On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains
Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=$ 0^{+} $, is subject to...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kamran, M. [verfasserIn] Imran, M. [verfasserIn] Athar, M. [verfasserIn] Imran, M. A. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Meccanica - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966, 47(2011), 3 vom: 25. Aug., Seite 573-584 |
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| Übergeordnetes Werk: |
volume:47 ; year:2011 ; number:3 ; day:25 ; month:08 ; pages:573-584 |
| Links: |
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| DOI / URN: |
10.1007/s11012-011-9467-4 |
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| Katalog-ID: |
SPR015688364 |
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| 100 | 1 | |a Kamran, M. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains |
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| 520 | |a Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=$ 0^{+} $, is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The most important things regarding this paper to mention are that (1) we extracted the expressions for the velocity field and the shear stress corresponding to the motion of a fractional second grade fluid as limiting cases of general solutions corresponding to the fractional Oldroyd-B fluid, this is not previously done in the literature to the best of our knowledge, and (2) the expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from convolution product and the integral of the product of the generalized G functions, in contrast with (Imran and Zamra in Commun. Nonlinear Sci. Numer. Simul. 16:226–238, 2011) in which the expression for the velocity field involving the convolution product as well as the integral of the product of the generalized G functions. | ||
| 650 | 4 | |a Fractional Oldroyd-B fluid |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Velocity field |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Shear stress |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Fractional calculus |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Integral transforms |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Imran, M. |e verfasserin |4 aut | |
| 700 | 1 | |a Athar, M. |e verfasserin |4 aut | |
| 700 | 1 | |a Imran, M. A. |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Meccanica |d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 |g 47(2011), 3 vom: 25. Aug., Seite 573-584 |w (DE-627)311009638 |w (DE-600)2004031-3 |x 1572-9648 |7 nnns |
| 773 | 1 | 8 | |g volume:47 |g year:2011 |g number:3 |g day:25 |g month:08 |g pages:573-584 |
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10.1007/s11012-011-9467-4 doi (DE-627)SPR015688364 (SPR)s11012-011-9467-4-e DE-627 ger DE-627 rakwb eng 600 ASE 33.11 bkl 50.30 bkl 50.31 bkl Kamran, M. verfasserin aut On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=$ 0^{+} $, is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The most important things regarding this paper to mention are that (1) we extracted the expressions for the velocity field and the shear stress corresponding to the motion of a fractional second grade fluid as limiting cases of general solutions corresponding to the fractional Oldroyd-B fluid, this is not previously done in the literature to the best of our knowledge, and (2) the expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from convolution product and the integral of the product of the generalized G functions, in contrast with (Imran and Zamra in Commun. Nonlinear Sci. Numer. Simul. 16:226–238, 2011) in which the expression for the velocity field involving the convolution product as well as the integral of the product of the generalized G functions. Fractional Oldroyd-B fluid (dpeaa)DE-He213 Velocity field (dpeaa)DE-He213 Shear stress (dpeaa)DE-He213 Fractional calculus (dpeaa)DE-He213 Integral transforms (dpeaa)DE-He213 Imran, M. verfasserin aut Athar, M. verfasserin aut Imran, M. A. verfasserin aut Enthalten in Meccanica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 47(2011), 3 vom: 25. Aug., Seite 573-584 (DE-627)311009638 (DE-600)2004031-3 1572-9648 nnns volume:47 year:2011 number:3 day:25 month:08 pages:573-584 https://dx.doi.org/10.1007/s11012-011-9467-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.11 ASE 50.30 ASE 50.31 ASE AR 47 2011 3 25 08 573-584 |
| spelling |
10.1007/s11012-011-9467-4 doi (DE-627)SPR015688364 (SPR)s11012-011-9467-4-e DE-627 ger DE-627 rakwb eng 600 ASE 33.11 bkl 50.30 bkl 50.31 bkl Kamran, M. verfasserin aut On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=$ 0^{+} $, is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The most important things regarding this paper to mention are that (1) we extracted the expressions for the velocity field and the shear stress corresponding to the motion of a fractional second grade fluid as limiting cases of general solutions corresponding to the fractional Oldroyd-B fluid, this is not previously done in the literature to the best of our knowledge, and (2) the expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from convolution product and the integral of the product of the generalized G functions, in contrast with (Imran and Zamra in Commun. Nonlinear Sci. Numer. Simul. 16:226–238, 2011) in which the expression for the velocity field involving the convolution product as well as the integral of the product of the generalized G functions. Fractional Oldroyd-B fluid (dpeaa)DE-He213 Velocity field (dpeaa)DE-He213 Shear stress (dpeaa)DE-He213 Fractional calculus (dpeaa)DE-He213 Integral transforms (dpeaa)DE-He213 Imran, M. verfasserin aut Athar, M. verfasserin aut Imran, M. A. verfasserin aut Enthalten in Meccanica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 47(2011), 3 vom: 25. Aug., Seite 573-584 (DE-627)311009638 (DE-600)2004031-3 1572-9648 nnns volume:47 year:2011 number:3 day:25 month:08 pages:573-584 https://dx.doi.org/10.1007/s11012-011-9467-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.11 ASE 50.30 ASE 50.31 ASE AR 47 2011 3 25 08 573-584 |
