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Modelling and analysis of thermal conductivity of a hybrid polymer composite reinforced with particulate rice husk and particulate carbon fibre

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Abstract

This study investigates the effective thermal conductivity of a polymer composite reinforced with particulate rice husk (PRH) and particulate carbon fibre (PCF) developed by hand lay-up process. The thermal conductivity of the developed composites at different fibre volume fraction % (FVF) of PRH and PCF at different particle size ratios is analysed by experimentation. Then a mathematical model is developed to find the analytical solution for effective thermal conductivity of the composites. For the developed model, a nonlinear AMPL (A Mathematical Programming Language) programming model is established to find the analytical solution. It is enthusiastic to observe that the experimental values for effective thermal conductivity are in close approximation with the analytical values obtained from the developed AMPL.

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Acknowledgements

The authors would like to acknowledge CSIR-IMMT, Bhubaneswar, India, for the laboratory support to conduct thermal conductivity test. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Government College of Engineering, Keonjhar, Odisha, 758002, India

    Dayanidhi Jena & Ramesh Chandra Mohapatra

  2. Department of Mechanical Engineering, IIT(ISM), Dhanbad, Jharkhand, 8826004, India

    Dayanidhi Jena & Alok Kumar Das

  3. CSIR-Institute of Minerals and Materials Technology, Bhubaneswar, Odisha, 751013, India

    Shaswat Kumar Das

Authors
  1. Dayanidhi Jena
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  2. Alok Kumar Das
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  3. Ramesh Chandra Mohapatra
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  4. Shaswat Kumar Das
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Contributions

D. Jena Conceptualization, Investigation, Methodology, Data Curation, Writing—Original Draft, A.K. Das- Methodology, Validation, Writing—Review & Editing and Supervision, R.C. Mohapatra- Visualization, Supervision, S.K. Das- Validation, Writing—Original Draft, Writing—Review & Editing.

Corresponding authors

Correspondence to Alok Kumar Das or Shaswat Kumar Das.

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Appendices

Appendix 1

(AMPL Programming and Data file).

Programming Model

File name- hybrid.mod

set inputs;

set layers;

param k{i in inputs};

param k_m;

param k_f1;

param k_f2;

param k_b = k_m;

param r2;

param fvf2;

var fvf1 <  = 0.075, >  = 0.07499999999;

var rr = (fvf1/fvf2)^0.333;

var r1 = rr*r2;

var s_rr = r2*(((88/21)*(1 + (rr)^3))/(fvf1 + fvf2))^0.333;

var k_a = k_m + 44/21*(r1/s_rr)^2*(k_f1—k_m);

var k_c = k_m + (2/3)*(22/7)*(r2/s_rr)^2*(k_f2-k_m);

minimize etcc: s_rr*k_a*k_b*k_c/(k_a*k_c*(s_rr-2*(r1 + r2)) + 2*k_b*(r1*k_c + r2*k_a));

File name- hybrid1.mod

set inputs;

set layers;

param k{i in inputs};

param k_m;

param k_f1;

param k_f2;

param r2;

param fvf2;

var fvf1 <  = 0.3, >  = 0.29999999999;

var rr = (fvf1/fvf2)^0.333;

var r1 = rr*r2;

var s_rr = r2*(((88/21)*(1 + (rr)^3))/(fvf1 + fvf2))^0.333;

var k_a = k_m + (44/21)*(r1/s_rr)^2*(k_f1—k_m) + ((22/7)/(r1*s_rr^2))*(r2*(r1 + r2-s_rr/2)^2-(r1 + r2-s_rr/2)^3*(1/3))*(k_f2—k_m);

var k_b = k_m + (44/7)*(1/s_rr^2*(s_rr-2*r1))*(r2*(r1 + r2-s_rr/2)^2-(r1 + r2-s_rr/2)^3*(1/3))*(k_f2—k_m);

minimize etcc: s_rr*k_a*k_b/(2*k_b*r1 + k_a*(s_rr-2*r1));

Data model

Hybrid.dat

set inputs: = f2 f1 m;

set layers: = a b c;

param k_m: = 0.363;

param k_f1: = 0.039;

param k_f2: = 2.5;

param r2: = 0.0001;

param fvf2: = 0.075.

Appendix 2

(Experimental and analytical model values of effective thermal conductivity of composites at different combination of compositions).

See Tables

Table 1 Effective thermal conductivity at size ratio (r1/r2) = 1, (r1 = r2 = 100microns) and at equal % of fillers
Full size table

1,

Table 2 Effective thermal conductivity at different radius ratio (r1/r2) & (r2 = 100microns) and at 2.5% Carbon
Full size table

2,

Table 3 Effective thermal conductivity at different radius ratio (r1/r2) & (r2 = 100microns) and at 5% Carbon
Full size table

3,

Table 4 Effective thermal conductivity at different radius ratio (r1/r2) & (r2 = 100 microns) and at 7.5% Carbon
Full size table

4.

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Jena, D., Das, A.K., Mohapatra, R.C. et al. Modelling and analysis of thermal conductivity of a hybrid polymer composite reinforced with particulate rice husk and particulate carbon fibre. J Therm Anal Calorim 147, 7761–7773 (2022). https://doi.org/10.1007/s10973-021-11098-2

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