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Multi-physics modeling of magnetohydrodynamic Carreau fluid flow with thermal radiation and Darcy–Forchheimer effects: a study on Soret and Dufour phenomena

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Abstract

The primary objective of this article is on examining the impacts of mixed convection flow of Carreau fluid past a permeable stretched surface with Soret and Dufour effects occurring. For the flow analysis, the Darcy–Forchheimer porosity medium is taken into account. In order to explore the transference analysis of heat and mass rate, the impressions of thermal radiation, viscous dissipation, heat generation, Arrhenius activation energy, convective heat, and mass conditions impacts are taken into consideration. The flow equations initially exist as PDEs, and we then employ appropriate similarity transformations to change them into ODEs. The R–K 4th order strategy based on the shooting approach is used to numerically solve these ODEs. Through various emergent variables, the numerical results for the velocity, temperature, and concentration fields are shown. For a variety of distinct variables, the physical quantities such as friction factor, local Nusselt number, and local Sherwood numbers are shown. It is noted that the velocity field is reduced by the magnetic field, but the Weissenberg number buoyancy ratio parameter exhibits the opposite tendency. Further, it is noticed that temperature and concentration distributions have an improving tendency for the Soret and Dufour parameter.

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Abbreviations

\(u, v\) :

Velocity components (m s−1)

\({\text{Sr}}\) :

Soret number

\(n\) :

Power law index

\(T\) :

Fluid temperature (K)

\(\theta_{{\text{w}}}\) :

Temperature ratio parameter

\(\nu_{{\text{f}}}\) :

Kinematic viscosity (m2 s−1)

\(E\) :

Activation energy

\(T_{{\text{w}}}\) :

Surface temperature (K)

\(g\) :

Acceleration due to gravity

\(\gamma\) :

Velocity slip parameter

\(\sigma_{{\text{f}}}\) :

Electric conductivity

\({\text{Gr}}_{{\text{C}}}\) :

Solutal Grashof number

\(k_{{\text{f}}}\) :

Thermal conductivity (W m−1 K−1)

\(C\) :

Fluid concentration

\(C_{{\text{p}}}\) :

Specific heat

\({\text{Sc}}\) :

Schmidt number

\(T_{\infty }\) :

Ambient temperature (K)

\(\beta i_{{\text{C}}}\) :

Mass Biot number

\({\text{Sh}}_{{\text{x}}}\) :

Local Sherwood number

\(C_{\infty }\) :

Ambient concentration

\({\text{We}}^{2}\) :

Weissenberg number

\({\text{Pr}}\) :

Prandtl number

\(\phi\) :

Dimensionless concentricity

\(C_{{\text{f}}}\) :

Skin friction coefficient

\({\text{Fr}}\) :

Darcy–Forchheimer

\(x,y\) :

Cartesian coordinates (m)

\({\text{Re}}\) :

Local Reynolds number

\(\eta\) :

Dimensionless similarity variable

\(M\) :

Hartman field

\(\rho_{{\text{f}}}\) :

Fluid density (kg m−3)

\({\text{Ec}}\) :

Ecker number

\(\mu_{{\text{f}}}\) :

Dynamic viscosity (kg m2 s−1)

\({\Gamma }\) :

Chemical reaction parameter

\(Q\) :

Heat sink parameter

\(\theta\) :

Dimensionless temperature

\({\text{Nu}}\) :

Local Nusselt number

\({\text{Gr}}_{{\text{T}}}\) :

Thermal Grashof number

\({\text{Nr}}\) :

Radiation parameter

\(C_{{\text{w}}}\) :

Surface volume friction

\({\text{Du}}\) :

Dufour number

\(u_{{\text{w}}}\) :

Stretching velocity (m s−1)

\(\beta i_{{\text{T}}}\) :

Thermal Biot number

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    M. Israr Ur Rehman & Haibo Chen

  2. Department of Mathematics, Women University of Azad Jammu and Kashmir, Bagh, 12500, Pakistan

    Aamir Hamid

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MIUR contributed to literature consultation; AH contributed to manuscript preparation; and HC was involved in investigation and methodology.

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Correspondence to M. Israr Ur Rehman.

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Ur Rehman, M.I., Chen, H. & Hamid, A. Multi-physics modeling of magnetohydrodynamic Carreau fluid flow with thermal radiation and Darcy–Forchheimer effects: a study on Soret and Dufour phenomena. J Therm Anal Calorim 148, 13883–13894 (2023). https://doi.org/10.1007/s10973-023-12699-9

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