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MHD 3-dimensional nanofluid flow induced by a power-law stretching sheet with thermal radiation, heat and mass fluxes

Sudipta Ghosh
Sudipta Ghosh
, 
Swati Mukhopadhyay
Swati Mukhopadhyay
 and 
Kuppalapalle Vajravelu
Kuppalapalle Vajravelu
   | Oct 15, 2020
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Published Online: Oct 15, 2020
Page range: 361 - 380
Received: Sep 17, 2019
Accepted: Dec 18, 2019
DOI: https://doi.org/10.2478/amns.2020.2.00036
Keywords
© 2020 Sudipta Ghosh et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Physical configuration of the problem.
Physical configuration of the problem.

Fig. 2

Influences of magnetic parameter M on (a) f′(η), velocity in the direction of x (b) g′(η), velocity in the direction of y, temperature θ (η) for (c) CWT (d) PHF and nanoparticle volume fraction ϕ(η) for (e) ZMF and (f) PMF.
Influences of magnetic parameter M on (a) f′(η), velocity in the direction of x (b) g′(η), velocity in the direction of y, temperature θ (η) for (c) CWT (d) PHF and nanoparticle volume fraction ϕ(η) for (e) ZMF and (f) PMF.

Fig. 3

Influences of λ, stretching ratio parameter on (a) f′(η), velocity in the direction of x (b) g′(η), velocity in the direction of y, temperature θ (η) for (c) CWT and (d) PHF and nanoparticle volume fraction ϕ(η) for (e) ZMF and (f) PMF.
Influences of λ, stretching ratio parameter on (a) f′(η), velocity in the direction of x (b) g′(η), velocity in the direction of y, temperature θ (η) for (c) CWT and (d) PHF and nanoparticle volume fraction ϕ(η) for (e) ZMF and (f) PMF.

Fig. 4

Influences of n, non-linearly stretching parameter on (a) f′(η), velocity in the direction of x (b) g′(η), velocity in the direction of y, (c) θ (η), temperature for PHF and (d) nanoparticle volume fraction ϕ(η) for PMF.
Influences of n, non-linearly stretching parameter on (a) f′(η), velocity in the direction of x (b) g′(η), velocity in the direction of y, (c) θ (η), temperature for PHF and (d) nanoparticle volume fraction ϕ(η) for PMF.

Fig. 5

Influences of thermophoresis parameter Nt on temperature θ (η) for (a) CWT and (b) PHF and on ϕ(η), nanoparticle volume fraction for (c) ZMF and (d) PMF.
Influences of thermophoresis parameter Nt on temperature θ (η) for (a) CWT and (b) PHF and on ϕ(η), nanoparticle volume fraction for (c) ZMF and (d) PMF.

Fig. 6

Influences of R, radiation parameter on temperature θ (η) for (a) CWT and (b) PHF and on nanoparticle volume fraction ϕ(η) for (c) ZMF and (d) PMF.
Influences of R, radiation parameter on temperature θ (η) for (a) CWT and (b) PHF and on nanoparticle volume fraction ϕ(η) for (c) ZMF and (d) PMF.

Fig. 7

Influences of Pr, Prandtl number on θ (η), temperature for (a) CWT and (b) PHF and on ϕ(η), nanoparticle volume fraction for (c) ZMF and (d) PMF.
Influences of Pr, Prandtl number on θ (η), temperature for (a) CWT and (b) PHF and on ϕ(η), nanoparticle volume fraction for (c) ZMF and (d) PMF.

Fig. 8

Effects of (a) Nb, the parameter for Brownian motion and (b) Sc, the Schimidt number on temperature θ (η) for PHF.
Effects of (a) Nb, the parameter for Brownian motion and (b) Sc, the Schimidt number on temperature θ (η) for PHF.

