Skip to main content
Erschienen in: Colloid and Polymer Science 6/2017

18.04.2017 | Original Contribution

Squeezing flow of second grade liquid subject to non-Fourier heat flux and heat generation/absorption

verfasst von: T. Hayat, M. Waleed Ahmed Khan, A. Alsaedi, M. Ijaz Khan

Erschienen in: Colloid and Polymer Science | Ausgabe 6/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Two-dimensional squeezing flow of second grade fluid between two parallel plates is addressed. The lower plate is stretched while the upper plate is either moving away or towards the lower one. Temperature-dependent thermal conductivity is considered. Further, heat source/sink is present. Unlike the classical situation, the heat flux by Cattaneo-Christov theory is adopted instead of Fourier’s heat conduction law. Homotopic convergent solutions of velocity and temperature are developed and analyzed. Reduction in the thermal layer thickness is observed for Cattaneo-Christov heat flux model when compared with that of Fourier’s law of heat conduction. It is observed that velocity profile is enhanced by increasing the squeezing parameter. Also, a positive squeezing parameter enhances the thermal field due to a higher squeezing force applied on the fluid.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Stefan MJ (1874) Versuch ber die scheinbare adhesion. Akad Wissensch Wien Math Natur 69:713 Stefan MJ (1874) Versuch ber die scheinbare adhesion. Akad Wissensch Wien Math Natur 69:713
2.
Zurück zum Zitat Reynolds O (1886) On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil. Philosophical Transactions of the Royal Society of London 177:157–234CrossRef Reynolds O (1886) On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil. Philosophical Transactions of the Royal Society of London 177:157–234CrossRef
3.
Zurück zum Zitat Archibald FR (1956) Load capacity and time relations for squeeze films. J Lubr Technol 78:A231–A245 Archibald FR (1956) Load capacity and time relations for squeeze films. J Lubr Technol 78:A231–A245
4.
Zurück zum Zitat Thorpe JF (1967) Further investigation of squeezing flow between parallel plates. Dev Theoret Appl Mech 3:635–648CrossRef Thorpe JF (1967) Further investigation of squeezing flow between parallel plates. Dev Theoret Appl Mech 3:635–648CrossRef
5.
Zurück zum Zitat Wang CY (1976) The squeezing of a fluid between two plates. J Appl Mech 43:579–582CrossRef Wang CY (1976) The squeezing of a fluid between two plates. J Appl Mech 43:579–582CrossRef
6.
Zurück zum Zitat Domairry G, Hatami M (2014) Squeezing Cu-water nanofluid flow analysis between parallel plates by DTM-Prade method. J Mol Liq 193:37–44CrossRef Domairry G, Hatami M (2014) Squeezing Cu-water nanofluid flow analysis between parallel plates by DTM-Prade method. J Mol Liq 193:37–44CrossRef
7.
Zurück zum Zitat Khan M, Rahman M (2015) Flow and heat transfer to modified second grade fluid over a non-linear stretching sheet. AIP Adv 5:087157CrossRef Khan M, Rahman M (2015) Flow and heat transfer to modified second grade fluid over a non-linear stretching sheet. AIP Adv 5:087157CrossRef
8.
Zurück zum Zitat Khan SI, Ahmed N, Khan U, Jan SU, Mohyud-Din ST (2015) Heat transfer analysis for squeezing flow between parallel disks. J Egyp Math Soc 23:445–450CrossRef Khan SI, Ahmed N, Khan U, Jan SU, Mohyud-Din ST (2015) Heat transfer analysis for squeezing flow between parallel disks. J Egyp Math Soc 23:445–450CrossRef
9.
Zurück zum Zitat P. Drazin and N. Riley, The Navier–Stokes equations: a classification of flows and exact solutions, Cambridge, 2006. P. Drazin and N. Riley, The Navier–Stokes equations: a classification of flows and exact solutions, Cambridge, 2006.
10.
Zurück zum Zitat Aristov SN, Knyazev DV (2012) Viscous fluid flow between moving parallel plates. Fluid Dyn 47(4):476–482CrossRef Aristov SN, Knyazev DV (2012) Viscous fluid flow between moving parallel plates. Fluid Dyn 47(4):476–482CrossRef
11.
