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2017 | OriginalPaper | Buchkapitel

4. Solution Techniques

verfasst von : Ahmer Mehmood

Erschienen in: Viscous Flows

Verlag: Springer International Publishing

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Abstract

In this chapter, some suitable solution techniques have been mentioned for the solution of boundary layer equations arising in this book.

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Literatur
1.
Zurück zum Zitat H. Blasius, Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z. Math. u Phys. 56, 1–37 (1908)MATH H. Blasius, Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z. Math. u Phys. 56, 1–37 (1908)MATH
2.
Zurück zum Zitat L. Prandtl, The mechanics of viscous fluids, ed. By W.F. Durand, in Aerodynamic Theory III (1935), pp. 34–208 L. Prandtl, The mechanics of viscous fluids, ed. By W.F. Durand, in Aerodynamic Theory III (1935), pp. 34–208
4.
Zurück zum Zitat S. Goldstein, Concerning some solutions of the boundary-layer equations in hydrodynamics. Proc. Cambr. Phil. Soc. 26, 1–30 (1930)CrossRefMATH S. Goldstein, Concerning some solutions of the boundary-layer equations in hydrodynamics. Proc. Cambr. Phil. Soc. 26, 1–30 (1930)CrossRefMATH
5.
Zurück zum Zitat L. Howarth, On the solution of the laminar boundary layer equations. Proc. Roy. Soc. London A 164, 547–579 (1938)CrossRefMATH L. Howarth, On the solution of the laminar boundary layer equations. Proc. Roy. Soc. London A 164, 547–579 (1938)CrossRefMATH
6.
Zurück zum Zitat R.A. Seban, R. Bond, Skin-friction and heat-transfer characteristics of a laminar boundary layer on a cylinder in axial incompressible flow. J. Aeronuat. Sci. 18, 671 (1951)CrossRefMATH R.A. Seban, R. Bond, Skin-friction and heat-transfer characteristics of a laminar boundary layer on a cylinder in axial incompressible flow. J. Aeronuat. Sci. 18, 671 (1951)CrossRefMATH
7.
Zurück zum Zitat S.N. Curle, Calculation of the axisymmetric boundary layer on a long thin cylinder. Proc R Soc Lond A Math. Phys. Sci. 372(1751), 555–564 (1980)CrossRefMATH S.N. Curle, Calculation of the axisymmetric boundary layer on a long thin cylinder. Proc R Soc Lond A Math. Phys. Sci. 372(1751), 555–564 (1980)CrossRefMATH
8.
Zurück zum Zitat C.Y. Wang, Fluid flow due to a stretching cylinder. Phys. Fluids 31, 466–468 (1988)CrossRef C.Y. Wang, Fluid flow due to a stretching cylinder. Phys. Fluids 31, 466–468 (1988)CrossRef
9.
Zurück zum Zitat S.J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, PhD Thesis, Shanghai Jiao Tong University, 1992 S.J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, PhD Thesis, Shanghai Jiao Tong University, 1992
10.
Zurück zum Zitat S.J. Liao, Beyond perturbation: introduction to the homotopy analysis method (Chapman & Hall/CRC, 2004) S.J. Liao, Beyond perturbation: introduction to the homotopy analysis method (Chapman & Hall/CRC, 2004)
11.
12.
Zurück zum Zitat S.J. Liao, I. Pop, Explicit analytic solution for similarity boundary layer equations. Int. J. Heat Mass Tranf. 47(1), 75–85 (2004)CrossRefMATH S.J. Liao, I. Pop, Explicit analytic solution for similarity boundary layer equations. Int. J. Heat Mass Tranf. 47(1), 75–85 (2004)CrossRefMATH
13.
Zurück zum Zitat C. Wang, J.M. Zhur, S.J. Liao, I. Pop, On the explicit analytic solutions of Cheng-Chang equations. Int. J. Heat Mass Transf. 46(10), 1855–1860 (2003)CrossRefMATH C. Wang, J.M. Zhur, S.J. Liao, I. Pop, On the explicit analytic solutions of Cheng-Chang equations. Int. J. Heat Mass Transf. 46(10), 1855–1860 (2003)CrossRefMATH
14.
