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Thermally radiated squeezed flow of magneto-nanofluid between two parallel disks with chemical reaction

  • Ikram Ullah
  • Muhammad Waqas
  • Tasawar Hayat
  • Ahmed Alsaedi
  • M. Ijaz Khan
Article

Abstract

This research is exhibited to visualize the squeezed flow of magneto-nanoliquid between two parallel disks. Transportations of heat and mass are characterized through thermal radiation and chemical reaction. Suitable similarity variables lead to dimensionless problem. The homotopic technique is adopted to find out the solutions. Behavior of sundry variables is declared graphically. Physical quantities of curiosity such as skin friction and Nusselt number at both disks are estimated and elaborated. Our investigation depicts that thermal field is augmented via radiation and Brownian diffusion variables. Besides, comparative table is also designed to validate our present outcomes with previous limiting study.

Keywords

Thermal radiation Squeezing flow Nanoparticles Parallel disks Chemical reaction 

List of symbols

u, v, w

Velocity components

x, r, z

Space coordinates

T

Temperature

Th

Upper-disk temperature

K

Second-grade parameter

B0

Uniform magnetic field strength

K1

Reaction rate

DB

Brownian diffusion coefficient

DT

Thermophoretic diffusion coefficient

kf

Thermal conductivity

α*

Thermal diffusivity

α1

Normal stress moduli

w0

Suction/blowing velocity

S

Suction/blowing parameter

Nb

Brownian motion parameter

Nt

Thermophoresis parameter

Derivative via η

f

Dimensionless velocity

θ

Dimensionless temperature

ϕ

Dimensionless concentration

Sq

Squeezing parameter

γ

Chemical reaction parameter

\({\mathcal{L}}_{\text{f}} ,{\mathcal{L}}_{\uptheta} ,{\mathcal{L}}_{\upphi}\)

Linear operator

M

Magnetic parameter

qr

Radiative heat flux

Le

Lewis number

Pr

Prandtl number

Cf0, Cf1

Skin friction at lower and upper disks

Nu0, Nu1

Nusselt number at lower and upper disks

Sh0, Sh1

Sherwood number at lower and upper disks

Rd

Radiation parameter

σ

Electrical conductivity

υ

Kinematic viscosity

ρf

Nanofluid density

η

Transformed coordinate

cp

Specific heat at constant pressure

Rer

Local Reynolds number

μ

Dynamic viscosity

(ρc)f

Fluid heat capacity

p

Pressure

(ρc)p

Nanoparticles effective heat capacity

Nf, Nθ, Nϕ

Nonlinear operators

\(B_{\text{i}}^{ * }\) = (i = 1–8)

Constants

\(\hbar_{\text{f}} ,\hbar_{\uptheta} ,\hbar_{\upphi}\)

