Similarity transformation-based modeling of the thermally-radiative tetra-hybrid Casson nanofluid flow over a nonlinear stretching sheet using the Clique polynomial collocation method

doi:10.1007/s10483-026-3335-6

Abstract

Abstract:

The flow of a tetra-hybrid Casson nanofluid (Al₂O₃-CuO-TiO₂-Ag/H₂O) over a nonlinear stretching sheet is investigated. The Buongiorno model is used to account for thermophoresis and Brownian motion, while thermal radiation is incorporated to examine its influence on the thermal boundary layer. The governing partial differential equations (PDEs) are reduced to a system of nonlinear ordinary differential equations (ODEs) with fully non-dimensional similarity transformations involving all independent variables. To solve the obtained highly nonlinear system of differential equations, a novel Clique polynomial collocation method is applied. The analysis focuses on the effects of the Casson parameter, power index, radiation parameter, thermophoresis parameter, Brownian motion parameter, and Lewis number. The key findings show that thermal radiation intensifies the thermal boundary layer, the Casson parameter reduces the velocity, and the Lewis number suppresses the concentration with direct relevance to polymer processing, coating flows, electronic cooling, and biomedical applications.

2010 MSC Number:

O351.2

U. L. MANIKANTA, K. J. GOWTHAM, B. J. GIREESHA, P. VENKATESH. Similarity transformation-based modeling of the thermally-radiative tetra-hybrid Casson nanofluid flow over a nonlinear stretching sheet using the Clique polynomial collocation method. Applied Mathematics and Mechanics (English Edition), 2026, 47(1): 185-202.

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Figures/Tables 10

Fig. 1

Table 1

Thermo-physical attributes of the base fluid and the nanoparticles[30]"

Property	Water	Al₂O₃	CuO	TiO₂	Ag
$ρ / (kg ⋅ m − 3)$	997.1	3 970	6 320	4 250	10 500
$k / (W ⋅ m − 1 ⋅ K − 1)$	0.613	40	76.5	8.95	429
$c p / (J ⋅ g − 1 ⋅ K − 1)$	4 179	765	531.8	686.2	235

Table 1

Table 2

Comparative evaluation with prior literature"

Author(s)	$− f ″ (0)$	$− θ ′ (0)$
Sakiadis^[1]	0.443 75	—
Tsou et al.^[38]	0.444	0.349 2
Andersson and Aarseth^[39]	0.444 551 6	0.354 124 7
Ahmad et al.^[40]	0.444 551 6	0.354 124 7
Present study	0.444 551 6	0.354 124 7

Table 2

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Table 3

List of fixed parameters along with supporting references"

Parameter	Value	Reference
$β$	1	[27]
$n$	0.5	[26]
$P r$	6.2	[13]
$R$	3	[8]
$N t$	0.5	[4]
$N b$	0.5	[4]
$L e$	2	[9]

Table 3

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