Zurück zum Zitat F.M. Allan, M.I. Syam, On analytic solution of the non-homogeneous Blasius problem. J. Comp. Appl. Math. 182, 355–365 (2005)CrossRef F.M. Allan, M.I. Syam, On analytic solution of the non-homogeneous Blasius problem. J. Comp. Appl. Math. 182, 355–365 (2005)CrossRef
15.
Zurück zum Zitat S.J. Liao, A uniformly valid analytic solution of 2D viscous flow past a semi infinite flat plate. J. Fluid Mech. 385, 101–128 (1999)MathSciNetCrossRefMATH S.J. Liao, A uniformly valid analytic solution of 2D viscous flow past a semi infinite flat plate. J. Fluid Mech. 385, 101–128 (1999)MathSciNetCrossRefMATH
16.
Zurück zum Zitat S.J. Liao, A. Campo, Analytic solutions of the temperature distribution in Blasius viscous flow problem. J. Fluid Mech. 453, 411–425 (2002)MathSciNetCrossRefMATH S.J. Liao, A. Campo, Analytic solutions of the temperature distribution in Blasius viscous flow problem. J. Fluid Mech. 453, 411–425 (2002)MathSciNetCrossRefMATH
17.
Zurück zum Zitat S.J. Liao, On the analytic solution of magnetohydrodynamics flows of non-Newtonian fluids over a stretching sheet. J. Fluid Mech. 488, 189–212 (2003)MathSciNetCrossRefMATH S.J. Liao, On the analytic solution of magnetohydrodynamics flows of non-Newtonian fluids over a stretching sheet. J. Fluid Mech. 488, 189–212 (2003)MathSciNetCrossRefMATH
18.
Zurück zum Zitat A. Mehmood, A. Ali, Analytic homotopy solution of generalized three-dimensional channel flow due to uniform stretching of the plate. Acta. Mech. Sin. 23, 503–510 (2007)MathSciNetCrossRefMATH A. Mehmood, A. Ali, Analytic homotopy solution of generalized three-dimensional channel flow due to uniform stretching of the plate. Acta. Mech. Sin. 23, 503–510 (2007)MathSciNetCrossRefMATH
19.
Zurück zum Zitat A. Mehmood, A. Ali, Analytic solution of three-dimensional viscous flow and heat transfer over a stretching flat surface by homotopy analysis method. J. Heat. Transf.-Trans. ASME 130, 121701 (2008). (1–7)CrossRef A. Mehmood, A. Ali, Analytic solution of three-dimensional viscous flow and heat transfer over a stretching flat surface by homotopy analysis method. J. Heat. Transf.-Trans. ASME 130, 121701 (2008). (1–7)CrossRef
20.
Zurück zum Zitat A. Mehmood, A. Ali, An explicit analytic solution of steady three-dimensional stagnation point flow of second grade fluid towards a heated plate. J. Appl. Mech.-Trans. ASME 75, 061003 (2008). (1–8)CrossRef A. Mehmood, A. Ali, An explicit analytic solution of steady three-dimensional stagnation point flow of second grade fluid towards a heated plate. J. Appl. Mech.-Trans. ASME 75, 061003 (2008). (1–8)CrossRef
21.
Zurück zum Zitat M. Sajid, T. Hayat, The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet. Chaos Solutions Fractals 39, 1317–1323 (2009)CrossRefMATH M. Sajid, T. Hayat, The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet. Chaos Solutions Fractals 39, 1317–1323 (2009)CrossRefMATH
22.
Zurück zum Zitat T. Hayat, M. Khan, M. Ayub, On the explicit analytic solution on Oldroyd 6-constant fluid. Int. J. Eng. Sci. 42, 123–135 (2004)MathSciNetCrossRefMATH T. Hayat, M. Khan, M. Ayub, On the explicit analytic solution on Oldroyd 6-constant fluid. Int. J. Eng. Sci. 42, 123–135 (2004)MathSciNetCrossRefMATH
23.