Nonzero auxiliary parameters

σ1

Stefan–Boltzmann constant

m1

Mean absorption coefficient

References

  1. 1.
    Stefan MJ. Versuch Uber die scheinbare adhesion, Akademie der Wissenschaften in Wien. Mathematik-Naturwissen. 1874;69:713.Google Scholar
  2. 2.
    Kuzma DC. Fluid inertia effects in squeeze films. Appl Sci Res. 1967;18:15–20.CrossRefGoogle Scholar
  3. 3.
    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;13:565–76.CrossRefGoogle Scholar
  4. 4.
    Sweet E, Vajravelu K, Van Gorder RA, Pop I. Analytical solution for the unsteady MHD flow of a viscous fluid between moving parallel plates. Commun Nonlinear Sci Numer Simul. 2011;16:266–73.CrossRefGoogle Scholar
  5. 5.
    Khan H, Qayyum M, Khan O, Ali M. Unsteady squeezing flow of Casson fluid with magnetohydrodynamic effect and passing through porous medium. Math Probl Eng. 2016;2016:4293721.CrossRefGoogle Scholar
  6. 6.
    Kumar KG, Gireesha BJ, Krishanamurthy MR, Rudraswamy NG. An unsteady squeezed flow of a tangent hyperbolic fluid over a sensor surface in the presence of variable thermal conductivity. Results Phys. 2017;7:3031–6.CrossRefGoogle Scholar
  7. 7.
    Adesanya SO, Ogunseye HA, Jangili S. Unsteady squeezing flow of a radiative Eyring–Powell fluid channel flow with chemical reactions. Int J Therm Sci. 2018;125:440–7.CrossRefGoogle Scholar
  8. 8.
    Balazadeh N, Sheikholeslami M, Ganji DD, Li Z. Semi analytical analysis for transient Eyring–Powell squeezing flow in a stretching channel due to magnetic field using DTM. J Mol Liq. 2018;260:30–6.CrossRefGoogle Scholar
  9. 9.
    Buongiorno J. Convective transport in nanofluids. ASME J Heat Transf. 2006;128:240–50.CrossRefGoogle Scholar
  10. 10.
    Akbarzadeh P. The analysis of MHD blood flows through porous arteries using a locally modified homogenous nanofluids model. Bio-Med Mater Eng. 2016;27:15–28.CrossRefGoogle Scholar
  11. 11.
    Hayat T, Waqas M, Shehzad SA, Alsaedi A. A model of solar radiation and Joule heating in magnetohydrodynamic (MHD) convective flow of thixotropic nanofluid. J Mol Liq. 2016;215:704–10.CrossRefGoogle Scholar
  12. 12.
    Das K, Jana S, Acharya N. Slip effects on squeezing flow of nanofluid between two parallel disks. Int J Appl Mech Eng. 2016;21:5–20.CrossRefGoogle Scholar
  13. 13.
    Hayat T, Ullah I, Muhammad T, Alsaedi A, Shehzad SA. Three-dimensional flow of Powell–Eyring nanofluid with heat and mass flux boundary conditions. Chin Phys B. 2016;25:074701.CrossRefGoogle Scholar
  14. 14.
    Akbarzadeh P. A new exact-analytical solution for convective heat transfer of nanofluids flow in isothermal pipes. J Mech. 2017.  https://doi.org/10.1017/jmech.2017.99.Google Scholar
  15. 15.
    Hayat T, Ullah I, Muhammad T, Alsaedi A. Thermal and solutal stratification in mixed convection three-dimensional flow of an Oldroyd-B nanofluid. Results Phys. 2017;7:3797–805.CrossRefGoogle Scholar
  16. 16.
    Sobamowo MG, Akinshilo AT. On the analysis of squeezing flow of nanofluid between two parallel plates under the influence of magnetic field. Alex Eng J. 2017.  https://doi.org/10.1016/j.aej.2017.07.001.Google Scholar
  17. 17.
    Hayat T, Ullah I, Alsaedi A, Farooq M. MHD flow of Powell–Eyring nanofluid over a non-linear stretching sheet with variable thickness. Results Phys. 2017;7:189–96.CrossRefGoogle Scholar
  18. 18.
    Akbarzadeh P. A locally modified single-phase model for analyzing magnetohydrodynamic boundary layer flow and heat transfer of nanofluids over nonlinearly stretching sheet with chemical reaction. J Theor Appl Mech. 2018;56:81–94.CrossRefGoogle Scholar
  19. 19.
    Hayat T, Ullah I, Waqas M, Alsaedi A. Flow of chemically reactive magneto cross nanoliquid with temperature-dependent conductivity. Appl Nanosci. 2018.  https://doi.org/10.1007/s13204-018-0813-x.Google Scholar
  20. 20.
    Akbarzadeh P. The onset of MHD nanofluid convection between a porous layer in the presence of purely internal heat source and chemical reaction. J Therm Anal Calorim. 2018;131:2657–72.CrossRefGoogle Scholar
  21. 21.
    Bird RB, Armstrong RC, Hassager O. Dynamics of polymeric liquids: fluid mechanics, vol. 1. 2nd ed. New York: Wiley; 1987.Google Scholar
  22. 22.