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10.1007/s11012-011-9467-4 doi (DE-627)SPR015688364 (SPR)s11012-011-9467-4-e DE-627 ger DE-627 rakwb eng 600 ASE 33.11 bkl 50.30 bkl 50.31 bkl Kamran, M. verfasserin aut On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=$ 0^{+} $, is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The most important things regarding this paper to mention are that (1) we extracted the expressions for the velocity field and the shear stress corresponding to the motion of a fractional second grade fluid as limiting cases of general solutions corresponding to the fractional Oldroyd-B fluid, this is not previously done in the literature to the best of our knowledge, and (2) the expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from convolution product and the integral of the product of the generalized G functions, in contrast with (Imran and Zamra in Commun. Nonlinear Sci. Numer. Simul. 16:226–238, 2011) in which the expression for the velocity field involving the convolution product as well as the integral of the product of the generalized G functions. Fractional Oldroyd-B fluid (dpeaa)DE-He213 Velocity field (dpeaa)DE-He213 Shear stress (dpeaa)DE-He213 Fractional calculus (dpeaa)DE-He213 Integral transforms (dpeaa)DE-He213 Imran, M. verfasserin aut Athar, M. verfasserin aut Imran, M. A. verfasserin aut Enthalten in Meccanica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 47(2011), 3 vom: 25. Aug., Seite 573-584 (DE-627)311009638 (DE-600)2004031-3 1572-9648 nnns volume:47 year:2011 number:3 day:25 month:08 pages:573-584 https://dx.doi.org/10.1007/s11012-011-9467-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.11 ASE 50.30 ASE 50.31 ASE AR 47 2011 3 25 08 573-584 |
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10.1007/s11012-011-9467-4 doi (DE-627)SPR015688364 (SPR)s11012-011-9467-4-e DE-627 ger DE-627 rakwb eng 600 ASE 33.11 bkl 50.30 bkl 50.31 bkl Kamran, M. verfasserin aut On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=$ 0^{+} $, is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The most important things regarding this paper to mention are that (1) we extracted the expressions for the velocity field and the shear stress corresponding to the motion of a fractional second grade fluid as limiting cases of general solutions corresponding to the fractional Oldroyd-B fluid, this is not previously done in the literature to the best of our knowledge, and (2) the expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from convolution product and the integral of the product of the generalized G functions, in contrast with (Imran and Zamra in Commun. Nonlinear Sci. Numer. Simul. 16:226–238, 2011) in which the expression for the velocity field involving the convolution product as well as the integral of the product of the generalized G functions. Fractional Oldroyd-B fluid (dpeaa)DE-He213 Velocity field (dpeaa)DE-He213 Shear stress (dpeaa)DE-He213 Fractional calculus (dpeaa)DE-He213 Integral transforms (dpeaa)DE-He213 Imran, M. verfasserin aut Athar, M. verfasserin aut Imran, M. A. verfasserin aut Enthalten in Meccanica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 47(2011), 3 vom: 25. Aug., Seite 573-584 (DE-627)311009638 (DE-600)2004031-3 1572-9648 nnns volume:47 year:2011 number:3 day:25 month:08 pages:573-584 https://dx.doi.org/10.1007/s11012-011-9467-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.11 ASE 50.30 ASE 50.31 ASE AR 47 2011 3 25 08 573-584 |
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10.1007/s11012-011-9467-4 doi (DE-627)SPR015688364 (SPR)s11012-011-9467-4-e DE-627 ger DE-627 rakwb eng 600 ASE 33.11 bkl 50.30 bkl 50.31 bkl Kamran, M. verfasserin aut On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=$ 0^{+} $, is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The most important things regarding this paper to mention are that (1) we extracted the expressions for the velocity field and the shear stress corresponding to the motion of a fractional second grade fluid as limiting cases of general solutions corresponding to the fractional Oldroyd-B fluid, this is not previously done in the literature to the best of our knowledge, and (2) the expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from convolution product and the integral of the product of the generalized G functions, in contrast with (Imran and Zamra in Commun. Nonlinear Sci. Numer. Simul. 16:226–238, 2011) in which the expression for the velocity field involving the convolution product as well as the integral of the product of the generalized G functions. Fractional Oldroyd-B fluid (dpeaa)DE-He213 Velocity field (dpeaa)DE-He213 Shear stress (dpeaa)DE-He213 Fractional calculus (dpeaa)DE-He213 Integral transforms (dpeaa)DE-He213 Imran, M. verfasserin aut Athar, M. verfasserin aut Imran, M. A. verfasserin aut Enthalten in Meccanica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 47(2011), 3 vom: 25. Aug., Seite 573-584 (DE-627)311009638 (DE-600)2004031-3 1572-9648 nnns volume:47 year:2011 number:3 day:25 month:08 pages:573-584 https://dx.doi.org/10.1007/s11012-011-9467-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.11 ASE 50.30 ASE 50.31 ASE AR 47 2011 3 25 08 573-584 |