Zurück zum Zitat Hayat T, Qayyum A, Alsaedi A (2015) Three-dimensional mixed convection squeezing flow. Appl Math Mech 36:47–60CrossRef Hayat T, Qayyum A, Alsaedi A (2015) Three-dimensional mixed convection squeezing flow. Appl Math Mech 36:47–60CrossRef
12.
Zurück zum Zitat Sheikholeslami M, Ganji DD, Ashorynejad HR (2013) Investigation of squeezing unsteady nanofluid flow using ADM. Powder Technol 239:259–265CrossRef Sheikholeslami M, Ganji DD, Ashorynejad HR (2013) Investigation of squeezing unsteady nanofluid flow using ADM. Powder Technol 239:259–265CrossRef
13.
Zurück zum Zitat Gupta AK, Ray SS (2015) Numerical treatment for investigation of squeezing unsteady nanofluid flow between two parallel plates. Powder Tech 279:282–289CrossRef Gupta AK, Ray SS (2015) Numerical treatment for investigation of squeezing unsteady nanofluid flow between two parallel plates. Powder Tech 279:282–289CrossRef
14.
Zurück zum Zitat Cattaneo C (1948) Sulla conduzione del calore. Atti Semin Mat Fis Univ Modena Reggio Emilia 3:83–101 Cattaneo C (1948) Sulla conduzione del calore. Atti Semin Mat Fis Univ Modena Reggio Emilia 3:83–101
15.
Zurück zum Zitat Christov CI (2009) On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction. Mech Res Commun 36:481–486CrossRef Christov CI (2009) On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction. Mech Res Commun 36:481–486CrossRef
16.
Zurück zum Zitat Ciarletta M, Straughan B (2010) Uniqueness and structural stability for the Cattaneo-Christov equations. Mech Res Commun 37:445–447CrossRef Ciarletta M, Straughan B (2010) Uniqueness and structural stability for the Cattaneo-Christov equations. Mech Res Commun 37:445–447CrossRef
17.
Zurück zum Zitat Tibullo V, Zampoli V (2011) A uniqueness result for the Cattaneo-Christov heat conduction model applied to incompressible fluids. Mech Res Commun 38:77–79CrossRef Tibullo V, Zampoli V (2011) A uniqueness result for the Cattaneo-Christov heat conduction model applied to incompressible fluids. Mech Res Commun 38:77–79CrossRef
18.
Zurück zum Zitat Han S, Zheng L, Li C, Zhang X (2014) Coupled flow and heat transfer in viscoelastic fluid with Cattaneo-Christov heat flux model. Appl Math Lett 38:87–93CrossRef Han S, Zheng L, Li C, Zhang X (2014) Coupled flow and heat transfer in viscoelastic fluid with Cattaneo-Christov heat flux model. Appl Math Lett 38:87–93CrossRef
19.
Zurück zum Zitat Mustafa M (2015) Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper convected Maxwell fluid. AIP Adv 5:047109CrossRef Mustafa M (2015) Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper convected Maxwell fluid. AIP Adv 5:047109CrossRef
20.
Zurück zum Zitat Hayat T, Farooq M, Alsaedi A, Al-Solamy F (2015) Impact of Cattaneo-Christov heat flux in the flow over a stretching sheet with variable thickness. AIP Adv 5:047109CrossRef Hayat T, Farooq M, Alsaedi A, Al-Solamy F (2015) Impact of Cattaneo-Christov heat flux in the flow over a stretching sheet with variable thickness. AIP Adv 5:047109CrossRef
21.
Zurück zum Zitat Ahmed J, Shahzad A, Khan M, Ali R (2015) A note on convective heat transfer of an MHD Jeffrey fluid over a stretching sheet. AIP Adv 5:117117CrossRef Ahmed J, Shahzad A, Khan M, Ali R (2015) A note on convective heat transfer of an MHD Jeffrey fluid over a stretching sheet. AIP Adv 5:117117CrossRef
22.
Zurück zum Zitat Langlois WE (1962) Isothermal squeeze films. Q Appl Math XX 20:131–150CrossRef Langlois WE (1962) Isothermal squeeze films. Q Appl Math XX 20:131–150CrossRef
23.
Zurück zum Zitat Verma RL (1981) A numerical solution for squeezing flow between parallel channels. Wear 72:89–95CrossRef Verma RL (1981) A numerical solution for squeezing flow between parallel channels. Wear 72:89–95CrossRef
24.
