Thermal characterization of porous longitudinal rectangular moving fin wetted with GO-MoS₂-Al₂O₃/C₂H₆O₂-H₂O ternary hybrid nanofluid

Figures & data

Figure 1. Schematic of ITHNFPFM with insulated and convective fin tip.

Table 1. Physical properties of the nanoparticles (Talbi et al. 2022; Pavithra et al. 2024).

Physical properties	$\mathit{\rho }$ (kg/m^3)	${\mathit{c}}_{\mathit{p}}$ (J/kg K)	${\mathit{k}}^{\prime }$ (W/mK)	$\mathit{\beta }$ (1/K)
Go	1800	717	5000	28.4$\times {10}^{-5}$
MoS2	5060	397.21	904.4	2.8424$\times {10}^{-5}$
Al2O3	3970	765	40	0.6$\times {10}^{-5}$
C2H6O2- H2O	1063.8	3630	0.387	5.8$\times {10}^{-5}$

Table 2. Validation of the 3-stage Lobatto – IIIa method at $X=0.4$ with the existing result of Talbi et al. (2022) when ${\psi }_1=0.02,{\psi }_2=0.02.$

$\mathit{\text{Nr}}$	$\mathit{n}$	$\mathit{\text{Bi}}$	Pe	${\mathit{m}}_2$	${\mathit{\theta }}_{\mathit{a}}$	$\mathit{\text{Nc}}$	$\mathit{\theta }\left(\mathit{X}\right)$ Talbi et al. (2022)	$\mathit{\theta }\left(\mathit{X}\right)$ Lobatto – IIIa method	Absolute error
0.2	1	1	1	0.2	0.2	2	0.792	0.7913	0.0007
2	1	1	1	1	0.2	0.4	0.7449	0.7448	0.0001
3	1	1	0.5	1	0.2	0.5	0.865	0.8645	0.0005
1	1	1	0.6	1	0.2	1	0.76	0.7592	0.0008
0.2	2	1	1	0.4	0.2	0.2	0.865	0.8648	0.0002
5	1	1	1	1	0.4	10	0.678	0.6774	0.0006

Table 3. Comparison of the proposed convective fin tip ITHNFPFM with the existing result of Talbi et al. (2022) (Numerical values of $\theta \left(X\right)$) at $X=0.4$ when ${\psi }_1=0.02,{\psi }_2=0.02 \mathrm{\text{and}}\mathrm{ }{\psi }_3=0.02.$

${\mathit{\theta }}_{\mathit{a}}$	$\mathit{n}$	Pe	$\mathit{\text{Nc}}$	$\mathit{\text{Nr}}$	${\mathit{m}}_2$	Talbi et al. (2022) $\mathit{\theta }\left(\mathit{X}\right)$	Current Outcome $\mathit{\theta }\left(\mathit{X}\right)$	Percentage improvement in the heat absorption
0.2	1	0.2	1	1	1	0.73	0.708	3.013699
0.2	1	0.4	1	1	1	0.74	0.72	2.702703
0.2	1	0.6	1	1	1	0.76	0.73	3.947368
0.2	1	0.8	1	1	1	0.78	0.746	3.947368
0.2	1	1	1	1	1	0.8	0.756	4.358974
0.2	1	0.5	0	2	1	0.76	0.7498	1.342105
0.2	1	0.5	0.4	2	1	0.75	0.7417	1.106667
0.2	1	0.5	0.8	2	1	0.74	0.734	0.810811
0.2	1	0.5	1.2	2	1	0.73	0.7266	0.465753
0.2	1	0.5	1.6	2	1	0.725	0.7195	0.758621
0.2	1	0.5	0.5	0	1	0.88	0.777	11.70455
0.2	1	0.5	0.5	2	1	0.87	0.71	18.3908
0.2	1	0.5	0.5	3	1	0.865	0.688	20.46243
0.2	1	0.5	0.5	4	1	0.86	0.67	22.09302
0.2	1	1	2	0.2	0.2	0.792	0.7853	0.84596
0.2	1	1	2	0.2	0.4	0.781	0.7766	0.56338
0.2	1	1	2	0.2	0.6	0.778	0.7684	1.233933
0.2	1	1	2	0.2	0.8	0.767	0.7605	0.847458
0.2	0	1	0.2	0.2	0.4	0.84	0.826	5.5
0.2	1	1	0.2	0.2	0.4	0.859	0.834	1.666667
0.2	2	1	0.2	0.2	0.4	0.865	0.84	2.910361
0.2	3	1	0.2	0.2	0.4	0.872	0.844	2.890173
0.2	4	1	0.2	0.2	0.4	0.881	0.847	3.211009
0.2	1	1	10	5	1	0.602	0.5405	10.21595
0.4	1	1	10	5	1	0.678	0.619	8.702065

