Abstract
Nanofluids have the ability to flow smoothly in micro-cavities in addition with scattering of the nanoparticles. Because of the good convection between nanoparticles and the base fluid, nanofluids can achieve a good thermal conductivity. The main advantages of adding nanosize particles with base fluid are to improve the ability of storing heat, effective surface area, heat transmission, collisions and interaction among the nanoparticles. The main aim of this research work is to examine the steady and incompressible nanofluid flow between parallel rotating plates. Viscose and joule dissipation effects are taken into account. To our knowledge, impact of electrical MHD and Hall effect with Cattaneo–Christov heat flux on the squeezing 3-D flow nanofluid between parallel rotating plates are not examined yet. Heat in the form of Cattaneo–Christov heat flux is applied. We used similarity transformations to transform the primary equations to a system of ordinary differential equations (ODEs). These ODEs are then solved through the standard procedure of homotopy analysis technique. The skin friction and Nusselt number are numerically tabulated under the influence of some focused parameters. The effects produced by different parameters on the velocity (components) and temperature profiles are graphically depicted and explained in a bit detail.
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- \(A_{1},A_{2},A_{3},A_{4}\) :
-
Nanofluid constants
- \(\hbox{Nu}_{{\mathrm{x}}}\) :
-
Local Nusselt number
- \(\hbox{Re}_{{\mathrm{x}}}\) :
-
Local Reynolds number \(\delta\) Suction parameter
- \(\gamma\) :
-
Thermal relaxation parameter
- \(C_{{\mathrm{f}}}\) :
-
Skin friction coefficient
- \(\rho\) :
-
Density (\(\hbox{kg}\,\hbox{m}^{-3}\))
- \(C_{{\mathrm{p}}}\) :
-
Specific heat (\(\hbox{J}\,{\hbox{kg}^{-1}\,\hbox{K}^{-1}}\))
- \(f, g, \theta\) :
-
Dimensionless velocities
- \(\sigma _{{\mathrm{nf}}}\) :
-
Electrical conductivity of nanofluid
- \(k^{\star }\) :
-
Mean absorption coefficient
- \(k_{{\mathrm{nf}}}\) :
-
Nanofluid thermal conductivity
- \(E_{{\mathrm{I}}}\) :
-
Electric field parameter
- \(\alpha\) :
-
Rotation parameter
- \(\kappa\) :
-
Vortex viscosity
- \(\lambda\) :
-
Heat flux relaxation
- \(\mu _{{\mathrm{f}}}\) :
-
Base fluid dynamic viscosity
- \(\infty\) :
-
Condition at infinity
- x, y and z :
-
Coordinates m
- B :
-
Magnetic parameter T
- \(P_{{\mathrm{r}}}\) :
-
Prandtl number
- \(\beta\) :
-
Squeezing parameter
- \(U_{{\mathrm{w}}}\) :
-
Stretching velocity (\(\hbox{m}\,\hbox{s}^{-1}\))
- T :
-
Fluid temperature (K)
- \(\mu\) :
-
Dynamic viscosity (mPa)
- E :
-
Electric field (\(\hbox{N}\,\hbox{C}^{-1}\))
- t :
-
Time (s)
- M :
-
Magnetic parameter Teslas
- \(E_{{\mathrm{c}}}\) :
-
Eckert numbers
- \(k_{{\mathrm{f}}}\) :
-
Base fluid thermal conductivity
- m :
-
Hall parameters
- \(\varphi\) :
-
volume fraction
- \(\zeta\) :
-
Independent variable
- S :
-
Suction injection parameter
- \(\mu _{{\mathrm{nf}}}\) :
-
Nanofluid fluid dynamic viscosity
- 0:
-
Reference condition
- \(B_{0}\) :
-
Magnetic field strength
References
Siddiqui AM, Irum S, Ansari AR. Unsteady squeezing flow of a viscous MHD fluid between parallel plates, a solution using the homotopy perturbation method. Math Model Anal. 2008;13(4):565–76.
Mustafa M, Hayat T, Obaidat S. On heat and mass transfer in the unsteady squeezing flow between parallel plates. Meccanica. 2012;47(7):1581–9.
Joneidi A, Domairry G, Babaelahi M. Effect of mass transfer on a flow in the magnetohydrodynamic squeeze film between two parallel disks with one porous disk. Chem Eng Commun. 2010;198(3):299–311.
Hayat T, Yousaf A, Mustafa M, Asghar S. Influence of heat transfer in the squeezing flow between parallel disks. Chem Eng Commun. 2012;199(8):1044–62.
Khan U, Ahmed N, Khan SI, Zaidi ZA, Xiao-Jun Y, Mohyud-Din ST. On unsteady two-dimensional and axisymmetric squeezing flow between parallel plates. Alex Eng J. 2014;53(2):463–8.
Khan U, Ahmed N, Zaidi Z, Asadullah M, Mohyud-Din ST. MHD squeezing flow between two infinite plates. Ain Shams Eng J. 2014;5(1):187–92.
Khan SI, Ahmed N, Khan U, Jan SU, Mohyud-Din S. Heat transfer analysis for squeezing flow between parallel disks. J Egypt Math Soc. 2015;23(2):445–50.
Stefan J. Versuche iiber die scheinbare adhesion. K. Akad. Wissenschaften, Math. Naturwissenchaftliche Klasse, Wien, Sitzungsberichte. 1874;69(1874):713.
