Advertisement

Effective Prandtl Number Model Influences on the \(\gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {H}}_2 {\hbox {O}}\) and \(\gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {C}}_2 {\hbox {H}}_6 {\hbox {O}}_2 \) Nanofluids Spray Along a Stretching Cylinder

  • Taza Gul
  • Saleem Nasir
  • Saeed Islam
  • Zahir Shah
  • M. Altaf Khan
Research Article - Mechanical Engineering

Abstract

The flow of common fluids (water, oils and ethylene glycol etc.) is diluted by adding different small particles of metals, and their oxides are more powerful to reduce the scientific issues related to quicker heat transfer. According to this indication, we have contemplated finite film of \(\gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {H}}_2 {\hbox {O}}\) and \(\gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {C}}_2 {\hbox {H}}_6 {\hbox {O}}_2 \) nanoliquid sprayed on an extending cylinder. In this scenario, uniform magnetic field \(B_0\) and constant reference temperature are employed on the stream of thin film nanofluid. The impact of effective Prandtl number, viscosity and thermal conductivity is derived from the experimental data (Sheikhzadeh et al. in J Appl Fluid Mech 10:209–219, 2017; Lee et al. in J Heat transf 121:280–289, 1992; Wang et al. in J Thermo Phys Heat Transf 13:474–480, 1999; Hamilton and Crosser in Ind Eng Chem Fundam 1:187–191, 1962; Maiga et al. in Super Lattices Microstruct 35:543–55, 2004; Hayat et al. in J Mol Liq. https://doi.org/10.1016/j.molliq.2018.06.029, 2018). The model problem is excellently converted into a set of proper self-comparable forms with the assistance of possible transformations. Analytical results of velocity and thermal profile are computed using homotopy analysis method for both \(\gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {H}}_2 {\hbox {O}}\) and \(\gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {C}}_2 {\hbox {H}}_6 {\hbox {O}}_2 \) nanoliquid. Furthermore, during coating analysis, rate of spray, pressure distribution, skin friction coefficient (surface drag force) \(C_{\mathrm{f}} \) and Nusselt number (the rate of heat transfer) Nu for both nanofluids are also intended. The impact of additional ingrained quantities like magnetic parameter M, volume fraction of nanoparticles \(\varphi \), Grashof number Gr, fluid thickness parameter \(\beta \), Prandtl number Pr and Reynolds number Re is portrayed numerically and graphically for both alumina particles. The key observation indicates that the temperature of \(\gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {C}}_2 {\hbox {H}}_6 {\hbox {O}}_2\) nanoliquid leading on \(\gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {H}}_2 {\hbox {O}}\) nanoliquid during the study. Due to greater viscosity and thermal conductivity, \({\hbox {C}}_2 {\hbox {H}}_6 {\hbox {O}}_2\)-based nanofluid is observed as upgraded common base fluid assimilated to \({\hbox {H}}_2\)O.

Keywords

Coating phenomena HAM MHD Nanofluid thin film Stretching cylinder \(\gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {H}}_2 {\hbox {O}}, \gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {C}}_2 {\hbox {H}}_6 {\hbox {O}}_2\) 

List of symbols

\(u, v \, w\)

Velocities components \(\left( {{\hbox {ms}}^{-1}} \right) \)

\(B_0 \)

Magnetic field strength \(\left( {{\hbox {NmA}}^{-1}} \right) \)

fg

Dimensional velocity profiles

T

Fluid temperature (K)

\(T_w \)

Cylinder surface temperature (K)

\(T_\delta \)

Free surface temperature (K)

M

Magnetic parameter

p

Pressure distribution

C

Stretching parameter

Pr

Prandtl number

Re

Local Reynolds number

Ec

Eckert number

Gr

Grashof number

Nu

Nusselt number

\(C_{\mathrm{f}}\)

Skin friction coefficient

\(W_w \)

Stretching velocity

\(U_w \)

Suction/injection speed

\(\left( {C_p } \right) _{\mathrm{f}}\)

Specific heat of base fluid \(\left( {\hbox {J/kgK}} \right) \)

\(k_{\mathrm{nf}}\)

Thermal conductivity (\({\hbox {Wm}}^{-1}K^{-1})\)

Greek symbols

\(\mu _{\mathrm{nf}}\)

