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  • Cited by 12
  • Volume 2, 3rd edition
  • C. S. Jog, Indian Institute of Science, Bangalore
Publisher:
Cambridge University Press
Online publication date:
May 2015
Print publication year:
2015
Online ISBN:
9781316134030

Book description

Fluid mechanics is the study of fluids including liquids, gases and plasmas and the forces acting on them. Its study is critical in predicting rainfall, ocean currents, reducing drag on cars and aeroplanes, and design of engines. The subject is also interesting from a mathematical perspective due to the nonlinear nature of its equations. For example, the topic of turbulence has been a subject of interest to both mathematicians and engineers: to the former because of its mathematically complex nature and to the latter group because of its ubiquitous presence in real-life applications. This book is a follow-up to the first volume and discusses the concepts of fluid mechanics in detail. The book gives an in-depth summary of the governing equations and their engineering related applications. It also comprehensively discusses the fundamental theories related to kinematics and governing equations, hydrostatics, surface waves and ideal fluid flow, followed by their applications.

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Contents

References
[1] Ackerberg R., C., The viscous incompressible flow inside a cone, J. Fluid Mech., 21(1), 47–81, 1965.
[2] Agrawal,, H. L., A new exact solution of the equations of viscous motion with axial symmetry, Quart. J. Mech. Appl. Math., 10(1), 42–44, 1957.
[3] Anderson, J. D., Modern Compressible Flow, with Historical Perspective, New York: Mc Graw-Hill, 1990.
[4] Ballal, B. and R. S., Rivlin, Flow of a Newtonian fluid between eccentric rotating cylinders: inertial effects, Arch. Rational Mech. Anal., 62(3), 237–294, 1977.
[5] Badr, O. E., M. N., Farah and A. E., Badran, A study of laminar motion of a viscous incompressible fluid between two parallel eccentric cylinders, Mech. Res. Comm., 19(1), 45–49, 1992.
[6] Barakat, R., Propagation of acoustic pulses from a circular cylinder, Acoust. Soc. Am., 33(12), 1759–1764, 1961.
[7] Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge: Cambridge University Press, 1967.
[8] Bennett, A., Lagrangian Fluid Dynamics, Cambridge: Cambridge University Press, 2006.
[9] Berker, R., A new solution of the Navier–Stokes equation for the motion of a fluid contained between two parallel plates rotating about the same axis, Arch. Mech. Stosowan., 31(2), 265–280, 1979.
[10] Brennen, C. E., Cavitation and Bubble Dynamics, New York: Oxford University Press, 1995.
[11] Chadwick, P., Continuum Mechanics, New York: Dover Publications, 1976.
[12] Chan, C. C. C., J. A. W., Elliott and M. C., Williams, Investigation of the dependence of inferred interfacial tension on rotation rate in a spinning drop tensiometer, J. Colloid Interface Sci, 260(1), 211–218, 2003.
[13] Chwang, A. T. and T. Y., Wu, Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows, J. Fluid Mech, 67(04), 787–815, 1975.
[14] Cochran, W. G., The flow due to a rotating disc, Proc. Camb. Phil. Soc., 30(03), 178–191, 1934.
[15] Coleman, B. D. and W., Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal., 13(1), 245–261, 1963.
[16] Coleman, B. D. and V. J., Mizel, Existence of caloric equations of state in thermodynamics, J. Chem. Phys, 40(4), 1116–1125, 1964.
[17] Deo, S. and A., Tiwari, On the solution of a partial differential equation representing irrotational flow in bispherical polar coordinates, Appl. Math. Computation, 205(1), 475–477, 2008.
[18] Darwin, C., Note on hydrodynamics, Math. Proc. Camb.Phil. Soc., 49(02), 342–354, 1953.
[19] DiPrima, R. C. and J. T., Stuart, Flow between eccentric rotating cylinders, ASME J. Tribology, 94(3), 266–274, 1972.
[20] Dorrepaal J., M., M. E., O'Neill and K. B., Ranger, Axisymmetric Stokes flow past a spherical cap, J. Fluid Mech., 75(02), 273–286, 1976.
[21] Edwardes, D., Steady motion of a viscous liquid in which an ellipsoid is constrained to rotate about a principla axis, Quart. J. Math., 26, 70–78, 1892.
[22] El-Saden M., R., Heat conduction in an eccentrically hollow, infinitely long cylinder with internal heat generation, Trans. AMSE, J. Heat Transfer, 83(4), 510–512, 1961.
[23] Erdelyi, A., et al. (Eds.) Tables of Integral Transforms, Vol. I, New York: McGraw-Hill, 1954.
