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.
Similar content being viewed by others
Abbreviations
- \(u, v \, w\) :
-
Velocities components \(\left( {{\hbox {ms}}^{-1}} \right) \)
- \(B_0 \) :
-
Magnetic field strength \(\left( {{\hbox {NmA}}^{-1}} \right) \)
- f, g :
-
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 (\({\hbox {Wm}}^{-1}K^{-1})\)
- \(\mu _{\mathrm{nf}}\) :
-
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
- :
-
Constant
- nf:
-
Nanofluid
- f:
-
Base fluid
- s:
-
Solid nanoparticles
- HAM:
-
Homotopy asymptotic method
- MHD:
-
Magneto-hydrodynamics
References
Choi, S.U.S.: Enhancing thermal conductivity of fluids with nanoparticles in developments and applications of non-Newtonians flows. ASME 66, 99–105 (1995)
Saidur, R.; Leong, K.Y.; Mohammad, H.A.: A review on applications and challenges of nanofluids. Renew. Sustain. Energy Rev. 15, 1646–1668 (2011)
Aliabadi, K.M.; Sahamiyan, M.: Performance of nanofluid flow in corrugated mini channels heat sink (CMCHS). Energy Convers. Manag. 108, 297–308 (2016)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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
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
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)
Sheikholeslami, M.; Gangi, D.D.; Ashorynejad, H.R.: Investigation of squeezing unstedy nanofluid flow using ADM. Powder Technol. 239, 259–265 (2013)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Liang, Z.; Zhou, H.: Numerical simulation of the thin film coating flow in two-dimension. Open J. Fluid Dyn. 7, 330–339 (2017)
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)
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)
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)
Wang, X.; Xu, X.; Choi, S.U.S.: Thermal conductivity of nanoparticles-fluid mixture. J. Thermo Phys. Heat Transf. 13, 474–480 (1999)
Hamilton, R.L.; Crosser, O.K.: Thermal conductivity of heterogeneous two component systems. Ind. Eng. Chem. Fundam. 1, 187–191 (1962)
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)
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
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)
Liao, S.J.: On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 147, 499–513 (2007)
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)
Acknowledgements
The authors are very thankful to the CUSIT and AWKUM for providing them with the opportunity of funding for this study.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
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.
Rights and permissions
About this article
Cite this article
Gul, T., Nasir, S., Islam, S. et al. 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. Arab J Sci Eng 44, 1601–1616 (2019). https://doi.org/10.1007/s13369-018-3626-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13369-018-3626-z