Method of obtaining dual-phase-lag times in aggregate porous materials with a nonhomogeneous inner structure

Abstract When working with porous non-Fourier heat conduction materials under the dual-phase-lag model, it becomes necessary to find out the values of the relaxation ( $$\tau_{{\text{q}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mtext>q</mml:mtext> </mml:msub> </mml:math> ) and thermalization ( $$\tau_{{\text{T}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mtext>T</mml:mtext> </mml:msub> </mml:math> ) times. In this article, we propose an experimental method to obtain these lagging times for aggregated carbon nanotubes (CNTs). The method, which can be used for any other material, consists of applying a transient heat pulse at one side of the specimen while registering the temperature–time curves at multiple points along it. The remaining faces of the specimen are thermally isolated. Then, an analytical model incorporating these boundary conditions is executed iteratively, varying the lagging times, to minimize the difference between the experimental and theoretical curves. Finally, the best fitting curve gives the best combination of $${\tau }_{\text{q}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mtext>q</mml:mtext> </mml:msub> </mml:math> and $${\tau }_{\text{T}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mtext>T</mml:mtext> </mml:msub> </mml:math> values. We also present the evolution of the lagging values along the specimen’s thickness in a CNT aggregate.