Chamkha AJ. Thermal radiation and buoyancy effects on hydromagnetic flow over an accelerating permeable surface with heat source or sink. Int J Eng Sci. 2000;38(15):1699–712.
Israel-Cookey C, Ogulu A, Omubo-Pepple V. Influence of viscous dissipation and radiation on unsteady MHD free-convection flow past an infinite heated vertical plate in a porous medium with time-dependent suction. Int J Heat Mass Transf. 2003;46(13):2305–11.
Mbeledogu I, Ogulu A. Heat and mass transfer of an unsteady MHD natural convection flow of a rotating fluid past a vertical porous flat plate in the presence of radiative heat transfer. Int J Heat Mass Transf. 2007;50(9–10):1902–8.
Jha BK. MHD free-convection and mass-transform flow through a porous medium. Astrophys Space Sci. 1991;175(2):283–9.
Agrawal H, Ram P, Singh V. Effects of hall current on the hydromagnetic free convection with mass transfer in a rotating fluid. Astrophys Space Sci. 1984;100(1–2):279–86.
Singh A, Sacheti NC. Finite difference analysis of unsteady hydromagnetic free-convection flow with constant heat flux. Astrophys Space Sci. 1988;150(2):303–8.
Animasaun L, Koriko OK, Adegbie KS, Babatunde HA, Ibraheem RO, Sandeep N, Mahanthesh B. Comparative analysis between 36 nm and 47 nm alumina-water nanofluid flows in the presence of Hall effect. J Therm Anal Calorim. 2019;135:87386.
Chamkha AJ. Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption. Int J Eng Sci. 2004;42(2):217–30.
Sheikholeslami M, Ganji D. Heat transfer of cu–water nanofluid flow between parallel plates. Powder Technol. 2013;235:873–9.
Tsou F, Sparrow EM, Goldstein RJ. Flow and heat transfer in the boundary layer on a continuous moving surface. Int J Heat Mass Transf. 1967;10(2):219–35.
Crane LJ. Flow past a stretching plate. Zeitschrift für angewandte Mathematik und Physik ZAMP. 1970;21(4):645–7.
Subramanian R, Senthil Kumar A, Vinayagar K, Muthusamy C. Experimental analyses on heat transfer performance of TiO2water nanofluid in double-pipe counter-flow heat exchanger for various flow regimes. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08887-1.
Gupta P, Gupta A. Heat and mass transfer on a stretching sheet with suction or blowing. Can J Chem Eng. 1977;55(6):744–6.
Khan W, Pop I. Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf. 2010;53(11–12):2477–83.
Abolbashari MH, Freidoonimehr N, Nazari F, Rashidi MM. Entropy analysis for an unsteady MHD flow past a stretching permeable surface in nano-fluid. Powder Technol. 2014;267:256–67.
Mishra S, Bhatti M. Simultaneous effects of chemical reaction and ohmic heating with heat and mass transfer over a stretching surface: a numerical study. Chin J Chem Eng. 2017;25(9):1137–42.
Domairry G, Aziz A. Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by homotopy perturbation method. Math Prob Eng. 2009;2009:1–19.
Hamza E. The magnetohydrodynamic effects on a fluid film squeezed between two rotating surfaces. J Phys D Appl Phys. 1991;24(4):547.
Hamza E, MacDonald D. A fluid film squeezed between two parallel plane surfaces. J Fluid Mech. 1981;109:147–60.
Sha Z, Dawar A, Alzahrani EO, Kumam P, Khan AJ, Islam S. Hall effect on couple stress 3D nanofluid flow over an exponentially stretched surface with cattaneo christov heat flux model. IEEE Access. 2019;7:64844–55.
Vo DD, Shah Z, Sheikholeslami M, Shafee A, Nguyen TK. Numerical investigation of MHD nanomaterial convective migration and heat transfer within a sinusoidal porous cavity. Phys Scr. 2019;94(11):115225.
Shah Z, Dawar A, Kumam P, Khan W, Islam S. Impact of nonlinear thermal radiation on MHD nanofluid thin film flow over a horizontally rotating disk. Appl Sci. 2019;9(8):1533.
Ameen I, Shah Z, Islam S, Nasir S, Khan W, Kumam P, Thounthong P. Hall and ion-slip effect on cnts nanofluid over a porous extending surface through heat generation and absorption. Entropy. 2019;21(8):801.
Rashidi MM, Shahmohamadi H, Dinarvand S. Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates. Math Prob Eng. 2008;2008:1–12.
Ahmad Farooq A, Shah Z, Alzahrani EO. Heat transfer analysis of a magneto-bio-fluid transport with variable thermal viscosity through a vertical ciliated channel. Symmetry. 2019;11(10):1240.
Alsaadi FE, Ullah I, Hayat T, Alsaadi FE. Entropy generation in nonlinear mixed convective flow of nanofluid in porous space influenced by Arrhenius activation energy and thermal radiation. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08648-0.
Acknowledgements
This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah under grant no. (RG-85-130-38). The authors, therefore, acknowledge with thanks DSR for technical and financial support.
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Shah, Z., Alzahrani, E.O., Alghamdi, W. et al. Influences of electrical MHD and Hall current on squeezing nanofluid flow inside rotating porous plates with viscous and joule dissipation effects. J Therm Anal Calorim 140, 1215–1227 (2020). https://doi.org/10.1007/s10973-019-09176-7
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DOI: https://doi.org/10.1007/s10973-019-09176-7