Zurück zum Zitat Hamza EA, MacDonald DA (1981) A fluid film squeezed between two parallel plane surfaces. J Fluid Mech 109:147–160CrossRef Hamza EA, MacDonald DA (1981) A fluid film squeezed between two parallel plane surfaces. J Fluid Mech 109:147–160CrossRef
25.
Zurück zum Zitat Domairry G, Aziz A (2009) Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by homotopy perturbation method. Math Probl Eng 2009:603916CrossRef Domairry G, Aziz A (2009) Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by homotopy perturbation method. Math Probl Eng 2009:603916CrossRef
26.
Zurück zum Zitat Hayat T, Yousuf A, Mustafa M, Obaidat S (2012) MHD squeezing flow of second grade fluid between two parallel disks. Int J Numer Methods Fluids 69:399–410CrossRef Hayat T, Yousuf A, Mustafa M, Obaidat S (2012) MHD squeezing flow of second grade fluid between two parallel disks. Int J Numer Methods Fluids 69:399–410CrossRef
27.
Zurück zum Zitat Qayyum A, Awais M, Alsaedi A, Hayat T (2012) Unsteady squeezing flow of Jeffery fluid between two parallel disks. Chin Phys Lett 29:034701CrossRef Qayyum A, Awais M, Alsaedi A, Hayat T (2012) Unsteady squeezing flow of Jeffery fluid between two parallel disks. Chin Phys Lett 29:034701CrossRef
28.
Zurück zum Zitat Majeed A, Zeeshan A, Ellahi R (2016) Unsteady ferromagnetic liquid flow and heat transfer analysis over a stretching sheet with the effect of dipole and prescribed heat flux. J Mol Liq 223:528–533CrossRef Majeed A, Zeeshan A, Ellahi R (2016) Unsteady ferromagnetic liquid flow and heat transfer analysis over a stretching sheet with the effect of dipole and prescribed heat flux. J Mol Liq 223:528–533CrossRef
29.
Zurück zum Zitat Waqas M, Khan MI, Farooq M, Alsaedi A, Hayat H, Yasmeen T (2016) Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition. Int J Heat Mass Transf 102:766–772CrossRef Waqas M, Khan MI, Farooq M, Alsaedi A, Hayat H, Yasmeen T (2016) Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition. Int J Heat Mass Transf 102:766–772CrossRef
30.
Zurück zum Zitat Akbar NS, Raza M, Ellahi R (2015) Influence of induced magnetic field and heat flux with the suspension of carbon nanotubes for the peristaltic flow in a permeable channel. J Magn Magn Mater 381:405–415CrossRef Akbar NS, Raza M, Ellahi R (2015) Influence of induced magnetic field and heat flux with the suspension of carbon nanotubes for the peristaltic flow in a permeable channel. J Magn Magn Mater 381:405–415CrossRef
31.
Zurück zum Zitat Hayat T, Khan MI, Waqas M, Alsaedi A (2017) Newtonian heating effect in nanofluid flow by a permeable cylinder. Result Phys 7:256–262CrossRef Hayat T, Khan MI, Waqas M, Alsaedi A (2017) Newtonian heating effect in nanofluid flow by a permeable cylinder. Result Phys 7:256–262CrossRef
32.
Zurück zum Zitat Akbar NS, Raza M, Ellahi R (2016) Endoscopic effects with entropy generation analysis in peristalsis for the thermal conductivity of nanofluid. Journal of Applied Fluid Mechanics 9(4):1721–1730 Akbar NS, Raza M, Ellahi R (2016) Endoscopic effects with entropy generation analysis in peristalsis for the thermal conductivity of nanofluid. Journal of Applied Fluid Mechanics 9(4):1721–1730
33.
Zurück zum Zitat Khan MI, Hayat T, Waqas M, Alsaedi A (2017) Outcome for chemically reactive aspect in flow of tangent hyperbolic material. J Mol Liq 230:143–151CrossRef Khan MI, Hayat T, Waqas M, Alsaedi A (2017) Outcome for chemically reactive aspect in flow of tangent hyperbolic material. J Mol Liq 230:143–151CrossRef
34.
Zurück zum Zitat Akbar NS, Raza M, Ellahi R (2015) Peristaltic flow with thermal conductivity of H2O + Cu nanofluid and entropy generation. Results in Physics 5:115–124CrossRef Akbar NS, Raza M, Ellahi R (2015) Peristaltic flow with thermal conductivity of H2O + Cu nanofluid and entropy generation. Results in Physics 5:115–124CrossRef
35.