Zurück zum Zitat T. Hayat, M. Khan, S. Asghar, Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid. Acta Mech. 168, 213–232 (2004)CrossRefMATH T. Hayat, M. Khan, S. Asghar, Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid. Acta Mech. 168, 213–232 (2004)CrossRefMATH
24.
Zurück zum Zitat S. Abbasbandy, The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phy. Lett. A 360, 109–113 (2006)MathSciNetCrossRefMATH S. Abbasbandy, The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phy. Lett. A 360, 109–113 (2006)MathSciNetCrossRefMATH
25.
Zurück zum Zitat Y. Liu, Z. Li, The homotopy analysis method for approximating the solution of the modified Korteweg-de Vries equation. Chaos Solution Fractals 39, 1–8 (2009)MathSciNetCrossRefMATH Y. Liu, Z. Li, The homotopy analysis method for approximating the solution of the modified Korteweg-de Vries equation. Chaos Solution Fractals 39, 1–8 (2009)MathSciNetCrossRefMATH
26.
Zurück zum Zitat T. Hayat, Z. Abbas, T. Javed, M. Sajid, Three-dimensional rotating flow induced by a shrinking sheet for suction. Chaos Solution Fractals 39, 1615–1626 (2009)CrossRefMATH T. Hayat, Z. Abbas, T. Javed, M. Sajid, Three-dimensional rotating flow induced by a shrinking sheet for suction. Chaos Solution Fractals 39, 1615–1626 (2009)CrossRefMATH
27.
Zurück zum Zitat S. Abbasbandy, F.S. Zakaria, Soliton solution for the fifth-order KdV equation with the homotopy analysis method. Nonlinear Dyns. 51(1), 83–87 (2008)MathSciNetMATH S. Abbasbandy, F.S. Zakaria, Soliton solution for the fifth-order KdV equation with the homotopy analysis method. Nonlinear Dyns. 51(1), 83–87 (2008)MathSciNetMATH
28.
Zurück zum Zitat J.H. He, An approximate solution technique depending upon an artificial parameter. Commun. Nonlinear Sci. Numer. Simmulat. 3, 92–97 (1998)CrossRefMATH J.H. He, An approximate solution technique depending upon an artificial parameter. Commun. Nonlinear Sci. Numer. Simmulat. 3, 92–97 (1998)CrossRefMATH
29.
Zurück zum Zitat J.H. He, Newton-like iteration method for solving algebraic equation. Commun. Nonlinear Sci. Numer. Simmulat. 3, 106–109 (1998)MathSciNetCrossRefMATH J.H. He, Newton-like iteration method for solving algebraic equation. Commun. Nonlinear Sci. Numer. Simmulat. 3, 106–109 (1998)MathSciNetCrossRefMATH
30.
Zurück zum Zitat E.I. Grigolyuk, V.I. Shalashilin, Problems of nonlinear deformation: the continuation method applied to nonlinear problems in solid mechanics (Kluwer Academic Publishers, Dordrecht, 1991)CrossRefMATH E.I. Grigolyuk, V.I. Shalashilin, Problems of nonlinear deformation: the continuation method applied to nonlinear problems in solid mechanics (Kluwer Academic Publishers, Dordrecht, 1991)CrossRefMATH
31.
Zurück zum Zitat J.C. Alexander, J.A. Yorke, A homotopy continuation method: numerically implementable topological procedures. Trans. Amer. Math. Soc. 242, 271–284 (1978)MathSciNetCrossRefMATH J.C. Alexander, J.A. Yorke, A homotopy continuation method: numerically implementable topological procedures. Trans. Amer. Math. Soc. 242, 271–284 (1978)MathSciNetCrossRefMATH
32.
33.
