Open Access

Effects of second-order slip and drag reduction in boundary layer flows

Kuppalapalle Vajravelu
Kuppalapalle Vajravelu
, 
Ronald Li
Ronald Li
, 
Mangalagama Dewasurendra
Mangalagama Dewasurendra
, 
Joseph Benarroch
Joseph Benarroch
, 
Nicholas Ossi
Nicholas Ossi
, 
Ying Zhang
Ying Zhang
, 
Michael Sammarco
Michael Sammarco
 and 
K.V. Prasad
K.V. Prasad
   | Oct 03, 2018
Applied Mathematics and Nonlinear Sciences's Cover Image
About this article
Previous Article
Next Article
Cite
Published Online: Oct 03, 2018
Page range: 291 - 302
Received: Mar 24, 2018
Accepted: Jun 17, 2018
DOI: https://doi.org/10.21042/AMNS.2018.1.00022
Keywords
© 2018 Kuppalapalle Vajravelu et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Physical model with coordinate system. δ1 represents the thickness of the boundary layer
Physical model with coordinate system. δ1 represents the thickness of the boundary layer

Fig. 2

Average square residual error versus order of approximation for: (I) Mn = 15, C = 0.001, λ1 = 0.3, γ = 1.0, and δ = –2.0, (II) Mn = 20, C = 0.01, λ1 = 0.2, γ = 0.5, and δ = –0.5, (III) Mn = 10, C = 0.1, λ1 = 0.1, γ = 0.1, and δ = –1.0.
Average square residual error versus order of approximation for: (I) Mn = 15, C = 0.001, λ1 = 0.3, γ = 1.0, and δ = –2.0, (II) Mn = 20, C = 0.01, λ1 = 0.2, γ = 0.5, and δ = –0.5, (III) Mn = 10, C = 0.1, λ1 = 0.1, γ = 0.1, and δ = –1.0.

Fig. 3

Similarity profile f(η) for various values of Mn and C. The direction of the arrows represents increasing Mn.
Similarity profile f(η) for various values of Mn and C. The direction of the arrows represents increasing Mn.

Fig. 4

Dimensionless velocity profile f′(η) and shear stress profile f″(η) for various values of Mn and γ.
Dimensionless velocity profile f′(η) and shear stress profile f″(η) for various values of Mn and γ.

Fig. 5

Dimensionless velocity profile f′(η) and shear stress profile f″(η) for various values of Mn and λ1.
Dimensionless velocity profile f′(η) and shear stress profile f″(η) for various values of Mn and λ1.

Fig. 6

Dimensionless velocity profile f′(η) and shear stress profile f″(η) for various values of δ and C.
Dimensionless velocity profile f′(η) and shear stress profile f″(η) for various values of δ and C.

Fig. 7

Dimensionless velocity profile f′(η) and shear stress profile f″(η) for various values of λ1 and C.
Dimensionless velocity profile f′(η) and shear stress profile f″(η) for various values of λ1 and C.

Fig. 8

Dimensionless skin friction coefficient –f″(0) versus λ1 for different values of Mn.
Dimensionless skin friction coefficient –f″(0) versus λ1 for different values of Mn.

Fig. 9

Dimensionless skin friction coefficient –f″(0) versus γ for different values of C.
Dimensionless skin friction coefficient –f″(0) versus γ for different values of C.

Fig. 10

Dimensionless skin friction coefficient –f″(0) versus δ for different values of C.
Dimensionless skin friction coefficient –f″(0) versus δ for different values of C.

Values of dimensionless skin friction coefficient – f ″(0) for different values of Mn, C, λ1, γ, and δ.

λ1γδMnC– f ″(0)– ℏE10
0.10.1–1.0100.00.38313670210.292981.5 × 10–9
0.10.39019234560.300551.5 × 10–9
0.20.39870056770.324511.3 × 10–8
200.00.25710082330.176783.4 × 10–7
0.10.26022391640.178303.1 × 10–7
0.20.26339718930.179822.9 × 10–7
0.10.1–2.0100.00.18470043070.293752.9 × 10–10
0.10.18808763450.300282.8 × 10–10
0.20.19156767740.326013.1 × 10–9
200.00.12671067470.180269.5 × 10–8
0.10.12819162970.181759.0 × 10–8
0.20.12969406880.183268.6 × 10–8
0.10.5-1.0100.00.33621989410.293181.1 × 10–9
0.10.34209690110.300251.1 × 10–9
0 20.34813567530.325291.0 × 10–8
200.00.23511516010.181264.2 × 10–7
0.10.23772475110.182724.0 × 10–7
0.20.24037060950.184203.9 × 10–7
0.20.1-1.0100.00.41803624930.293001.9 × 10–9
0 10.42639737380.300671.9 × 10–9
0.20.43503064540.324401.5 × 10–8
200.00.28048748620.176684.1 × 10–7
0.10.28389507900.178193.8 × 10–7
0.20.28735746040.179723.5 × 10–7

Comparison of skin friction coefficient for different values of C and λ1 in the absence of magnetic parameter Mn, first-order slip parameter γ, and second-order slip parameter δ.

Cλ1Vajravelu and Mohapatra [11]Present work
NumericalApproximateHAM- ℏE10
000.46980.40810.46941.076981.8 × 10–4
0–0.40.37510.33980.37511.068851.5 × 10–6
0–0.80.14900.14110.14901.045242.5 × 10–8
–0.200.61900.55460.61901.087152.2 × 10–5
–0.2–0.40.45780.41980.45781.072851.7 × 10–7
–0.2–0.80.17570.16570.17561.049662.7 × 10–9
eISSN:
2444-8656
Language:
English
Publication timeframe:
2 times per year
Journal Subjects:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics
Journal RSS Feed