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Cattaneo–Christov-based study of AL2O3–Cu/EG Casson hybrid nanofluid flow past a lubricated surface with cross diffusion and thermal radiation

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Abstract

Casson fluid possesses yield stress and has great importance in biomechanics and polymer processing industries. In the present study, a mathematical model is presented to Cattaneo–Christov-based study on the heat and mass transfer, as well as entropy generation analysis of a thermal system in the presence of the Casson hybrid nanofluid over lubricated surfaces at a stagnation point. A power-law (shear-thinning) fluid is utilized for lubrication. Implementing the continuity of velocity and shear stress of Casson and power-law fluids creates interfacial conditions. We also incorporated thermal radiation effects and a uniform transverse magnetic field in the present study. The similarity techniques are used to reduce the governing nonlinear partial differential equation to a set of the ordinary differential equation. For the numerical solution of the considered problem, we have used MATLAB-based Bvp4c method. The results are presented for hybrid alumina-copper/ethylene glycol (Al2O3–Cu/EG) nanofluid. The computed results are original, and it has been noticed that the present results have excellent agreement with the results of the previous extending literature. It has been observed that the Nusselt number or heat transfer rate of hybrid nanofluid flow is better as compared to nanofluid flow.

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Abbreviations

β:

The Casson parameter

βC :

Volumetric expansion’s coefficients due to concentration

βT :

Volumetric expansion’s coefficients due to temperature

λ:

Thermal relaxation time period

b :

Temperature/concentration length dimension

T m :

The mean fluid temperature s

K T :

The thermal diffusion ratio

K r1 :

The chemical reaction parameter

λ1 :

The thermal buoyancy parameter and

λ2 :

The concentration buoyancy parameter

Ns :

Entropy production

\(\hat{U}_{e}\) :

Non-uniform velocity fluids temperatures

\(\hat{C}\) :

Fluid concentration

\(\hat{T}_{b}\) :

The surface temperature

\(\hat{C}_{b}\) :

The surface concentration

k s1 :

Thermals conductivity of first particle

k s2 :

Thermals conductivity of second particle

k f :

Thermals conductivity of base fluids

k nf :

Thermals conductivity of the nanofluid

k h nf :

Thermals conductivity of the hybrid nanofluids

S :

Depends on the shape factor through the H–C models

ρs1 :

Density of the first nanoparticles

ρs1 :

Density of the second nanoparticles

(c p)hnf :

Specifics heats for the hybrid nanofluid

P y :

Fluid’s yield stress

πc :

Critical product

D m :

Species diffusivity

σ*:

Stefan Boltzmann constant

k*:

Consistency coefficients

γ:

Thermal relaxation time period

M:

The magnetic parameter

μL :

The lubricant viscosity

′Ω:

The dimensionless temperature gradient

S c :

Schmidt number

B r :

The Brinkman number

S r :

Soret number

K r :

The chemical reaction parameter

R e :

The permeability Reynolds numbers

P r :

The Prandtl number

R :

Thermal radiation parameter

μhnf :

The dynamic viscosity of the hybrid nanofluid

ρhnf :

The density of the hybrid nanofluids

σhnf :

Electrical conductivity of hybrid nanofluid

υhnf :

The kinametic viscosity of hybrid nanofluid

HNF:

Hybrid nanofluid

SP:

Stagnation point

MC:

Mixed convection

SFC:

Skin friction coefficients

c p :

Specifics heats at constant pressure

η:

Scaled boundary layer coordinate

θ:

Self-similar temperature

μ:

Dynamic viscosity

υ:

Kinematic viscosity

ρ:

Density

σ:

Electric conductivity

ϕ 1 :

First nanoparticle volume fraction

ϕ 2 :

Second nanoparticle volume fraction

nf:

Nanofluid

hnf:

Hybrid nanofluid

s1:

First nanoparticles

s2:

Second nanoparticles

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Authors and Affiliations

  1. Department of Mathematics, Air University Islamabad, Multan Campus, Multan, 60000, Pakistan

    Abdul Rauf &  Faisal

  2. Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari, 61100, Pakistan

    Tahir Mushtaq

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  1. Abdul Rauf
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  2. Faisal
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Correspondence to Abdul Rauf.

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Rauf, A., Faisal & Mushtaq, T. Cattaneo–Christov-based study of AL2O3–Cu/EG Casson hybrid nanofluid flow past a lubricated surface with cross diffusion and thermal radiation. Appl Nanosci 12, 2059–2076 (2022). https://doi.org/10.1007/s13204-022-02495-6

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