| Literature DB >> 25906319 |
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Abstract
Year: 2015 PMID: 25906319 PMCID: PMC4408140 DOI: 10.1371/journal.pone.0125328
Source DB: PubMed Journal: PLoS One ISSN: 1932-6203 Impact factor: 3.240
Fig 5Velocity profiles for various values of M = 1,3,6,0 keeping R = 1 and γ = 1 fixed.
The effect of permeability constant M on the Normal velocity profiles is shown in (a) while the effect on the longitudinal velocity profiles is shown in (b).
HPM solutions along with absolute residuals for various R when γ = 1 and M = 3.
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| Solution | Residual | Solution | Residual | Solution | Residual | |
| 0.0 | 0. | 0. | 0. | 0. | 0. | 0. |
| 0.1 | 0.0779056 | 7.94082×10-7 | 0.0758376 | 1.07178×10-9 | 0.0746634 | 2025321×10-9 |
| 0.2 | 0.157102 | 1.2091×10-6 | 0.153132 | 1.88369×10-9 | 0.150878 | 2.65694×10-9 |
| 0.3 | 0.23889 | 9.05355×10-7 | 0.23334 | 2.10531×10-9 | 0.230192 | 9.23882×10-10 |
| 0.4 | 0.32459 | 3.44432×10-7 | 0.317923 | 1.41494×10-9 | 0.314146 | 1.56557×10-9 |
| 0.5 | 0.415552 | 2.53517×10-6 | 0.408346 | 2.23822×10-10 | 0.404268 | 3.09459×10-9 |
| 0.6 | 0.513164 | 5.28935×10-6 | 0.50608 | 2.26552×10-9 | 0.502076 | 2.99595×10-9 |
| 0.7 | 0.618869 | 7.77624×10-6 | 0.612606 | 3.67602×10-9 | 0.609071 | 1.86451×10-9 |
| 0.8 | 0.734172 | 8.81226×10-6 | 0.729421 | 3.68216×10-9 | 0.726742 | 7.09482×10-10 |
| 0.9 | 0.860657 | 7.25419×10-6 | 0.858038 | 2.57384×10-9 | 0.856564 | 1.02005×10-10 |
| 1.0 | 1. | 2.67891×10-6 | 1. | 1.04787×10-9 | 1. | 8.59397×10-21 |
HPM solutions along with absolute residuals for various γ when M = 1 and R = 0.3.
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| Solution | Residual | Solution | Residual | Solution | Residual | |
| 0.0 | 0. | 0. | 0. | 0. | 0. | 0. |
| 0.1 | -0.00104157 | 4.04403×10-8 | 0.0551344 | 3.82927×10-12 | 0.0754476 | 1.49494×10-12 |
| 0.2 | 0.00408732 | 6.45840×10-8 | 0.11299 | 7.82407×10-12 | 0.152381 | 2.63267×10-12 |
| 0.3 | 0.0215448 | 6.60535×10-8 | 0.176287 | 1.09622×10-11 | 0.232285 | 2.95503×10-12 |
| 0.4 | 0.0574657 | 5.05202×10-8 | 0.247744 | 1.10414×10-11 | 0.316647 | 2.01172×10-12 |
| 0.5 | 0.117953 | 2.95181×10-8 | 0.330078 | 6.50968×10-12 | 0.406955 | 2.54463×10-13 |
| 0.6 | 0.209071 | 1.22993×10-8 | 0.426004 | 1.10312×10-12 | 0.5047 | 3.09242×10-12 |
| 0.7 | 0.336849 | 2.02592×10-9 | 0.538238 | 7.30838×10-12 | 0.611375 | 5.06706×10-12 |
| 0.8 | 0.507281 | 2.84278×10-9 | 0.669498 | 8.72680×10-12 | 0.728478 | 5.09570×10-12 |
| 0.9 | 0.726341 | 6.33995×10-9 | 0.822506 | 6.65201×10-12 | 0.857515 | 3.56648×10-12 |
| 1.0 | 1. | 1.38222×10-8 | 1. | 3.95861×10-12 | 1. | 1.43396×10-12 |
RK4 solutions along with absolute residuals for various R when γ = 1 and M = 3.
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| Solution | Residual | Solution | Residual | Solution | Residual | |
| 0.0 | 0. | 9.50912×10-5 | 0. | 6.14718×10-5 | 0. | 3.53857×10-5 |
| 0.1 | 0.0779056 | 5.47777×10-6 | 0.0758376 | 3.44574×10-6 | 0.0746634 | 1.76807×10-6 |
| 0.2 | 0.157102 | 1.35127×10-6 | 0.153132 | 8.4865×10-7 | 0.150878 | 4032163×10-7 |
| 0.3 | 0.23889 | 3.7631×10-7 | 0.23334 | 2.35587×10-7 | 0.230192 | 1.18306×10-7 |
| 0.4 | 0.32459 | 1.08892×10-7 | 0.317923 | 6.83416×10-8 | 0.314146 | 3.48009×10-8 |
| 0.5 | 0.415551 | 9.31167×10-9 | 0.408346 | 4.7683×10-9 | 0.404268 | 1.37043×10-10 |
| 0.6 | 0.513164 | 1.37754×10-7 | 0.50608 | 8.29938×10-8 | 0.502076 | 3.42575×10-8 |
| 0.7 | 0.618869 | 4.58691×10-7 | 0.612606 | 2.76956×10-7 | 0.609071 | 1.16329×10-7 |
| 0.8 | 0.734172 | 1.67895×10-6 | 0.729421 | 10.1238×10-6 | 0.726742 | 4.23736×10-7 |
| 0.9 | 0.860657 | 6.88124×10-6 | 0.858038 | 4.14347×10-6 | 0.856564 | 1.727×10-6 |
| 1.0 | 1. | 1.43274×10-4 | 1. | 8.5963×10-5 | 1. | 3.5341×10-5 |