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Fig. 1
(a) Moving long porous slider; (b) Coordinate system.
Fig. 2
ħ curves for the series h‴(0), f′(0) and g′(0) for R = 1.
Fig. 3
Variations of h by increasing Reynolds number R.
Fig. 4
Variations of f by increasing Reynolds number R.
Fig. 5
Variations of g by increasing Reynolds number R.
Fig. 6
Normalized lift and drag as a function of Reynolds number.
Convergence of HAM solutions for different order of approximations for R = 10 when ħh = ħf = ħg = −1.
order of approximation
h ‴(0)
f ′(0)
g ′(0)
5
-37.8737
-3.51618
-2.37722
10
-38.1065
-3.45718
-2.41558
15
-38.1026
-3.46067
-2.41123
20
-38.1024
-3.4605
-2.40905
25
-38.1024
-3.46051
-2.40864
30
-38.1024
-3.46051
-2.40861
35
-38.1024
-3.46051
-2.40862
40
-38.1024
-3.46051
-2.40862
Comparison of the Homotopy pade approximations (HPA) [40, 40] solution with the numerical solution [2] and long series (LS) [16] for different values of the Reynolds number R.
h ‴(0)
f ′(0)
g ′(0)
R
HPA
Numerical
LS
HPA
Numerical
LS
HPA
Numerical
LS
0.2
-12.465
-12.465
-12.447
-1.088
-1.088
-1.085
-1.030
-1.030
-1.030
1
-14.365
-14.365
-14.196
-1.405
-1.405
-1.406
-1.153
-1.153
-1.165
5
-24.583
-24.584
-22.893
-2.527
-2.528
-2.991
-1.766
-1.766
-1.859
13.8
-48.480
-48.484
-48.068
-4.021
-4.022
-4.224
-2.806
----
-2.807
51.6
-149.67
-149.67
----
-7.553
-7.553
—
-5.302
-5.301
—
70
-197.96
----
----
-8.757
----
—
-6.144
----
—
100
-275.90
----
----
-10.40
----
—
-7.288
----
—
300
-788.43
----
----
-17.815
----
—
-12.516
----
—
500
-1291.1
----
----
-22.670
----
—
-15.368
----
—
1000
-2526.4
----
----
-30.432
----
—
-20.062
----
—
The [m,m] homotopy-Pade approximations of h‴(0), f′(0) and g′(0) when R = 10.