Analysis of convective-radiative heat transfer in dovetail longitudinal fins with shape-dependent hybrid nanofluids: a study using the Hermite wavelet method

doi:10.1007/s10483-025-3218-9

Abstract

Abstract:

A distinguished category of operational fluids, known as hybrid nanofluids, occupies a prominent role among various fluid types owing to its superior heat transfer properties. By employing a dovetail fin profile, this work investigates the thermal reaction of a dynamic fin system to a hybrid nanofluid with shape-based properties, flowing uniformly at a velocity U. The analysis focuses on four distinct types of nanoparticles, i.e., Al₂O₃, Ag, carbon nanotube (CNT), and graphene. Specifically, two of these particles exhibit a spherical shape, one possesses a cylindrical form, and the final type adopts a platelet morphology. The investigation delves into the pairing of these nanoparticles. The examination employs a combined approach to assess the constructional and thermal exchange characteristics of the hybrid nanofluid. The fin design, under the specified circumstances, gives rise to the derivation of a differential equation. The given equation is then transformed into a dimensionless form. Notably, the Hermite wavelet method is introduced for the first time to address the challenge posed by a moving fin submerged in a hybrid nanofluid with shape-dependent features. To validate the credibility of this research, the results obtained in this study are systematically compared with the numerical simulations. The examination discloses that the highest heat flux is achieved when combining nanoparticles with spherical and platelet shapes.

Key words: Hermite wavelet method, radiation, convection, dovetail fin, nanoparticle configuration

2010 MSC Number:

O351.2

C. G. PAVITHRA, B. J. GIREESHA, S. SUSHMA, K. J. GOWTHAM. Analysis of convective-radiative heat transfer in dovetail longitudinal fins with shape-dependent hybrid nanofluids: a study using the Hermite wavelet method. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 357-372.

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Figures/Tables 15

Fig. 1

Table 1

The thermo-physical properties of the composite nanoliquid[22-23]"

Property	Hybrid nanofluid
Density	$ρ hnf = ρ 1 ϕ 1 + ρ 2 ϕ 2 + (1 − ϕ 1 − ϕ 2) ρ f$
Heat capacity	$(ρ c p) hnf = ϕ 1 (ρ c p) 1 + ϕ 2 (ρ c p) 2 + (1 − ϕ 1 − ϕ 2) (ρ c p) f$
Coefficient of thermal expansion	$(ρ β) hnf = ϕ 1 (ρ β) 1 + ϕ 2 (ρ β) 2 + (1 − ϕ 1 − ϕ 2) (ρ β) f$

Table 1

Table 2

The thermal conductivity and efficient dynamic viscosity of the nanofluid"

Shape	Thermal conductivity	Dynamic viscosity
Spherical $(n = 3)$	$k nf1 k f = k p1 + 2 k f + 2 ϕ (k 1 − k f) k p1 + 2 k f − ϕ (k 1 − k f)$	$μ nf1 = μ f (1 + 2.5 ϕ + 6.2 ϕ 2)$
Cylindrical $(n = 4.9)$	$k nf2 k f = k p2 + 3.9 k f + 3.9 ϕ (k p2 − k f) k p2 + 3.9 k f − ϕ (k p2 − k f)$	$μ nf2 = μ f (1 + 13.5 ϕ + 904.4 ϕ 2)$
Platelet (5.7)	$k nf3 k f = k p3 + 4.7 k f + 24.7 ϕ (k p3 − k f) k p3 + 4.7 k f − ϕ (k p3 − k f)$	$μ nf2 = μ f (1 + 37.1 ϕ + 612.6 ϕ 2)$

Table 2

Table 3

The thermal and physical characteristics of water and nanoparticles[14,23]"

Property	H₂O	Al₂O₃	Cu	CNT	Graphene
$ρ / (kg ⋅ m − 3)$	997.1	3 970	8 933	2 100	2 200
$k$ / $(W ⋅ m − 1 ⋅ K − 1)$	0.613	40	400	3 007.4	5 000
$c p$ / $(J ⋅ kg − 1 ⋅ K − 1)$	4 179	765	385	410	790
$β / K − 1$	$2.1 × 106$	$2.4 × 105$	$5.1 × 105$	$2 × 105$	$− 0.8 × 105$
Shape	—	Spherical	Spherical	Cylindrical	Platelet

Table 3

Table 4

Comparison of the present work with previous studies"

$ω$	Hoshyar et al. (HPM)^[24]	Gireesha et al.^[21]	Present result
0	1	1	1
0.2	0.975 973 539	0.975 973 537	0.975 973 531 2
0.4	0.957 555 090	0.957 555 088	0.957 555 079 4
0.6	0.944 540 815	0.944 540 812	0.944 540 801 8
0.8	0.936 788 323	0.936 788 321	0.936 788 309 2
1	0.934 213 444	0.934 213 441	0.934 213 428 3

Table 4

Fig. 2

Fig. 3

Fig. 4

Fig. 5

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Fig. 9

Fig. 10

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