Dynamic viscosity of nanofluid (mPa)

\(\beta _{\mathrm{nf}} \)

Thermal expansion coefficient

\(\rho _{\mathrm{nf}} \)

Nanofluid density (Kgm\(^{-3}\))

\(\upsilon _{\mathrm{nf}} \)

Kinematic Viscosity

\(\xi \)

Similarity variable

\(\varphi \)

Nanoparticle volume fraction

\(\Theta \)

Dimensional heat profiles

\(\sigma _{\mathrm{nf}} \)

Electrical conductivity

\(\beta \)

Non-dimensional thickness

\(\tau \)

Surface shear stress

h

Auxiliary constant

Open image in new window

Constant

Subscripts

nf

Nanofluid

f

Base fluid

s

Solid nanoparticles

Abbreviations

HAM

Homotopy asymptotic method

MHD

Magneto-hydrodynamics

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The authors are very thankful to the CUSIT and AWKUM for providing them with the opportunity of funding for this study.

Compliance with ethical standards

Competing Interests

The authors state that they have no competing interest.

Authors’ contributions

The model of the problem was designed by TG using the available data from the experimental approach of \(\gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {H}}_2 {\hbox {O}}\) and \(\gamma {\hbox {Al}}_2 {\hbox {O}}_3\)\({\hbox {C}}_2 {\hbox {H}}_6 {\hbox {O}}_2 \). TG and SN solved the problem, and SI, ZS and MAK participated in the results and discussion. All the authors read and approved the final manuscript.