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Enthalten in Meccanica 47(2011), 3 vom: 25. Aug., Seite 573-584 volume:47 year:2011 number:3 day:25 month:08 pages:573-584 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR015688364</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220111022547.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201006s2011 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11012-011-9467-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR015688364</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s11012-011-9467-4-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">600</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">33.11</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">50.30</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">50.31</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kamran, M.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2011</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=$ 0^{+} $, is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The most important things regarding this paper to mention are that (1) we extracted the expressions for the velocity field and the shear stress corresponding to the motion of a fractional second grade fluid as limiting cases of general solutions corresponding to the fractional Oldroyd-B fluid, this is not previously done in the literature to the best of our knowledge, and (2) the expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from convolution product and the integral of the product of the generalized G functions, in contrast with (Imran and Zamra in Commun. Nonlinear Sci. Numer. Simul. 16:226–238, 2011) in which the expression for the velocity field involving the convolution product as well as the integral of the product of the generalized G functions.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fractional Oldroyd-B fluid</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Velocity field</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Shear stress</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fractional calculus</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integral transforms</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Imran, M.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Athar, M.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Imran, M. 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Kamran, M. |
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Kamran, M. ddc 600 bkl 33.11 bkl 50.30 bkl 50.31 misc Fractional Oldroyd-B fluid misc Velocity field misc Shear stress misc Fractional calculus misc Integral transforms On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains |
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600 ASE 33.11 bkl 50.30 bkl 50.31 bkl On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains Fractional Oldroyd-B fluid (dpeaa)DE-He213 Velocity field (dpeaa)DE-He213 Shear stress (dpeaa)DE-He213 Fractional calculus (dpeaa)DE-He213 Integral transforms (dpeaa)DE-He213 |
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on the unsteady rotational flow of fractional oldroyd-b fluid in cylindrical domains |
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On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains |
| abstract |
Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=$ 0^{+} $, is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The most important things regarding this paper to mention are that (1) we extracted the expressions for the velocity field and the shear stress corresponding to the motion of a fractional second grade fluid as limiting cases of general solutions corresponding to the fractional Oldroyd-B fluid, this is not previously done in the literature to the best of our knowledge, and (2) the expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from convolution product and the integral of the product of the generalized G functions, in contrast with (Imran and Zamra in Commun. Nonlinear Sci. Numer. Simul. 16:226–238, 2011) in which the expression for the velocity field involving the convolution product as well as the integral of the product of the generalized G functions. |
| abstractGer |
Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=$ 0^{+} $, is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The most important things regarding this paper to mention are that (1) we extracted the expressions for the velocity field and the shear stress corresponding to the motion of a fractional second grade fluid as limiting cases of general solutions corresponding to the fractional Oldroyd-B fluid, this is not previously done in the literature to the best of our knowledge, and (2) the expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from convolution product and the integral of the product of the generalized G functions, in contrast with (Imran and Zamra in Commun. Nonlinear Sci. Numer. Simul. 16:226–238, 2011) in which the expression for the velocity field involving the convolution product as well as the integral of the product of the generalized G functions. |
| abstract_unstemmed |
Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=$ 0^{+} $, is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The most important things regarding this paper to mention are that (1) we extracted the expressions for the velocity field and the shear stress corresponding to the motion of a fractional second grade fluid as limiting cases of general solutions corresponding to the fractional Oldroyd-B fluid, this is not previously done in the literature to the best of our knowledge, and (2) the expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from convolution product and the integral of the product of the generalized G functions, in contrast with (Imran and Zamra in Commun. Nonlinear Sci. Numer. Simul. 16:226–238, 2011) in which the expression for the velocity field involving the convolution product as well as the integral of the product of the generalized G functions. |
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| title_short |
On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains |
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https://dx.doi.org/10.1007/s11012-011-9467-4 |
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| author2 |
Imran, M. Athar, M. Imran, M. A. |
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10.1007/s11012-011-9467-4 |
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2024-07-03T17:57:59.258Z |
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| score |
7.4006987 |