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)
Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium. (English) Zbl 1172.76051
Summary: The problem of peristaltic flow of a Newtonian fluid with heat transfer in a vertical asymmetric channel through porous medium is studied under long-wavelength and low-Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The analytical solution has been obtained for the temperature, from which an axial velocity, stream function and pressure gradient have been derived. The effects of permeability parameter, Grashof number, heat source/sink parameter, phase difference, varying channel width and wave amplitudes on the pressure gradient, velocity, pressure drop, the phenomenon of trapping and shear stress are discussed numerically and explained graphically.
MSC:
76S05Flows in porous media; filtration; seepage
76D05Navier-Stokes equations (fluid dynamics)
80A20Heat and mass transfer, heat flow
References:
[1]Eytan, O.; Elad, D.: Analysis of intra-uterine fluid motion induced by uterine contractions, Bull. math. Biol. 61, 221-238 (1999)
[2]El Shehawey, E. F.; Husseny, S. Z. A.: Effects of porous boundaries on peristaltic transport through a porous medium, Acta mech. 143, 165-177 (2000) · Zbl 0969.76084 · doi:10.1007/BF01170946
[3]El Shehawey, E. F.; El Sebaei, W.: Peristaltic transport in a cylindrical tube through a porous medium, Internat. J. Math. math. Sci. 24, 217-230 (2000) · Zbl 0962.76101 · doi:10.1155/S0161171200004737
[4]Mishra, Manoranjan; Rao, Adabala Ramachandra: Peristaltic transport of a Newtonian fluid in an asymmetric channel, Zamp 54, 532-550 (2003) · Zbl 1099.76545 · doi:10.1007/s00033-003-1070-7
[5]Hayat, T.; Ali, N.; Asghar, S.: Hall effects on peristaltic flow of a Maxwell fluid in a porous medium, Phys. lett. A 363, 397-403 (2007) · Zbl 1197.76126 · doi:10.1016/j.physleta.2006.10.104
[6]Srinivas, S.; Pushparaj, V.: Non-linear peristaltic transport in an inclined asymmetric channel, Commun. nonlinear sci. Numer. simul. 13, 1782-1795 (2008)
[7]Ali, Nasir; Hayat, Tasawar; Asghar, Saleem: Peristaltic flow of a Maxwell fluid in a channel with compliant walls, Chaos, solitons & fractals 39, 407-416 (2009) · Zbl 1197.76017 · doi:10.1016/j.chaos.2007.04.010
[8]Kothandapani, M.; Srinivas, S.: Non-linear peristaltic transport of Newtonian fluid in an inclined asymmetric channel through a porous medium, Phys. lett. A 372, 1265-1276 (2008) · Zbl 1217.76105 · doi:10.1016/j.physleta.2007.09.040
[9]Hariharan, Prasanna; Seshadri, V.; Banerjee, Rupak K.: Peristaltic transport of non-Newtonian fluid in a diverging tube with different waveforms, Math. comput. Model. 48, 998-1017 (2008) · Zbl 1187.76606 · doi:10.1016/j.mcm.2007.10.018
[10]Ikbal, Md. Asif; Chakravarty, Santabrata; Mandal, Prashanta Kumar: An unsteady transport phenomenon of non-Newtonian fluid – a generalized approach, Appl. math. Comput. 201, 16-34 (2008) · Zbl 1228.76205 · doi:10.1016/j.amc.2007.11.051
[11]Vajravelu, K.; Radhakrishnamacharya, G.; Radhakrishnamurty, V.: Peristaltic flow and heat transfer in a vertical porous annulus, with long-wavelength approximation, Int. J. Nonlinear mech. 42, 754-759 (2007) · Zbl 1200.76192 · doi:10.1016/j.ijnonlinmec.2007.02.014
[12]Radhakrishnamacharya, G.; Srinivasulu, Ch.: Influence of wall properties on peristaltic transport with heat transfer, CR mec. 335, 369-373 (2007) · Zbl 1144.76067 · doi:10.1016/j.crme.2007.05.002
[13]Srinivas, S.; Kothandapani, M.: Peristaltic transport in an asymmetric channel with heat transfer – a note, Int. comm., heat and mass transfer 35, 514-522 (2008)
[14]Mekheimer, Kh.S.; Elmaboud, Y. Abd: The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus: application of an endoscope, Phys. lett. A 372, 1657-1665 (2008) · Zbl 1217.76106 · doi:10.1016/j.physleta.2007.10.028
[15]Ali, N.; Hayat, T.; Sajid, M.: Peristaltic flow of a couple stress fluid in asymmetric channel, Biorheology 44, 125-138 (2007)
[16]Reddy, M. V. Subba; Rao, A. Ramachandra; Sreenath, S.: Peristaltic motion of a power-law fluid in an asymmetric channel, Int. J. Non-linear mech. 42, 1153-1161 (2007)
[17]Kothandapani, M.; Srinivas, S.: On the influence of wall properties in the MHD peristaltic transport with heat transfer and porous medium, Phys. lett. A 372, 4586-4591 (2008) · Zbl 1221.76044 · doi:10.1016/j.physleta.2008.04.050
[18]Hayat, T.; Javed, Merylam; Asghar, S.: MHD peristaltic motion of Johnson-Segalman fluid in a channel with compliant walls, Phys. lett. A 372, 5026-5036 (2008) · Zbl 1221.76219 · doi:10.1016/j.physleta.2008.03.065
[19]Kothandapani, M.; Srinivas, S.: Peristaltic transport of a Jeffery fluid under the effect of magnetic field in an asymmetric channel, Int. J. Non-linear mech. 43, 915-924 (2008)
[20]Srinivas, S.; Kothandapani, M.: The influence of heat and mass transfer on MHD peristaltic flow through a porous space with complaint walls, Appl. math. Comput. 213, 197-208 (2009) · Zbl 1165.76052 · doi:10.1016/j.amc.2009.02.054
[21]Nield, D. A.; Bejan, A.: Convection in porous media, (1999)
[22], Handbook of porous media (2002)
[23]Pop, I.; Ingham, D. B.: Convective heat transfer: computational and mathematical of modeling viscous fluids and porous media, (2001)
[24]Bejan, A.; Kraus, A. D.: Heat transfer handbook, (2003)
[25]Canny, M. J.; Phillips, O. M.: Quantitative aspects of a theory of translocation, Ann. botany 27, 379-402 (1963)
[26]Aikman, D. P.; Anderson, W. P.: A quantitative investigation of a peristaltic model for phloem translocation, Ann. botany 35, 761-772 (1971)