Zurück zum Zitat V. Marinca, N. Herisanu, L. Nemes, Optimal homotopy asymptotic method with application to thin film flow. Cent. Eur. J. Phys. 6(3), 648–653 (2008) V. Marinca, N. Herisanu, L. Nemes, Optimal homotopy asymptotic method with application to thin film flow. Cent. Eur. J. Phys. 6(3), 648–653 (2008)
34.
Zurück zum Zitat K. Yabushita, M. Yamashita, K. Tsuboi, An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method. J. Phys. A: Math. Theor. 40, 8403–8416 (2007)MathSciNetCrossRefMATH K. Yabushita, M. Yamashita, K. Tsuboi, An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method. J. Phys. A: Math. Theor. 40, 8403–8416 (2007)MathSciNetCrossRefMATH
35.
Zurück zum Zitat Z. Niu, C. Wang, A one-step optimal homotopy analysis method for non-linear differential equations. Commun. Nonlinear Sci. Numer. Simulat. 15, 2026–2036 (2010)CrossRefMATH Z. Niu, C. Wang, A one-step optimal homotopy analysis method for non-linear differential equations. Commun. Nonlinear Sci. Numer. Simulat. 15, 2026–2036 (2010)CrossRefMATH
36.
Zurück zum Zitat S.J. Liao, An optimal homotopy analysis approach for strongly nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simulat. 15, 2003–2016 (2010)MathSciNetCrossRefMATH S.J. Liao, An optimal homotopy analysis approach for strongly nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simulat. 15, 2003–2016 (2010)MathSciNetCrossRefMATH
37.
Zurück zum Zitat S. Munawar, A. Mehmood, A. Ali, Effects of slip on flow between two stretchable disks using optimal homotopy analysis method. Can. J. Appl. Sci. 1(2), 50–68 (2011) S. Munawar, A. Mehmood, A. Ali, Effects of slip on flow between two stretchable disks using optimal homotopy analysis method. Can. J. Appl. Sci. 1(2), 50–68 (2011)
38.
Zurück zum Zitat T.Y. Na, Computational methods in engineering boundary value problems (Academic Press, New York, 1979)MATH T.Y. Na, Computational methods in engineering boundary value problems (Academic Press, New York, 1979)MATH
39.
Zurück zum Zitat H.B. Keller, in A New Difference Scheme for Parabolic Problems. Numerical Solution of Partial Differential Equations, II, ed. By J. Bramble (Academic Press, New York, 1970) H.B. Keller, in A New Difference Scheme for Parabolic Problems. Numerical Solution of Partial Differential Equations, II, ed. By J. Bramble (Academic Press, New York, 1970)
40.
Zurück zum Zitat H.B. Keller, T. Cebeci, Accurate numerical methods for boundary-layer flows-I. Two-dimensional laminar flows. AIAA J. 10, 1193 (1971)CrossRefMATH H.B. Keller, T. Cebeci, Accurate numerical methods for boundary-layer flows-I. Two-dimensional laminar flows. AIAA J. 10, 1193 (1971)CrossRefMATH
41.
Zurück zum Zitat H.B. Keller, T. Cebeci, Accurate numerical methods for boundary-layer flows-II. Two-dimensional turbulent flows. AIAA J. 10, 1193 (1972)MathSciNetCrossRefMATH H.B. Keller, T. Cebeci, Accurate numerical methods for boundary-layer flows-II. Two-dimensional turbulent flows. AIAA J. 10, 1193 (1972)MathSciNetCrossRefMATH
42.
Zurück zum Zitat T. Cebeci, H.B. Keller, On the computation of unsteady boundary layers, Recent research on unsteady boundary layers (IUTAM Symp. 1971), vol. I, p. 1082, Les Presses de I’ Universitė Laval, Quebee, Canada T. Cebeci, H.B. Keller, On the computation of unsteady boundary layers, Recent research on unsteady boundary layers (IUTAM Symp. 1971), vol. I, p. 1082, Les Presses de I’ Universitė Laval, Quebee, Canada
43.