References

  1. 1.
    Choi, S.U.S.: Enhancing thermal conductivity of fluids with nanoparticles in developments and applications of non-Newtonians flows. ASME 66, 99–105 (1995)Google Scholar
  2. 2.
    Saidur, R.; Leong, K.Y.; Mohammad, H.A.: A review on applications and challenges of nanofluids. Renew. Sustain. Energy Rev. 15, 1646–1668 (2011)CrossRefGoogle Scholar
  3. 3.
    Aliabadi, K.M.; Sahamiyan, M.: Performance of nanofluid flow in corrugated mini channels heat sink (CMCHS). Energy Convers. Manag. 108, 297–308 (2016)CrossRefGoogle Scholar
  4. 4.
    Li, X.; Zou, C.; Zhou, L.; Qi, A.: Experimental study on the thermo-physical properties of diathermic oil based SiC nanofluids for high temperature applications. Int. J. Heat Mass Transf. 97(63), 1–7 (2016)Google Scholar
  5. 5.
    Naik, M.T.; Sundar, L.S.: Investigation into thermophysical properties of glycol based CuO nanofluid for heat transfer applications. World Acad. Sci. Eng. Technol. 59, 440–446 (2011)Google Scholar
  6. 6.
    Khan, U.; Ahmed, N.; Mohy-ud-Din, S.T.: Numerical investigation for three dimensional squeezing flow of nanofluid in a rotating channel with lower stretching wall suspended by carbon nanotubes. Appl. Therm. Eng. 113, 1107–1117 (2017)CrossRefGoogle Scholar
  7. 7.
    Sow, T.M.O.; Halelfadl, S.; Lebourlout, S.; Nguyen, C.T.: Experimental study of the freezing point of c-Al\(_{2}\)O\(_{3}\) water nanofluid. Adv. Mech. Eng. 4, 162961 (2012)CrossRefGoogle Scholar
  8. 8.
    Maciver, D.S.; Tobin, H.H.; Barth, R.T.: Catalytic aluminas I. Surface chemistry of eta and gamma alumina. J. Catal. 2, 487–497 (1963)CrossRefGoogle Scholar
  9. 9.
    Alshomrani, A.S.; Gul, T.: A convective study of Al\(_{2}\)O\(_{3}\)–H\(_{2}\)O and Cu–H\(_{2}\)O nano-liquid films sprayed over a stretching cylinder with viscous dissipation. Eur. Phys. J. Plus 132(495), 1–16 (2017)Google Scholar
  10. 10.
    Nguyen, C.T.; Roy, G.; Gauthier, C.; Galanis, N.: Heat transfer enhancement using Al\(_{2}\)O\(_{3}\)–water nanofluid for an electronic liquid cooling system. Appl. Therm. Eng. 27, 1501–1506 (2007)CrossRefGoogle Scholar
  11. 11.
    Kulkarni, D.P.; Vajjha, R.S.; Das, D.K.; Oliva, D.: Application of aluminum oxide nanofluids in diesel electric generator as jacket water coolant. Appl. Therm. Eng. 28, 1774–1781 (2008)CrossRefGoogle Scholar
  12. 12.
    Zamzamian, A.; Oskouie, S.N.; Doosthoseini, A.; Joneidi, A.; Pazouki, M.: Experimental investigation of forced convective heat transfer coefficient in nanofluids of Al\(_{2}\)O\(_{3}\)/EG and CuO/EG in a double pipe and plate heat exchangers under turbulent flow. Exp. Therm. Fluid Sci. 35, 495–502 (2011)CrossRefGoogle Scholar
  13. 13.
    Sebdani, S.; Mahmoodi, M.; Hashemi, S.: Effect of nanofluid variable properties on mixed convection in a square cavity. Int. J. Therm. Sci. 52, 112–126 (2012)CrossRefGoogle Scholar
  14. 14.
    Rashidi, M.M.; Ganesh, V.N.; Abdul, H.A.K.; Ganga, B.; Lorenzini, G.: Influences of an effective Prandtl number model on nano boundary layer flow of \(\gamma \)Al\(_{2}\)O\(_{3}\)–H\(_{2}\)O and \(\gamma \)Al\(_{2}\)O\(_{3}\)–C\(_{2}\)H\(_{6}\)O\(_{2}\) over a vertical stretching sheet. Int. J. Heat Mass Transf. 98, 616–623 (2016)CrossRefGoogle Scholar
  15. 15.
    Ahmed, N.; Adnan, K.U.; Mohyud-Din, S.T.: Influence of an effective Prandtl number model on squeezed flow of \(\gamma \)Al\(_{2}\)O\(_{3}\)–H\(_{2}\)O and \(\gamma \)Al\(_{2}\)O\(_{3}\)–C\(_{2}\)H\(_{6}\)O\(_{2}\) nanofluids. J. Mol. Liq. 238, 447–454 (2017)CrossRefGoogle Scholar
  16. 16.
    Ahmed, N.; Adnan, K.U.; Mohyud-Din, S.T.: Theoretical investigation of unsteady thermally stratified flow of \(\gamma \)Al\(_{2}\)O\(_{3}\)–H\(_{2}\)O and \(\gamma \)Al\(_{2}\)O\(_{3}\)–C\(_{2}\)H\(_{6}\)O\(_{2}\) nanofluidsthrough a thin slit. J. Phys. Chem. Solids (2018).  https://doi.org/10.1016/j.jpcs.2018.01.046 CrossRefGoogle Scholar
  17. 17.