Fig. 9

Effects of Nb, the parameter for Brownian motion for (a) ZMF and (b) PMF and Schmidt number Sc for (c) ZMF and (d) PMF on nanoparticle volume fraction φ(η).
Effects of Nb, the parameter for Brownian motion for (a) ZMF and (b) PMF and Schmidt number Sc for (c) ZMF and (d) PMF on nanoparticle volume fraction φ(η).

Fig. 10

The streamline of the flow for (a) n = 0.5 and (b) n = 5.0.
The streamline of the flow for (a) n = 0.5 and (b) n = 5.0.

Fig. 11

Distributions of (a)− f″(0) (b)−g″(0) (c) −θ′ (0) [for CWT] (d) −ϕ′ (0) [for ZMF] with λ, stretching ratio parameter for diverse values of magnetic field parameter M.
Distributions of (a)− f″(0) (b)−g″(0) (c) −θ′ (0) [for CWT] (d) −ϕ′ (0) [for ZMF] with λ, stretching ratio parameter for diverse values of magnetic field parameter M.

Fig. 12

Distributions of (a) −θ′ (0) for CWT (b) −ϕ′ (0) for ZMF with Nb, Brownian motion parameter for diverse values of Nt, thermophoresis parameter.
Distributions of (a) −θ′ (0) for CWT (b) −ϕ′ (0) for ZMF with Nb, Brownian motion parameter for diverse values of Nt, thermophoresis parameter.

Comparisons for the values of f″(0) and g″(0) in the absence of magnetic field

N λ f″(0) g″(0)
Khan et al. (2015) Raju et al. (2016) Present study Khan et al. (2015) Raju et al. (2016) Present study
1 0 −1 −1 −1 0 0 0
0.5 −1.22474 −1.2247431 −1.2247429 −0.612372 −0.6123721 −0.6123720
1.0 −1.414214 −1.4142141 −1.4142140 −1.414214 −1.4142140 −1.4142140
3 0 −1.624356 −1.6243560 −1.6243560 0 0 0
0.5 −1.989422 −1.9894221 −1.9894220 −0.994711 −0.9947110 −0.9947110
1.0 −2.297186 −2.2971860 −2.2971860 −2.297186 −2.2971860 −2.2971860

Comparisons of the values of f″(0) and g″(0) in the absence of the magnetic field for different grid sizes

N f″(0) g″(0)
Grid size 0.01 Grid size 0.03 Grid size 0.01 Grid size 0.03
1 0 −1 −1 0 0
0.5 −1.2247429 −1.2247429 −0.6123720 −0.6123720
1.0 −1.4142140 −1.4142140 −1.4142140 −1.4142140
3 0 −1.6243560 −1.6243560 0 0
0.5 −1.9894220 −1.9894220 −0.9947110 −0.9947110
1.0 −2.2971860 −2.2971860 −2.2971860 −2.2971860

Values of −θ′(0) and −ϕ′(0) for different values of thermophoresis parameter Nt and Prandtl number Pr with n = 4.0, λ = 0.9, Nb = 0.7, Pr = 2.0, R = 0.5, Sc = 15.0

Nt Pr
1.0 1.5 2.0 2.5
−θ′(0) −ϕ′(0) −θ′(0) −ϕ′(0) −θ′(0) −ϕ′(0) −θ′(0) −ϕ′(0)
0.3 1.04746 −0.44891 1.29932 −0.55685 1.52625 −0.65416 1.72719 −0.744224
0.6 0.97822 −0.838474 1.18042 −1.01179 1.35314 −1.15983 1.4979 −1.28392
0.9 0.914269 −1.17549 1.07387 −1.08369 1.20209 −1.54554 1.30267 −1.67486
1.2 0.855295 −1.46622 0.978737 −1.67784 1.07114 −1.83624 1.13802 −1.9509
1.5 0.80098 −1.71639 0.894035 −1.91579 0.958127 −2.05313 1.00002 −2.14289
1.8 0.751003 −1.93115 0.818763 −2.10539 0.860844 −2.2136 0.88466 −2.27486
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