Zurück zum Zitat T. Cebeci, H.B. Keller, Laminar boundary layers with assigned wall shear, Lecture Notes in Physics (Proc. Int. Conf. Numer. Methods Fluid Dynam., 3rd), vol. 19 (Springer, Berlin and New York, 1973) T. Cebeci, H.B. Keller, Laminar boundary layers with assigned wall shear, Lecture Notes in Physics (Proc. Int. Conf. Numer. Methods Fluid Dynam., 3rd), vol. 19 (Springer, Berlin and New York, 1973)
44.
Zurück zum Zitat T. Cebeci, A.M.O. Smith, Analysis of turbulent boundary layers (Academic Press Inc., New York, 1974)MATH T. Cebeci, A.M.O. Smith, Analysis of turbulent boundary layers (Academic Press Inc., New York, 1974)MATH
45.
Zurück zum Zitat T. Cebeci, P. Bradshaw, Momentum transfer in boundary layers (Hemisphere Publishing Company, UK, 1977)MATH T. Cebeci, P. Bradshaw, Momentum transfer in boundary layers (Hemisphere Publishing Company, UK, 1977)MATH
46.
Zurück zum Zitat Th. von. Karman, Über laminare und turbulente Reibung, ZAMM, 1 (1921) 233–252; NACA TM 1092 (1946) Th. von. Karman, Über laminare und turbulente Reibung, ZAMM, 1 (1921) 233–252; NACA TM 1092 (1946)
47.
Zurück zum Zitat K. Pohlhausen, Zur näherungsweisen Integration der Differentialgleichung der laminaren Reibungsschicht. ZAMM 1, 252–268 (1921)CrossRefMATH K. Pohlhausen, Zur näherungsweisen Integration der Differentialgleichung der laminaren Reibungsschicht. ZAMM 1, 252–268 (1921)CrossRefMATH
48.
Zurück zum Zitat H. Holstein, T. Bohlen, Ein einfaches Verfahren zur Berechnung lamimarer Reibungsschichten, die dem Näherungsansatz von. K. Pohlhausen genügen, Lilienthal-Bericht S 10 (1940), pp. 5–16 H. Holstein, T. Bohlen, Ein einfaches Verfahren zur Berechnung lamimarer Reibungsschichten, die dem Näherungsansatz von. K. Pohlhausen genügen, Lilienthal-Bericht S 10 (1940), pp. 5–16
49.
Zurück zum Zitat H. Schlichting, Boundary-layer theory, 6th edn. (McGraw-Hill Book Company, 1968). Translated by J. Kestin H. Schlichting, Boundary-layer theory, 6th edn. (McGraw-Hill Book Company, 1968). Translated by J. Kestin
51.
Zurück zum Zitat I.V. Shevchuk, Convective heat and mass transfer in rotating disk systems (Springer, Heidelberg, 2009)CrossRefMATH I.V. Shevchuk, Convective heat and mass transfer in rotating disk systems (Springer, Heidelberg, 2009)CrossRefMATH
52.
Zurück zum Zitat B.C. Sakiadis, Boundary-layer behavior on continuous solid surfaces: II. The boundary-layer on a continuous flat surface. AIChE 7(2), 221–225 (1961)CrossRef B.C. Sakiadis, Boundary-layer behavior on continuous solid surfaces: II. The boundary-layer on a continuous flat surface. AIChE 7(2), 221–225 (1961)CrossRef
53.
Zurück zum Zitat B.C. Sakiadis, Boundary-layer behavior on continuous solid surfaces: III. The boundary-layer on a continuous cylindrical surface. AIChE 7(3), 467–472 (1961)CrossRef B.C. Sakiadis, Boundary-layer behavior on continuous solid surfaces: III. The boundary-layer on a continuous cylindrical surface. AIChE 7(3), 467–472 (1961)CrossRef
Metadaten
Titel
Solution Techniques
verfasst von
Ahmer Mehmood
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-55432-7_4

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