    Hayat T, Khalid H, Waqas M, Alsaedi A, Ayub M. Homotopic solutions for stagnation point flow of third-grade nanoliquid subject to magnetohydrodynamics. Results Phys. 2017;7:4310–7.CrossRefGoogle Scholar
  23. 23.
    Hayat T, Ullah I, Alsaedi A, Waqas M, Ahmad B. Three-dimensional mixed convection flow of Sisko nanoliquid. Int J Mech Sci. 2017;133:273–82.CrossRefGoogle Scholar
  24. 24.
    Zaigham Zia QM, Ullah I, Waqas M, Alsaedi A, Hayat T. Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface. Results Phys. 2018;8:1275–82.CrossRefGoogle Scholar
  25. 25.
    Waqas M, Hayat T, Shehzad SA, Alsaedi A. Analysis of forced convective modified Burgers liquid flow considering Cattaneo–Christov double diffusion. Results Phys. 2018;8:908–13.CrossRefGoogle Scholar
  26. 26.
    Hayat T, Ullah I, Alsaedi A, Ahmad B. Modeling tangent hyperbolic nanoliquid flow with heat and mass flux conditions. Eur Phys J Plus. 2017;132:112.CrossRefGoogle Scholar
  27. 27.
    Waqas M, Hayat T, Shehzad SA, Alsaedi A. Transport of magnetohydrodynamic nanomaterial in a stratified medium considering gyrotactic microorganisms. Phys B. 2018;529:33–40.CrossRefGoogle Scholar
  28. 28.
    Cortell R. Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field. Int J Heat Mass Transf. 2006;49:1851–6.CrossRefGoogle Scholar
  29. 29.
    Hayat T, Zubair M, Waqas M, Alsaedi A, Ayub M. Application of non-Fourier heat flux theory in thermally stratified flow of second grade liquid with variable properties. Chin J Phys. 2017;55:230–41.CrossRefGoogle Scholar
  30. 30.
    Hayat T, Zubair M, Waqas M, Alsaedi A, Ayub M. Impact of variable thermal conductivity in doubly stratified chemically reactive flow subject to non-Fourier heat flux theory. J Mol Liq. 2017;234:444–51.CrossRefGoogle Scholar
  31. 31.
    Sheremet MA. Natural convection combined with thermal radiation in a square cavity filled with a viscoelastic fluid. Int J Numer Methods Heat Fluid Flow. 2018;28:624–40.CrossRefGoogle Scholar
  32. 32.
    Hayat T, Ullah I, Muhammad T, Alsaedi A. Radiative three-dimensional flow with Soret and Dufour effects. Int J Mech Sci. 2017;133:829–37.CrossRefGoogle Scholar
  33. 33.
    Reddy GJ, Kumar M, Umavathi JC, Sheremet MA. Transient entropy analysis for the flow of a second grade fluid over a vertical cylinder. Can J Phys. 2018.  https://doi.org/10.1139/cjp-2017-0672.Google Scholar
  34. 34.
    Liao SJ. On the homotopy analysis method for nonlinear problems. Appl Math Comput. 2004;147:499–513.Google Scholar
  35. 35.
    Hayat T, Waqas M, Shehzad SA, Alsaedi A. Effects of Joule heating and thermophoresis on stretched flow with convective boundary conditions. Sci Iran. 2014;21:682–92.Google Scholar
  36. 36.
    Hayat T, Ullah I, Alsaedi A, Asghar S. MHD stagnation-point flow of Sisko liquid with melting heat transfer and heat generation/absorption. J Therm Sci Eng Appl. 2018.  https://doi.org/10.1115/1.4040032.Google Scholar
  37. 37.
    Turkyilmazoglu M. An effective approach for evaluation of the optimal convergence control parameter in the homotopy analysis method. Filomat. 2016;30:1633–50.CrossRefGoogle Scholar
  38. 38.
    Hayat T, Qayyum S, Waqas M, Ahmed B. Influence of thermal radiation and chemical reaction in mixed convection stagnation point flow of Carreau fluid. Results in Physics. 2017;7:4058–4064.CrossRefGoogle Scholar
  39. 39.
    Waqas M, Hayat T, Farooq M, Shehzad SA, Alsaedi A. Cattaneo–Christov heat flux model for flow of variable thermal conductivity generalized Burgers fluid. J Mol Liq. 2016;220:642–8.CrossRefGoogle Scholar
  40. 40.
    Hayat T, Ullah I, Alsaedi A, Ahmad B. Simultaneous effects of non-linear mixed convection and radiative flow due to Riga-plate with double stratification. J Heat Transf. 2018.  https://doi.org/10.1115/1.4039994.Google Scholar
  41. 41.
    Hayat T, Jabeen S, Shafiq A, Alsaedi A. Radiative squeezing flow of second grade fluid with convective boundary conditions. PLoS ONE. 2016;11:e0152555.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Ikram Ullah
    • 1
  • Muhammad Waqas
    • 1
  • Tasawar Hayat
    • 1
    • 2
  • Ahmed Alsaedi
    • 2
  • M. Ijaz Khan
    • 1
  1. 1.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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