Zurück zum Zitat Hayat T, Khan MI, Farooq M, Yasmeen T, Alsaedi A (2016) Water-carbon nanofluid flow with variable heat flux by a thin needle. J Mol Liq 224:786–791CrossRef Hayat T, Khan MI, Farooq M, Yasmeen T, Alsaedi A (2016) Water-carbon nanofluid flow with variable heat flux by a thin needle. J Mol Liq 224:786–791CrossRef
36.
Zurück zum Zitat Liao SJ (2012) Homotopy analysis method in non-linear differential equations. Springer and Higher Education Press, HeidelbergCrossRef Liao SJ (2012) Homotopy analysis method in non-linear differential equations. Springer and Higher Education Press, HeidelbergCrossRef
37.
Zurück zum Zitat Abbasbandy S, Yurusoy M, Gulluce H (2014) Analytical solutions of non-linear equations of power-law fluids of second grade over an infinite porous plate. Math Comp Appl 19:124 Abbasbandy S, Yurusoy M, Gulluce H (2014) Analytical solutions of non-linear equations of power-law fluids of second grade over an infinite porous plate. Math Comp Appl 19:124
38.
Zurück zum Zitat Turkyilmazoglu M (2012) Solution of the Thomas-Fermi equation with a convergent approach. Commun Nonlinear Sci NumerSimulat 17:4097–4103CrossRef Turkyilmazoglu M (2012) Solution of the Thomas-Fermi equation with a convergent approach. Commun Nonlinear Sci NumerSimulat 17:4097–4103CrossRef
39.
Zurück zum Zitat Hayat T, Khan MI, Waqas M, Alsaedi A (2017) Mathematical modeling of non-Newtonian fluid with chemical aspects: a new formulation and results by numerical technique. Colloid Surface A: Physicochemical Eng Aspect 518:263–272CrossRef Hayat T, Khan MI, Waqas M, Alsaedi A (2017) Mathematical modeling of non-Newtonian fluid with chemical aspects: a new formulation and results by numerical technique. Colloid Surface A: Physicochemical Eng Aspect 518:263–272CrossRef
40.
Zurück zum Zitat Hayat T, Khan MI, Farooq M, Yasmeen T, Alsaedi A (2016) Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions. J Mol Liq 220:49–55CrossRef Hayat T, Khan MI, Farooq M, Yasmeen T, Alsaedi A (2016) Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions. J Mol Liq 220:49–55CrossRef
41.
Zurück zum Zitat Lin Y, Zheng L, Ma L, Chen G (2015) MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation. Int J Heat Mass Transf 84:903–911CrossRef Lin Y, Zheng L, Ma L, Chen G (2015) MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation. Int J Heat Mass Transf 84:903–911CrossRef
42.
Zurück zum Zitat Khan MI, Hayat T, Waqas M, Khan MI, Alsaedi A (2017) Impact of heat generation/absorption and homogeneous-heterogeneous reactions on flow of Maxwell fluid. J Mol Liq 233:465–470CrossRef Khan MI, Hayat T, Waqas M, Khan MI, Alsaedi A (2017) Impact of heat generation/absorption and homogeneous-heterogeneous reactions on flow of Maxwell fluid. J Mol Liq 233:465–470CrossRef
43.
Zurück zum Zitat Khan MI, Waqas M, Hayat T, Alsaedi A (2017) A comparative study of Casson fluid with homogeneous-heterogeneous reactions. J Colloid Interface Sci 498:85–90CrossRef Khan MI, Waqas M, Hayat T, Alsaedi A (2017) A comparative study of Casson fluid with homogeneous-heterogeneous reactions. J Colloid Interface Sci 498:85–90CrossRef
Metadaten
Titel
Squeezing flow of second grade liquid subject to non-Fourier heat flux and heat generation/absorption
verfasst von
T. Hayat
M. Waleed Ahmed Khan
A. Alsaedi
M. Ijaz Khan
Publikationsdatum
18.04.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Colloid and Polymer Science / Ausgabe 6/2017
Print ISSN: 0303-402X
Elektronische ISSN: 1435-1536
DOI
https://doi.org/10.1007/s00396-017-4089-6

Weitere Artikel der Ausgabe 6/2017

Colloid and Polymer Science 6/2017 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.