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Numerical spectral examination of EMHD mixed convective flow of second-grade nanofluid towards a vertical Riga plate using an advanced version of the revised Buongiorno’s nanofluid model

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Abstract

Present communication aims to determine the impact of Cattaneo–Christov model and convective boundary on second-grade nanofluid flow alongside a Riga pattern. Zero mass flux is accounted at the solid surface of Riga pattern such that the fraction of nanoparticles maintains itself on strong retardation. The impact of Lorentz forces generated by Riga pate is also an important aspect of the study. The governing nonlinear problem is converted into ordinary problems via suitably adjusted transformations. Spectral local linearization method has been incorporated to find the solutions of the nonlinear problems. Variation in horizontal movement of the nanofluid, thermal distribution and concentration distribution of the nanoparticles has been noted for various fluid parameters. The results are plotted graphically. Outcomes indicate that the horizontal movement gains enhancement for elevated values of modified Hartman factor. Thermal state of the nanofluid and concentration of nanoparticles receive reduction for incremental values of relaxation time parameters. Numerical results for skin friction and heat flux have been reported in tabular form. The CPU run time and residual error are obtained to check the efficiency of the method used for finding the solution.

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Abbreviations

\(\text {SLLM}\) :

Spectral local linearization method

\(\text {EMHD}\) :

Electro-magnetohydrodynamics

\(\text {ODE}\) :

Ordinary differential equation

\(\text {PDE}\) :

Partial differential equation

x, y :

Cartesian coordinates/m

u, v :

Velocity components/m s\(^{-1}\)

\(u=ax\) :

Velocity /m s\(^{-1}\)

a :

Positive constant/s\(^{-1}\)

T :

Local temperature/K

\(T_\infty\) :

Ambient temperature/K

g :

Gravitational acceleration/m s\(^{-2}\)

\(j_0\) :

Current density/A m\(^{-2}\)

\(\nu\) :

Kinematic viscosity/m\(^{2}\)  s\(^{-1}\)

\(\rho\) :

Density/kg m\(^{-3}\)

\(\beta _\mathrm{{T}}\) :

Thermal coefficient/K\(^{-1}\)

\(\alpha\) :

Thermal diffusivisity/m\(^{2}\) s\({-1}\)

b :

Width of magnets/m

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

Skin friction (wall drag force)

\(\mathrm{{Nu}}_\mathrm{{x}}\) :

Local Nusselt number

\(B_{\mathrm{{it}}}\) :

Biot number

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

Brownian diffusion/\(\mathrm{{m}}^2\,\mathrm{{s}}^{-1}\)

\(\mathrm{{Re}}_\mathrm{{x}}\) :

Local Reynolds number

\(\mathrm{{Gr}}_\mathrm{{x}}\) :

Local Grashof number

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

Thermophoretic diffusion/\(\mathrm{{m}}^2\,\mathrm{{s}}^{-1}\)

\(\delta\) :

Second-grade nanofluid parameter

\(h_{{\mathrm{{f}}}}\) :

Heat transfer coefficient

H :

Modified Hartman number

\(\beta _1\) :

Dimensionless parameter

Pr:

Prandtl number

Nb:

Brownian diffusion parameter

Nt:

Thermophoresis parameter

\(\lambda _1, \lambda _2\) :

Fluid parameters

\(\kappa\) :

Richardson number

Le:

Lewis number

C :

Concentration distributions

\(\sigma\) :

Electric conductivity of the base fluid/(\(\Omega\) m)\(^{-1}\)

\(\tau\) :

Ratio of heat capacity of fluid and nanoparticles

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Acknowledgements

The authors are highly obliged and thankful to unanimous reviewers for their valuable comments on the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Ghulam Rasool

  2. Faculty of Sciences Aïn Chock, Laboratory of Mechanics, Hassan II University, B.P.5366, Mâarif, Casablanca, Morocco

    Abderrahim Wakif

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Correspondence to Ghulam Rasool.

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Rasool, G., Wakif, A. Numerical spectral examination of EMHD mixed convective flow of second-grade nanofluid towards a vertical Riga plate using an advanced version of the revised Buongiorno’s nanofluid model. J Therm Anal Calorim 143, 2379–2393 (2021). https://doi.org/10.1007/s10973-020-09865-8

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