Figure 2. (a) Repercussion of P$e$ on $\theta .$ $\left(X\right)$ and (b) repercussion of P$e$ on $\theta .$ $\left(X\right)$

Figure 3. (a) Repercussion of $\mathit{\text{Nc}}$ on $\theta \left(X\right)$ for convective fin tip and (b) repercussion of $\mathit{\text{Nc}}$ on $\theta \left(X\right)$ for insulated fin tip.

Figure 4. (a) Repercussion of $\mathit{\text{Nr}}$ on $\theta \left(X\right)$ for convective fin tip and (b) repercussion of $\mathit{\text{Nr}}$ on $\theta \left(X\right)$ for an insulated fin tip.

Figure 5. (a) Repercussion of $n$ on $\theta \left(X\right)$ for a convective fin tip and (b) repercussion of $n$ on $\theta \left(X\right)$ for an insulated fin tip.

Figure 6. (a) Repercussion of $m_2$ on $\theta \left(X\right)$ for a convective fin tip and (b) repercussion of $m_2$ on $\theta \left(X\right)$ for an insulated fin tip.

Figure 7. (a) Repercussion of ${\theta }_a$ on $\theta \left(X\right)$ for a convective fin tip and (b) repercussion of ${\theta }_a$ on $\theta \left(X\right)$ for an insulated fin tip.

Figure 8. Repercussion of $\mathit{\text{Bi}}$ on $\theta \left(X\right)$ for an insulated fin tip.

Figure 9. Heat transfer rate ${-\theta }^{\prime }\left(0\right)$ for various values of $\mathit{\text{Nc}}$ in Convective and insulated fin tips when ${\psi }_1={\psi }_2={\psi }_3=0.02,{\theta }_a=0.1,n=\mathit{\text{Pe}}=\mathit{\text{Bi}}=1.$ $\mathrm{ }$

Figure 10. Heat transfer rate ${-\theta }^{\prime }\left(0\right)$ for various values of $\mathit{\text{Nr}}$ in Convective and insulated fin tips when ${\psi }_1={\psi }_2={\psi }_3=0.02,{\theta }_a=0.1,n=\mathit{\text{Pe}}=\mathit{\text{Bi}}=1.$ $\mathrm{ }$

Figure 11. Heat transfer rate ${-\theta }^{\prime }\left(0\right)$ for various values of $m_2$ in Convective and insulated fin tips when ${\psi }_1={\psi }_2={\psi }_3=0.02,{\theta }_a=0.1,n=\mathit{\text{Pe}}=\mathit{\text{Bi}}=1.$ $\mathrm{ }$

Figure 12. Repercussion of Shape factor on $\theta \left(X\right)$ for various values of $\mathit{\text{Nr}}.$

Figure 13. Temperature profile of convective fin tip in various shape combinations of GO - MoS₂ - Al₂O₃ ternary hybrid nanofluid for different values of $\mathit{\text{Nr}}.$

Figure 14. Temperature profile of convective fin tip in lamina shape combination of GO - MoS₂ - Al₂O₃ ternary hybrid nanofluid for various values of $\mathit{\text{Nr}}.$

Talbi, N., Kezzar, M., Malaver, M., Tabet, I., Sari, M. R., Metatla, A., & Eid, M. R. (2022). Increment of heat transfer by graphene-oxide and molybdenum-disulfide nanoparticles in ethylene glycol solution as working nanofluid in penetrable moveable longitudinal fin. Waves in Random and Complex Media, 1–23. https://doi.org/10.1080/17455030.2022.2026527

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Data availability statement

The data that support the findings of this study are available from the corresponding author [R.G.P.], upon reasonable request.