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Thermal conductivity of porous sintered metal powder and the Langmuir shape factor

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A Correction to this article was published on 16 April 2021

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Abstract

The objective of this study is to re-examine the classical parallel and classical series models of the effective thermal conductivity of porous media and review the underlying assumptions used to develop these asymptotic models. The Langmuir shape factor concept is introduced to gain insight into these classical models and add extra degrees of freedom to formulate semi-empirical correlations for the effective thermal conductivity based on the parallel, series, and combination of parallel and series heat flow configurations. The analytical models reveal the average areas of the heat flow as potential targets for curve fitting equations with fitting parameters. Experimental data for sintered porous copper were used to calibrate the theoretical models. Correlations for the effective thermal conductivity, Langmuir shape factors, average heat conduction areas, and the average lengths of the heat transfer pathway of the two phases as functions of porosity were obtained and compared graphically.

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Abbreviations

A :

cross-sectional/contact area for heat flow, m2

a :

fitting parameter

k :

thermal conductivity, W/m-K

L :

length of heat transfer pathway, m

m :

fitting parameter

n :

fitting parameter

P :

porosity

\( \dot{q} \) :

heat transfer rate, W

R 2 :

coefficient of determination

RMSE:

Root Mean Square Error

S :

Langmuir shape factor, m

ΔT :

temperature difference, K

e:

effective

f:

fluid-phase

s:

solid-phase

p :

parallel model

s :

series model

\( \overline{} \) :

normalized

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Acknowledgments

We gratefully acknowledge the support of Kuwait University.

Data availability statement

The datasets generated or analyzed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering and Petroleum, Kuwait University, P. O. Box 5969, 13060, Safat, Kuwait

    Osama M. Ibrahim & Sorour Alotaibi

  2. Kuwait Oil Company (K.S.C.), P.O. Box 9758, 61008, Ahmadi, Kuwait

    Ahmed H. Al-Saiafi

Authors
  1. Osama M. Ibrahim
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  2. Ahmed H. Al-Saiafi
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  3. Sorour Alotaibi
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Contributions

Conceptualization, Methodology, Analysis, Writing-Original Draft by O.M. Ibrahim, and A.H. Al-Saiafi. Validation, Writing-Review, and Editing by O.M. Ibrahim and S. Alotaibi. The autho(s) read and approved the final manuscript.

Corresponding author

Correspondence to Osama M. Ibrahim.

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The authors declare no conflict of interest.

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The original version of this article was revised: typographical errors were corrected throughout the chapter.

Appendices

Appendix A

1.1 Experimental data

Table 1 Experimental measurements of the effective thermal conductivity of sintered copper powder
Full size table

Appendix B

1.1 Equation Summary of the classical and re-examined models

Table 2 The classical and re-examined parallel models
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Table 3 The classical and re- examined series models
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Table 4 The re-examined parallel-series model
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Ibrahim, O.M., Al-Saiafi, A.H. & Alotaibi, S. Thermal conductivity of porous sintered metal powder and the Langmuir shape factor. Heat Mass Transfer 57, 1289–1304 (2021). https://doi.org/10.1007/s00231-021-03032-x

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