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On the Method of Inverse Mapping for Solutions of Coupled Systems of Nonlinear Differential Equations Arising in Nanofluid Flow, Heat and Mass Transfer

Mangalagama Dewasurendra
Mangalagama Dewasurendra
 e 
Kuppalapalle Vajravelu
Kuppalapalle Vajravelu
   | 03 ott 2018
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Pubblicato online: 03 ott 2018
Pagine: 1 - 14
Ricevuto: 12 nov 2017
Accettato: 05 feb 2018
DOI: https://doi.org/10.21042/AMNS.2018.1.00001
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© 2018 Mangalagama Dewasurendra and Kuppalapalle Vajravelu, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Flow configuration.
Flow configuration.

Fig. 2

Plot of E(c0,δ), the squared residual error over η ∈ [0,499] as a function of c0 and δ using parameter values Le = 2, Nb = 2,Pr = 1, Nt = 1, n = 0.5, A = 0.1314. The error function has minimum E(c0,δ,A) = 9.71 × 10–5 where c0 = –0.6195 and δ = 0.8462963.
Plot of E(c0,δ), the squared residual error over η ∈ [0,499] as a function of c0 and δ using parameter values Le = 2, Nb = 2,Pr = 1, Nt = 1, n = 0.5, A = 0.1314. The error function has minimum E(c0,δ,A) = 9.71 × 10–5 where c0 = –0.6195 and δ = 0.8462963.

Fig. 3

Plot of E(c0,δ), the squared residual error over η ∈ [0,499] as a function of c0 and δ using parameter values Le = 3, Nb = 1,Pr = 5, Nt = 0, n = 1, A = 7.8902. The error function has minimum E(c0,δ,A) = 9.41 × 10–5 where c0 = –9.30195 and δ = 1.03944.
Plot of E(c0,δ), the squared residual error over η ∈ [0,499] as a function of c0 and δ using parameter values Le = 3, Nb = 1,Pr = 5, Nt = 0, n = 1, A = 7.8902. The error function has minimum E(c0,δ,A) = 9.41 × 10–5 where c0 = –9.30195 and δ = 1.03944.

Fig. 4

Plot of E(c0,δ), the squared residual error over η ∈ [0,499] as a function of c0 and δ using parameter values Le = 2, Nb = 2,Pr = 7, Nt = 0.5, n = 0.8, A = 0.24764. The error function has minimum E(c0,δ,A) = 8.28 × 10–5 where c0 = –0.690605 and δ = 0.8462963.
Plot of E(c0,δ), the squared residual error over η ∈ [0,499] as a function of c0 and δ using parameter values Le = 2, Nb = 2,Pr = 7, Nt = 0.5, n = 0.8, A = 0.24764. The error function has minimum E(c0,δ,A) = 8.28 × 10–5 where c0 = –0.690605 and δ = 0.8462963.

Fig. 5

Plot of f̂(η), where Curve 1 has Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, Curve 2 has Le = 3, Nb = 1, Pr = 5, Nt = 0, n = 1, and Curve 3 has Le = 2, Nb = 2, Pr = 7, Nt = 0.5, n = 0.8 using their respective error-minimizing convergence control parameter.
Plot of f̂(η), where Curve 1 has Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, Curve 2 has Le = 3, Nb = 1, Pr = 5, Nt = 0, n = 1, and Curve 3 has Le = 2, Nb = 2, Pr = 7, Nt = 0.5, n = 0.8 using their respective error-minimizing convergence control parameter.

Fig. 6

Plot of f̂′(η), where Curve 1 has Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, Curve 2 has Le = 3, Nb = 1, Pr = 5, Nt = 0, n = 1, and Curve 3 has Le = 2, Nb = 2, Pr = 7, Nt = 0.5, n = 0.8 using their respective error-minimizing convergence control parameter.
Plot of f̂′(η), where Curve 1 has Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, Curve 2 has Le = 3, Nb = 1, Pr = 5, Nt = 0, n = 1, and Curve 3 has Le = 2, Nb = 2, Pr = 7, Nt = 0.5, n = 0.8 using their respective error-minimizing convergence control parameter.