[24] Erdogan, M. E., C. E., Imrak, On the comparison of the solutions obtained by two different transform methods for the second problem of Stokes for Newtonian fluid, Int. J. Non-linear Mech., 44(1), 27–30, 2009.
[25] Erdogan, M. E., Unsteady viscous flow between eccentric rotating disks, Int. J. of Non-linear Mech., 30(5), 711–717, 1995.
[26] Erdogan, M. E., Flow due to parallel disks rotating about non-coincident axis with one of them oscillating in its plane, Int. J. of Non-linear Mech., 34(6), 1019–1030, 1999.
[27] Fan, C. and B. T., Chao, Unsteady, laminar, incompressible flow through rectangular ducts, Zeitschrift fr Angewandte Mathematik und Physik, 16(3), 351–360, 1965.
[28] Fetecau, C., D., Vieru and C., Fetecau, A note on the second problem of Stokes for Newtonian fluid, Int. J. of Non-linear Mech., 43(5), 451–457, 2008.
[29] Filon, L. N. N., The forces on a cylinder in a stream of viscous fluid, Proc. R. Soc. Lond. Ser. A, 113(763), 7–27, 1926.
[30] Goldstein, S., The steady flow of viscous fluid past a fixed spherical obstacle at small Reynolds number, Proc. R. Soc. Lond. Ser. A, 123(791), 225–235, 1929.
[31] Goodbody, A. M., Cartesian Tensors with Applications to Mechanics, Fluid Mechanics and Elasticity, New York: Ellis Horwood Limited, 1982.
[32] Greenhill, A. G., Fluid motion between confocal elliptic cylinders and confocal ellipsoids, Quart. J. Math. Oxford Ser., 16, 227–256, 1879.
[33] Greenspan, H. P. and D. S., Butler, On the expansion of a gas into vacuum, J. Fluid Mech., 13(01), 101–119, 1963.
[34] Greenspan, M., Piston radiator: Some extensions of the theory, J. Acoust. Soc. Am., 65(3), 608–621, 1979.
[35] Gupta, S., D., Poulikakos and V., Kurtcuoglu, Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid, Phys. Fluids, 20(9), 093607-1:12, 2008.
[36] Guria, M., R. N., Jana and S. K., Ghosh, Unsteady Couette flow in a rotating system, Int. J. Non-linear Mech., 41(6), 838–843, 2006.
[37] Gurtin, M. E., An Introduction to Continuum Mechanics, San Diego: Academic Press, 1981.
[38] Hall, O., A. D., Gilbert and C. P., Hills, Converging flow between coaxial cones, Fluid Dyn. Res., 41(1), 1:25, 2009.
[39] Hartland, S. and R. W., Hartley, Axisymmetric Fluid-Liquid Interfaces, New York: Elsevier Scientific Pub. Co., 1976.
[40] Hasegawa, T., N., Inoue and K., Matsuzawa, A new rigorous expansion for the velocity potential of a circular piston source, J. Acoust. Soc. Am., 74(3), 1044–1047, 1983.
[41] Haslam, M. and M., Zamir, Pulsatile flow in tubes of elliptic cross sections, Ann. of Biomed. Eng., 26(5), 780–787, 1998.
[42] Hay, G. E., The method of images applied to the problem of torsion, Proc. Lond. Math. Soc., s2-45(1), 382–397, 1939.
[43] Hepworth, H. K. and W., Rice, Laminar flow between parallel plates with arbitrary time-varying pressure gradient and arbitrary initial velocity, J. Appl. Mech., 34(1), 215–216, 1967.
[44] Heyda, J. F., A Green's function solution for the case of laminar incompressible flow between non-concentric circular cylinders, J. Franklin Inst., 267(1), 25–34, 1959.
[45] Hill, J. M. and J. N., Dewynne, Heat Conduction, Boston: Blackwell Scientific Publications, 1987.
[46] Hunter, S. C., Mechanics of Continuous Media, Chichester: Ellis Horwood Limited, 1983.
[47] Jeffery, G. B., Steady rotation of a solid of revolution in a viscous fluid, Proc. Lond. Math. Soc., 14, 327–338, 1915.
[48] Jeffery, G. B., The rotation of two cylinders in a viscous flow, Proc. of the Royal Society of London. Series A, 101(709), 169–174, 1922.
[49] Jog, C. S. and Rakesh, Kumar, Shortcomings of discontinuous-pressure finite element methods on a class of transient problems, Int. J. Numer. Meth. Fluids, 62(3), 313–326, 2010.
[50] Jog, C. S., A finite element method for compressible flow, Int. J. Numer. Meth. Fluids, 66(7), 852–874, 2011.
