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Numerical Treatments to Analyze the Nonlinear Radiative Heat Transfer in MHD Nanofluid Flow with Solar Energy

  • Research Article-Physics
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Abstract

In the current study, the nonlinear radiative heat transfer effects due to solar radiation in magneto-hydrodynamic (MHD) nanofluidic problem are analyzed effectively by novel application of numerical computing by Adams predictor–corrector and explicit backward difference solvers. The governing relations of PDEs for the model are transformed into the system of ODEs, and numerical solvers are applied to the transformed system to study the effect of radiation parameter along with thermophoresis parameter, Brownian motion parameter, magnetic field parameter, Lewis number, Prandtl number, Eckert number and Biot number on velocity, temperature and nanoparticle concentration profiles. The comparative study of both solvers is provided in sufficient number of graphical and numerical illustrations to prove the worth in terms of accuracy, robustness and stability.

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Abbreviations

\( (u,w) \) :

Components of velocity profile

\( (U,W) \) :

Coordinate axes

\( T \) :

Fluid temperature

\( p \) :

Fluid pressure

\( \upsilon \) :

Dynamic viscosity

C :

Nanoparticle concentration

\( q_{\text{r}} \) :

Radiative heat flux parameter

H 0 :

Strength of uniform magnetic field

\( D_{\text{B}} \) :

Brownian parameter

\( D_{\text{T}} \) :

Thermophoretic diffusion parameter

\( R_{d} \) :

Radiation parameter

\( N_{\text{t}} \) :

Thermophoresis parameter

\( N_{b} \) :

Brownian motion parameter

\( M \) :

Magnetic parameter

\( Le \) :

Lewis Number

\( \Pr \) :

Prandtl number

\( E_{c} \) :

Eckert number

\( \rho \) :

Density

\( \sigma^{*} \) :

Stefan–Boltzmann constant

\( k^{*} \) :

Mean absorption coefficient

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

Based fluid density

\( \alpha \) :

Based fluid thermal diffusivity

\( f(\eta ) \) :

Velocity Profile

\( \theta (\eta ) \) :

Temperature Profile

\( \phi (\eta ) \) :

Concentration Profile

\( u_{w} \left( x \right) \) :

Stretching velocity along horizontal axis

\( u_{\infty } (x) \) :

Free stream velocity

\( \left( {\rho c} \right)_{f} \) :

Heat capacity of fluid

\( \left( {\rho c} \right)_{p} \) :

Heat capacity of nanofluid

\( \gamma \) :

Biot number

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

Electrical Conductivity

\( \lambda \) :

Ratio of rates of free stream velocity to stretching sheet velocity

\( \tau \) :

Ratio of heat capacity of nanoparticle to heat capacity of fluid

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Saeed Ehsan Awan & Muhammad Asif Zahoor Raja

  2. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, 64002, Taiwan, R. O. C.

    Muhammad Asif Zahoor Raja

  3. School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, SA, Australia

    Ammara Mehmood

  4. Department of Electronic Engineering, Engineering College, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan

    Shahab Ahmad Niazi

  5. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Sadia Siddiqa

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  1. Saeed Ehsan Awan
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Correspondence to Ammara Mehmood.

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Awan, S.E., Raja, M.A.Z., Mehmood, A. et al. Numerical Treatments to Analyze the Nonlinear Radiative Heat Transfer in MHD Nanofluid Flow with Solar Energy. Arab J Sci Eng 45, 4975–4994 (2020). https://doi.org/10.1007/s13369-020-04593-5

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