    Khan, U.; Adnan, A.N.; Mohyud-Din, S.T.: 3D squeezedflow of \(\gamma {\text{ Al }}_2 {\text{ O }}_3\)\({\text{ H }}_2 {\text{ O }}\) and \(\gamma {\text{ Al }}_2 {\text{ O }}_3\)\({\text{ C }}_2 {\text{ H }}_6 {\text{ O }}_2 \) nanofluids: a numerical study. Int. J. Hydrog. Energy 42(39), 24620 (2017).  https://doi.org/10.1016/j.ijhydene.2017.07.090 CrossRefGoogle Scholar
  18. 18.
    Pop, C.V.; Fohanno, S.; Polidori, G.; Nguyen, C.T.: Analysis oflaminar-to-turbulent threshold with water cAl\(_{2}\)O\(_{3}\) and ethyleneglycol-cAl\(_{2}\)O\(_{3}\) nanofluids in free convection. In: Proceedings of the 5th IASME/WSEAS Int. Conference on Heat Transfer, Thermal Engineering and Environment. pp. 188–194 (2007)Google Scholar
  19. 19.
    Sheikholeslami, M.; Gangi, D.D.; Ashorynejad, H.R.: Investigation of squeezing unstedy nanofluid flow using ADM. Powder Technol. 239, 259–265 (2013)CrossRefGoogle Scholar
  20. 20.
    Gul, A.; Khan, I.; Shafie, S.: Energy transfer in mixed convection MHD flow of nanofluid containing different shapes of nanoparticles in a channel filled with saturated porous medium. Nanoscale Res. Lett. 10, 490 (2015)CrossRefGoogle Scholar
  21. 21.
    Khan, N.S.; Gul, T.; Islam, S.; Khan, I.; Alqahtani, A.M.; Alshomrani, A.S.: Magneto-hydrodynamic nanoliquid thin film sprayed on a stretching cylinder with heat transfer. Appl. Sci. 7(271), 1–25 (2017)Google Scholar
  22. 22.
    Sheikholeslami, M.; Bhatti, M.M.: Active method for nanofluid heat transfer enhancement by means of EHD. Int. J. Heat Mass Transf. 109, 115–122 (2017)CrossRefGoogle Scholar
  23. 23.
    Sheikholeslami, M.; Rokni, H.B.: Magnetic nanofluid natural convection in the presence of thermal radiation considering variable viscosity. Eur. Phys. J. Plus 132, 238–245 (2017)CrossRefGoogle Scholar
  24. 24.
    Sheikholeslami, M.; Rokni, H.B.: Numerical modeling of nanofluid natural convection in a semi annulus in existence of Lorentz force. Comput. Methods Appl. Mech. Eng. 317, 419–430 (2017)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Shankar, B.; Yirga, Y.: Unsteady heat and mass transfer in MHD flow of nanofluids over stretching sheet with a non-uniform heat source/sink. Int. J. Math. Comput. Sci. Eng. 7, 1267–1275 (2013)Google Scholar
  26. 26.
    Nandy, S.K.; Mahapatra, T.R.: Effects of slip and heat generation/absorption on MHD stagnation flow of nanofluid past a stretching/shrinking surface with convective boundary conditions. Int. J. Heat Mass Transf. 64, 1091–1100 (2013)CrossRefGoogle Scholar
  27. 27.
    Rashidi, M.M.; Abelman, S.; Mehr, N.F.: Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid. Int. Heat Mass Transf. 62, 515–525 (2013)CrossRefGoogle Scholar
  28. 28.
    Babu, M.J.; Sandeep, N.: Three-dimensional MHD slip flow of nanofluids over a slandering stretching sheet with thermophoresis and Brownian motion effects. Adv. Powder Technol. 27, 2039–2050 (2016)CrossRefGoogle Scholar
  29. 29.
    Sheikholeslami, M.; Sadoughi, M.: Mesoscopic method for MHD nanofluid flow inside a porous cavity considering various shapes of nanoparticles. Int. J. Heat Mass Transf. 113, 106–114 (2017)CrossRefGoogle Scholar
  30. 30.
    Changdar, S.; De, S.: Analytical solution of mathematical model of MHD blood nanofluid flowing through an inclined multiple stenosed arteries. J. Nanofluids 6(6), 1198–1205 (2017)CrossRefGoogle Scholar
  31. 31.
    Sheikholeslami, M.; Shehzad, S.A.: Magnetohydrodynamic nanofluid convective flow in a porous enclosure by means of LBM. Int. J. Heat Mass Transf. 2017(113), 796–805 (2017)CrossRefGoogle Scholar
  32. 32.
    Sheikholeslami, M.; Shamlooei, M.: Fe\(_{3}\)O\(_{4}\)eH\(_{2}\)O nanofluid natural convection in presence of thermal radiation. Int. J. Hydrog. Energy 42(9), 5708–5718 (2017)CrossRefGoogle Scholar
  33. 33.
