zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Oscillatory flows of second grade fluid in a porous space. (English) Zbl 1197.35206
Summary: The exact analytical solutions are developed for the magnetohydrodynamic flows of the second grade fluid in a porous medium. The analysis is performed using modified Darcy’s law and takes into account the effect of the Hall current. Closed form solutions are given for three problems using the Fourier sine transform. Comparison has been made with the existing results and are found to be in excellent agreement. The graphs are plotted for various emerging parameters and discussed.

MSC:
35Q35PDEs in connection with fluid mechanics
76W05Magnetohydrodynamics and electrohydrodynamics
76S05Flows in porous media; filtration; seepage
76A05Non-Newtonian fluids
35C05Solutions of PDE in closed form
35A22Transform methods (PDE)
WorldCat.org
Full Text: DOI
References:
[1] Hayat, T.; Nadeem, S.; Asghar, S.; Siddiqui, A. M.: Effect of Hall current on unsteady flow of a second grade fluid in a rotating system. Chem. eng. Comm. 192, 1272-1284 (2005)
[2] Hayat, T.; Khan, M.; Ayub, M.: Exact solution of flow problems of an Oldroyd-B fluid. Appl. math. Comput. 151, 105-119 (2004) · Zbl 1039.76001
[3] Hayat, T.; Naz, R.; Asghar, S.: Hall effect on unsteady duct flow of a non-Newtonian fluid in a porous medium. Appl. math. Comput. 157, 103-114 (2004) · Zbl 1108.76084
[4] Asghar, S.; Parveen, S.; Hanif, S.; Siddiqui, A. M.; Hayat, T.: Hall effects on the unsteady hydromagnetic flows of an Oldroyd-B fluid. Internat. J. Engrg. sci. 41, 609-619 (2003) · Zbl 1211.76138
[5] Fetecau, C.; Fetecau, C.: Decay of potential vortex in a Maxwell fluid. Intetnat. J. Non-linear mech. 28, 985-990 (2003) · Zbl 1287.76043
[6] Fetecau, C.; Fetecau, C.: The Rayleigh Stokes problem for heated second grade fluid. Intetnat. J. Non-linear mech. 37, 1011-1015 (2002)
[7] Fetecau, C.; Fetecau, C.: Decay of potential vortex in an Oldroyd -B fluid. Intetnat. J. Non-linear mech. 43, 340-351 (2005) · Zbl 1211.76008
[8] Tan, W. C.; Xu, M. Y.: The impulsive motion of a flat plate in a generalized second fluid. Mech. res. Comm. 29, 3-9 (2002) · Zbl 1151.76368
[9] Tan, W. C.; Masuoka, T.: Stokes first problem for second grade fluid in a porous half space. Intetnat. J. Non-linear mech. 40, 515-522 (2005) · Zbl 05138608
[10] Tan, W. C.; Masuoka, T.: Stokes first problem for an Oldroyd-B fluid in a porous half space. Phys. fluids 17 (2005) · Zbl 1187.76517
[11] Chen, C. I.; Chen, C. K.; Yang, Y. T.: Unsteady unidirectional flow of an Oldroyd-B fluid in a circular duct with different given volume flow rate. Heat mass transfer 40, 203-209 (2004)
[12] Fetecau, C.; Fetecau, C.: Starting solutions for unsteady unidirectional flows of a second grade fluid. Internat. J. Engrg. sci. 43, 781-789 (2005) · Zbl 1211.76032
[13] Rajagopal, K. R.: On the creeping flow of second order fluid. J. non-Newtonian fluid mech. 48, 239-246 (1984) · Zbl 0568.76015
[14] Dunn, J. E.; Fosdick, R. L.: Thermodynamics, stability and boundedness of fluids of complexity 2 and fluids of second grade. Arch. ration. Mech. anal. 56, 191-252 (1974) · Zbl 0324.76001
[15] Fosdick, R. L.; Rajagopal, K. R.: Uniqueness and drag for fluids of second grade in steady motion. Intetnat. J. Non-linear mech. 13, 131-137 (1978) · Zbl 0392.76005
[16] Dunn, J. E.; Rajagopal, K. R.: Fluids of differential type: critical review and thermodynamic analysis. Internat. J. Engrg. sci. 33, 689-729 (1995) · Zbl 0899.76062
[17] Rajagopal, K. R.: On boundary conditions for fluids of the differential type. Navier--Stokes equations and related non-linear problems (1995)
[18] Rajagopal, K. R.; Gupta, A. S.: An exact solution for the flow of a non-Newtonian fluid past an infinite porous plate. Meccanica 19, 1948-1954 (1984) · Zbl 0552.76008
[19] Grandshteyn, I. S.; Ryzhik, I. M.: Alanjeffreytables of integrals, series and products. Tables of integrals, series and products (1994)
[20] Erdogan, M. E.: A note on an unsteady flow of a viscous fluid due to an oscillating plane wall. Intetnat. J. Non-linear mech. 35, 1-6 (2000) · Zbl 1006.76028
[21] Rajagopal, K. R.: A note on unsteady unidirectional flows of a non-Newtonian fluid. Intetnat. J. Non-linear mech. 17, 369-373 (1982) · Zbl 0527.76003