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Estimation of contact heat transfer between curvilinear contacts using inverse method and group method of data handling (GMDH)-type neural networks

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Abstract

Precise knowledge of thermal contact conductance (TCC) across fixed solid contacts of flat-flat and curvilinear surfaces is becoming a crucial topic in advanced industrial applications such as thermal management of electronic packaging and nuclear energy production. In this study, at first, TCC across fixed solid contacts of flat-flat and cylinder-cylinder contacts has been calculated by inverse solution method. Furthermore, the accuracy of inverse method for estimation of TCC between flat-flat and cylinder-cylinder contacts has been evaluated based on the error analysis. Then, the GMDH (group method of data handling) algorithm has been used for heat transfer function estimation between contact surfaces based on input–output data which has been achieved from the experimental investigation and the inverse method using the Conjugate Gradient Method (CGM) with Adjoint problem. Different models of GMDH algorithm are applied and the optimal model is selected based on the common error criteria of RMSE (root mean square error). According to the results, the inverse method is accurate enough to predict TCC between flat-flat and cylinder-cylinder contacts with the root mean square error of 0.167 and 0.205, respectively. Also, it has shown that among the different models of GMDH algorithm, Genetic algorithm obtained by SVD method, make the best algorithm for TTC identification in fixed flat-flat and cylinder-cylinder contacting surfaces. Meanwhile, the attained Root Mean Square Error (RMSE) of the Genetic algorithm obtained by SVD method compared with the experimental results for flat-flat and cylinder-cylinder are 0.1459 and 0.1758, respectively.

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Abbreviations

CGM :

Conjugate gradient method

h c :

Thermal contact conductance

k :

Thermal conductivity

q :

Heat flux

T :

Temperature

R :

Result function

x :

Cartesian spatial coordinate

RMSE :

Root mean square error

L :

Length

t :

Time

Y :

Measured temperatures

T 0 :

Constant temperature at x = 0 (K)

T i :

Initial temperature (K)

α :

Thermal diffusivity

β :

Search step size

γ :

Conjugation coefficient

λ :

Lagrange multiplier satisfying the Adjoint problem

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Authors and Affiliations

  1. Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    Shayan Fathi, Mohammad Eftekhari Yazdi & Armen Adamian

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  1. Shayan Fathi
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  2. Mohammad Eftekhari Yazdi
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Correspondence to Mohammad Eftekhari Yazdi.

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Fathi, S., Eftekhari Yazdi, M. & Adamian, A. Estimation of contact heat transfer between curvilinear contacts using inverse method and group method of data handling (GMDH)-type neural networks. Heat Mass Transfer 56, 1961–1970 (2020). https://doi.org/10.1007/s00231-020-02832-x

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