    Khan, Y.; Wua, Q.; Faraz, N.; Yildirim, A.: The effect of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet. Comput. Math Appl. 61, 3391–3399 (2011)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Khan, W.; Gul, T.; Idrees, M.; Islam, S.; Khan, I.; Dennis, L.C.C.: Thin film Williamson nanofluid flow with varying viscosity and thermal conductivity on a time-dependent stretching sheet. Appl. Sci. 6, 334–342 (2016)CrossRefGoogle Scholar
  35. 35.
    Ali, L.; Islam, S.; Gul, T.; Khan, I.; Dennis, L.C.C.; Khan, W.; Khan, A.: The Brownian and thermophoretic analysis of the non-Newtonian Williamson fluid flow of thin film in a porous space over an unstable stretching surface. Appl. Sci. 7, 404–412 (2017)CrossRefGoogle Scholar
  36. 36.
    Aziz, R.C.; Hashim, I.; Alomari, A.K.: Thin film flow and heat transfer on an unsteady stretching sheet with internal heating. Meccanica 46, 349–357 (2011)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Prashant, G.M.; Jagdish, T.; Abel, M.S.: Thin film flow and heat transfer on an unsteady stretching sheet with thermal radiation, internal heating in presence of external magnetic field. Phys. Fluid Dyn. 3, 1–6 (2016)MathSciNetGoogle Scholar
  38. 38.
    Fakour, M.; Rahbari, A.; Khodabandeh, E.; Ganji, D.D.: Nanofluid thin film flow and heat transfer over an unsteady stretching elastic sheet by LSM. J. Mech. Sci. Technol. 32(1), 177–183 (2018)CrossRefGoogle Scholar
  39. 39.
    Liang, Z.; Zhou, H.: Numerical simulation of the thin film coating flow in two-dimension. Open J. Fluid Dyn. 7, 330–339 (2017)CrossRefGoogle Scholar
  40. 40.
    Dandapat, B.S.; Singh, S.K.; Maity, S.: Thin film flow of bi-viscosity liquid over an unsteady stretching sheet, an analytical solution. Int. J. Mech. Sci. 130, 367–374 (2017)CrossRefGoogle Scholar
  41. 41.
    Sheikhzadeh, G.A.; Fakhar, M.M.; Khorasanizadeh, H.: Experimental investigation of laminar convection heat transfer of Al\(_{2}\)O\(_{3}\)-ethylene glycol–water nanofluid as a coolant in a car radiator. J. Appl. Fluid Mech. 10, 209–219 (2017)CrossRefGoogle Scholar
  42. 42.
    Lee, S.; Choi, S.U.S.; Li, S.; Eastman, J.A.: Measuring thermal conductivity of fluids containing oxide nanoparticles. J. Heat transfer. 121, 280–289 (1992)CrossRefGoogle Scholar
  43. 43.
    Wang, X.; Xu, X.; Choi, S.U.S.: Thermal conductivity of nanoparticles-fluid mixture. J. Thermo Phys. Heat Transf. 13, 474–480 (1999)CrossRefGoogle Scholar
  44. 44.
    Hamilton, R.L.; Crosser, O.K.: Thermal conductivity of heterogeneous two component systems. Ind. Eng. Chem. Fundam. 1, 187–191 (1962)CrossRefGoogle Scholar
  45. 45.
    Maiga, S.E.B.; Nguyen, C.T.; Galanis, N.; Roy, G.: Heat transfer behaviors of nanofluids in a uniformly heated tube. Super Lattices Microstruct. 35, 543–55 (2004)CrossRefGoogle Scholar
  46. 46.
    Hayat, T.; Shah, F.; Khan, M.I., Khan, M.I., Alsaedi, A.: Entropy analysis for comparative study of effective Prandtl number and without effective Prandtl number via \(\gamma {\rm Al\mathit{}_2 {\rm O}}_3\)\({\rm H\mathit{}_2 {\rm O}}\) and \(\gamma {\rm Al\mathit{}_2 {\rm O}}_3\)\({\rm C\mathit{}_2 {\rm H}}_6 {\rm O}_2\) nanoparticles. J. Mol. Liq. (2018).  https://doi.org/10.1016/j.molliq.2018.06.029 CrossRefGoogle Scholar
  47. 47.
    Liao, S.J.: An approximate solution technique which does not depend upon small parameters: a special example. Int. J. NonLinear. Mech. 32, 815–822 (1997)CrossRefGoogle Scholar
  48. 48.
    Liao, S.J.: On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 147, 499–513 (2007)MathSciNetzbMATHGoogle Scholar
  49. 49.
    Gul, T.; Ferdous, K.: The experimental study to examine the stable dispersion of the graphene nanoparticles and to look at the GO-H\(_{2}\)O nanofluid flow between two rotating disks. Appl. Nanosci. 8, 1711–1728 (2018)CrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of MathematicsCity University of Science and Information Technology (CUSIT)PeshawarPakistan
  2. 2.Department of MathematicsAbdul Wali Khan University MardanMardanPakistan

Personalised recommendations