<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this article, the lubrication of a long porous slider in which the fluid is injected into the porous bottom is considered. The similarity transformations reduce the governing problem of Navier-Stokes equations to coupled nonlinear ordinary differential equations which are solved by HAM. Solutions are obtained for much larger values of Reynolds number compared to analytical and numerical methods. The results comprise good agreement between approximate and numerical solutions. HAM gives rapid convergent series solutions which show that this method is efficient, accurate and has advantages over other methods. Further, homotopy-pade’ technique is used to accelerate the convergence of series solution.</p></abstract>

In this article, the lubrication of a long porous slider in which the fluid is injected into the porous bottom is considered. The similarity transformations reduce the governing problem of Navier-Stokes equations to coupled nonlinear ordinary differential equations which are solved by HAM. Solutions are obtained for much larger values of Reynolds number compared to analytical and numerical methods. The results comprise good agreement between approximate and numerical solutions. HAM gives rapid convergent series solutions which show that this method is efficient, accurate and has advantages over other methods. Further, homotopy-pade’ technique is used to accelerate the convergence of series solution.

Homotopy analysis method for the solution of lubrication of a long porous slider

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Homotopy analysis method for the solution of lubrication of a long porous slider"}

In this article, the lubrication of a long porous slider in which the fluid is injected into the porous bottom is considered. The similarity transformations...

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

		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	----	—

[m, m]	h ‴(0)	f ′(0)	g ′(0)
[5,5]	-38.1021	-3.46043	-2.40875
[10,10]	-38.1024	-3.46051	-2.40862
[15,15]	-38.1024	-3.46051	-2.40862
[20,20]	-38.1024	-3.46051	-2.40862

Homotopy analysis method for the solution of lubrication of a long porous slider

Published Online: Nov 01, 2016

Page range: 507 - 516

Received: Jun 05, 2016

Accepted: Nov 01, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00040

Keywords
Porous slider, Reynolds number, HAM, Homotopy-Pade’ approximations

© 2016 Vishwanath B.Awati, Manjunath Jyoti, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Convergence of HAM solutions for different order of approximations for R = 10 when ħh = ħf = ħg = −1.

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.

The [m,m] homotopy-Pade approximations of h‴(0), f′(0) and g′(0) when R = 10.

Homotopy analysis method for the solution of lubrication of a long porous slider

Published Online: Nov 01, 2016

Page range: 507 - 516

Received: Jun 05, 2016

Accepted: Nov 01, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00040

KeywordsPorous slider, Reynolds number, HAM, Homotopy-Pade’ approximations

© 2016 Vishwanath B.Awati, Manjunath Jyoti, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Convergence of HAM solutions for different order of approximations for R = 10 when ħh = ħf = ħg = −1.

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.

The [m,m] homotopy-Pade approximations of h‴(0), f′(0) and g′(0) when R = 10.

Keywords
Porous slider, Reynolds number, HAM, Homotopy-Pade’ approximations