[51] Jog, C. S., An outward-wave-favoring finite element based strategy for exterior acoustic problems, Int. J. Acoustics Vibration, 18(1), 27–38, 2013.
[52] Jog, C. S. and A., Nandy, Conservation properties of the trapezoidal rule in linear time domain analysis of acoustics and structures, ASME J. Vibration Acoustics, 137(2), 021010, 2015.
[53] Kanwal, R. P., Slow steady rotation of axially symmetric bodies in a viscous fluid, J. Fluid Mech., 10(01), 17–24, 1961.
[54] Khamrui, S. R., On the flow of a viscous fluid through a tube of elliptic section under the influence of a periodic pressure gradient, Bull. Calcutta Math. Soc., 49, 57–60, 1957.
[55] Khuri, S. A. and A. M., Wazwaz, The solution of a partial differential equation arising in fluid flow theory, Appl. Maths Computation, 77(2–3), 295–300, 1996.
[56] Khuri, S. A. and A. M., Wazwaz, On the solution of a partial differential equation arising in Stokes flow, Appl. Maths Computation, 85(2–3), 139–147, 1997.
[57] Joseph, D. D., Potential flow of viscous fluids: Historical notes, Int. J. Multiphase Flow, 32(3), 285–310, 2006.
[58] Lai, C.-Y., K. R., Rajagopal and A. Z., Szeri, Asymmetric flow between parallel rotating disks, J. Fluid Mech., 146, 203–225, 1984.
[59] Lai, C.-Y., K. R., Rajagopal and A. Z., Szeri, Asymmetric flow above a rotating disk, J. Fluid Mech., 157, 471–492, 1985.
[60] Lamb, H., Hydrodynamics, New York: Dover Publications, 1945.
[61] Mallick, D. D., Nonuniform rotation of an infinite circular cylinder in an infinite viscous liquid, ZAMM, 37(9/10), 385–392, 1957.
[62] Malvern, L. E., Introduction to the Mechanics of a Continuous Medium, New Jersey: Prentice Hall Inc., 1969.
[63] Marsden, J. E. and Hughes, T. J. R., Mathematical Foundations of Elasticity, New York: Dover Publications, 1983.
[64] Mast, T. D. and Y., Feng, Simplified expansions for radiation from a baffled circular piston, J. Acoust. Soc. Am., 118(6), 3457–3464, 2005.
[65] MATLAB User's Guide, Natick, Massachusetts: The Math Works Inc., 2011.
[66] Matunobu, Y., Pressure flow relationships for steady flow through an eccentric double circular tube, Fluid Dynamics Res., 4(2), 139–149, 1988.
[67] Moody D., M., Unsteady expansion of an ideal gas into a vacuum, J. Fluid Mech., 214, 455–468, 1990.
[68] Morton W., B., On the displacements of the particles and their paths in some cases of two-dimensional motion of a frictionless liquid, Proc. R. Soc. Lond. Ser. A, 89(608), 106–124, 1913.
[69] Muhammad, G., N. A., Shah and M., Mushtaq, Indirect boundary element method for calculation of potential flow around a prolate spheroid, J. Am. Sci., 6(1), 148–156, 2010.
[70] Mellor, G. L., P. J., Chapple and V. K., Stokes, On the flow between a rotating and a stationary disk, J. Fluid Mech., 31(1), 95–112, 1968.
[71] Miksis, M., J. M., Vanden-Broeck and J. B., Keller, Axisymmetric bubble or drop in a uniform flow, J. Fluid Mech., 108, 89–100, 1981.
[72] Noll, W., A mathematical theory ofthe mechanical behavior ofcontinuous media, Arch. Rational Mech. Anal. 2(1), 197–226, 1958. Reprinted in Noll, W.The foundations of mechanics and thermodynamics, Berlin: Springer-Verlag, 1974.
[73] Oberhettinger, F., On transient solutions of the ‘baffled piston’ problem, J. Res. Natl. Bur. Stand., 65B(1), 1–6, 1961.
[74] Ozisik, M. N., Heat Conduction, New York: John Wiley, 1993.
[75] Padmavathi, B. S., G. P., Rajashekhar and T., Amarnath, A note on complete general solutions of Stokes equations, Quart. J. Mech. Appl. Math., 51(3), 383–388, 1998.
[76] Palaniappan, D., S. D., Nigam, T., Amarnath and R., Usha, Lamb's solution of Stokes's equations: A sphere theorem, Quart. J. Mech. Appl. Math., 45(1), 47–56, 1992.
[77] Parter, S. V. and K. R., Rajagopal, Swirling flow between rotating plates, Arch. Rational Mech. Anal., 86(4), 305–315, 1984.
[78] Payne, L. E., On axially symmetric flow and the method of generalized electrostatics, Quart. Appl. Math., 10(3), 197–204, 1952.
