang He, Zhichao Li & Zhaozhi Wang

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  1. Xiaowei Wang
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Correspondence to Huiping Li.

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Wang, X., Li, H., He, L. et al. Estimated temperature-dependent interfacial heat transfer coefficient during gas cooling based on firefly algorithm and finite element method. Heat Mass Transfer 55, 2545–2558 (2019). https://doi.org/10.1007/s00231-019-02608-y

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