Fig. 7

Plot of θ̂(η), where Curve 1 has Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, Curve 2 has Le = 3, Nb = 1, Pr = 5, Nt = 0, n = 1, and Curve 3 has Le = 2, Nb = 2, Pr = 7, Nt = 0.5, n = 0.8 using their respective error-minimizing convergence control parameter.
Plot of θ̂(η), where Curve 1 has Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, Curve 2 has Le = 3, Nb = 1, Pr = 5, Nt = 0, n = 1, and Curve 3 has Le = 2, Nb = 2, Pr = 7, Nt = 0.5, n = 0.8 using their respective error-minimizing convergence control parameter.

Fig. 8

Plot of ϕ̂(η), where Curve 1 has Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, Curve 2 has Le = 3, Nb = 1, Pr = 5, Nt = 0, n = 1, and Curve 3 has Le = 2, Nb = 2, Pr = 7, Nt = 0.5, n = 0.8 using their respective error-minimizing convergence control parameter.
Plot of ϕ̂(η), where Curve 1 has Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, Curve 2 has Le = 3, Nb = 1, Pr = 5, Nt = 0, n = 1, and Curve 3 has Le = 2, Nb = 2, Pr = 7, Nt = 0.5, n = 0.8 using their respective error-minimizing convergence control parameter.

Fig. 9

Comparison of f(η), θ(η) and ϕ(η) obtained by the MDDiM 3-term approximation and shooting method solutions with Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, where Curve 1 is shooting method results of f(η), Curve 2 is MDDiM results of f(η), Curve 3 is shooting method results of θ(η), Curve 4 is MDDiM results of θ(η), Curve 5 is shooting method results of ϕ(η), Curve 6 is MDDiM results of ϕ(η).
Comparison of f(η), θ(η) and ϕ(η) obtained by the MDDiM 3-term approximation and shooting method solutions with Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, where Curve 1 is shooting method results of f(η), Curve 2 is MDDiM results of f(η), Curve 3 is shooting method results of θ(η), Curve 4 is MDDiM results of θ(η), Curve 5 is shooting method results of ϕ(η), Curve 6 is MDDiM results of ϕ(η).

Fig. 10

Plot of Residual Error function verses Terms of approximation, where Curve 1 has Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, Curve 2 has Le = 3, Nb = 1, Pr = 5, Nt = 0, n = 1, and Curve 3 has Le = 2, Nb = 2, Pr = 7, Nt = 0.5, n = 0.8 using their respective error-minimizing convergence control parameter.
Plot of Residual Error function verses Terms of approximation, where Curve 1 has Le = 2, Nb = 2, Pr = 1, Nt = 1, n = 0.5, Curve 2 has Le = 3, Nb = 1, Pr = 5, Nt = 0, n = 1, and Curve 3 has Le = 2, Nb = 2, Pr = 7, Nt = 0.5, n = 0.8 using their respective error-minimizing convergence control parameter.

Fig. 11

Plot of |–f̂″(0)| versus n, using Le = 3, Nb = 1, Pr = 5 and Nt = 0.
Plot of |–f̂″(0)| versus n, using Le = 3, Nb = 1, Pr = 5 and Nt = 0.

Fig. 12

Plot of |–θ̂′(0)|, where Curve 1 is |–θ̂′(0)| versus Nt using Le = 3, Nb = 1, Pr = 5, n = 1, Curve 2 is |–θ̂′(0)| versus Nb using Le = 3, Pr = 5, Nt = 0, n = 1.
Plot of |–θ̂′(0)|, where Curve 1 is |–θ̂′(0)| versus Nt using Le = 3, Nb = 1, Pr = 5, n = 1, Curve 2 is |–θ̂′(0)| versus Nb using Le = 3, Pr = 5, Nt = 0, n = 1.

Fig. 13

Plot of |–ϕ̂′(0)|, where Curve 1 is |–ϕ̂′(0)| versus Nt using Le = 2, Nb = 2, Pr = 1, n = 0.5, Curve 2 is |–ϕ̂′(0)| versus Nb using Le = 2, Pr = 1, Nt = 1, n = 0.5.
Plot of |–ϕ̂′(0)|, where Curve 1 is |–ϕ̂′(0)| versus Nt using Le = 2, Nb = 2, Pr = 1, n = 0.5, Curve 2 is |–ϕ̂′(0)| versus Nb using Le = 2, Pr = 1, Nt = 1, n = 0.5.

Minimum of the squared residual error E(A,c0,δ) for three different sets of parameters.

LeNbPrNtnAc0δE(c0,δ,A)
22110.50.1314–0.61950.6739.71 × 10–5
315017.8902–9.30201.03949.71 × 10–5
2270.50.80.2476–0.69060.84638.28 × 10–5
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