[79] Payne, L. E. and W. H., Pell, The Stokes flow problem for a class of axially symmetric bodies, J. Fluid Mech., 7(04), 529–549, 1960.
[80] Phan-Thien, N. and R. I., Tanner, Viscoelastic squeeze-film flows-Maxwell fluids, J. Fluid Mech., 129, 265–281, 1983.
[81] Phan-Thien, N. and W., Walsh, Squeeze-film flow of an Olroyd-B fluid: Similarity solution and limiting Weissenberg number, J. Appl. Math. Phys. (ZAMP), 35(6), 747–758, 1984.
[82] Ponnusamy, S., Foundations of Complex Analysis, Oxford: Alpha Science International Limited, Second Edition, 2006.
[83] Prakash, S., Laminar flow in an annulus with arbitrary time-varying pressure gradient and arbitrary initial velocity, J. Appl. Mech., 36(2), 309–311, 1969.
[84] Prakash, S., Note on the problem of unsteady viscous flow past a flat plate, Ind. J. Pure Appl. Math., 2(2), 283–289, 1971.
[85] Princen, H. M., I. Y. Z., Zia and S. G., Mason, Measurement of interfacial tension from the shape of a spinning drop, J. Colloid Interface Sci., 23(1), 99–107, 1967.
[86] Proudman, I. and J. R. A., Pearson, Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder, J. Fluid Mech., 2(03), 237–262, 1957.
[87] Saatdjian, E., N., Midoux and J. C., Andre, On the solution of Stokes equations between confocal ellipses, Phys. Fluids, 6(12), 3833–3846, 1994.
[88] Schlicting, H., Boundary Layer Theory, New York: McGraw-Hill, 1979.
[89] Sidrak, S., The drag on a circular cylinder in a stream of viscous liquid at small Reynolds numbers, Proc. R. Irish Acad. Sec. A, 53, 17–30, 1950/51.
[90] Silhavy, M., The Mechanics and Thermodynamics of Continuous Media, Berlin: Springer-Verlag, 1997.
[91] Snyder W., T., G. A., Goldstein, An analysis of fully developed laminar flow in an eccentric annulus, Report No. 8, State Univ. New York, 1–18, 1963.
[92] Sparrow, E. M., Laminar flow in isosceles triangular ducts, AIChE Journal, 8(5), 599–604, 1962.
[93] Stoker, J. J., Water Waves, New York: Interscience Publishers, 1957.
[94] Straughan, B., Heat waves, New York: Springer, 2011.
[95] Tachibana, M. and Y., Iemoto, Steady flow around, and drag on a circular cylinder moving at low speeds in a viscous liquid between two parallel planes, Fluid Dyn. Res., 2(2), 125–137, 1987.
[96] Tomotika, S., T., Aoi, The steady flow of a viscous fluid past an elliptic cylinder and a flat plate at small Reynolds numbers, Quart. J. Mech. Appl. Math., 6(3), 290–312, 1953.
[97] Truesdell, C., Rational Thermodynamics, New York: Springer-Verlag, 1984.
[98] Van Dyke, M.Perturbation Methods in Fluid Dynamics, New York: Academic Press, 1964.
[99] Venkatlaxmi, A., B. S., Padmavathi and T., Amarnath, Unsteady Stokes equations: Some complete general solutions, Proc. Ind. Acad. Sci. (Math. Sci.), 114(2), 203–213, 2003.
[100] Verma, P. D., The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid between two co-axial cylinders, Proc. Ind. Acad. Sci. Math., 26(5), 447–458, 1960.
[101] Verma, P. D., The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a tube of elliptic cross section, Proc. Indian Acad. Sci. Math., 26(3), 282–297, 1960.
[102] Vonnegut, B., Rotating bubble method for the determination of surface and interfacial tension, Rev. Sci. Instr., 13(1), 6–9, 1942.
[103] Wannier, G. H., A contribution to the hydrodynamics of lubrication, Quart. Appl. Math., 8, 1–32, 1950.
[104] Wang, C. Y., Exact solutions of the unsteady Navier–Stokes equations, Appl. Mech. Rev., 42(11), S269–S282, 1989.
[105] White, F. M., Fluid Mechanics, New York: McGraw-Hill International Edition, 1994.
[106] White, F. M., Viscous Fluid Flow, New York: McGraw-Hill, 1991.
[107] Wolfram, S., Mathematica, Champaign, Illinois: Wolfram Research Inc., 2014.
[108] Yakubovich, E. I. and D. A., Zenkovich, Matrix approach to Lagrangian fluid dynamics, J. Fluid Mech., 443, 167–196, 2001.

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