Journal of Thermal Analysis and Calorimetry

, Volume 136, Issue 3, pp 1433–1445 | Cite as

Analysis of the effects of inclination angle, nanoparticle volume fraction and its size on forced convection from an inclined elliptic cylinder in aqueous nanofluids

  • Chandi SasmalEmail author


In this work, a detailed numerical investigation has been carried out to study the forced convection heat transfer from an inclined elliptic cylinder of a fixed aspect ratio of 0.5 immersed in a streaming water-based Al2O3 nanofluid using the two-phase Buongiorno’s model. In particular, this study presents extensive numerical results on how the cylinder inclination angle, nanoparticle volume fraction and its size are going to influence the local flow, temperature and nanoparticle concentration fields in the vicinity of the cylinder surface as well as the gross engineering parameters like the drag coefficient and Nusselt number over the following ranges of conditions as: Reynolds number, \(0.01 \le Re \le 40\); cylinder inclination angle, \(0 \le \lambda \le 90\); nanoparticle volume fraction, \(0 \le \phi \le 0.06\) and two nanoparticle sizes (dnp), namely 30 nm and 60 nm. It has been found that both the Nusselt number and drag force increase with \(\phi\), but decrease with dnp under otherwise identical conditions. On the other hand, at a particular value of Re, \(\phi\) and dnp, the value of the average Nusselt number increases with the increasing values of \(\lambda\), whereas the value of the drag coefficient decreases. Finally, from an application standpoint, a simple analytical formula for the average Nusselt number is provided as a function of Re, \(\phi\) and \(\lambda\) which will facilitate the interpolation of the present results for the intermediate values of these governing parameters.


Nanofluids Elliptic cylinder Forced convection Buongiorno’s model Inclination angle 

List of symbols


Semi-minor axis (m)


Semi-major axis (m)


Aspect ratio of the cylinder (= a/b), dimensionless


Specific heat capacity of base fluid (J kg−1 K−1)


Specific heat capacity of nanoparticle (J kg−1 K−1)


Specific heat capacity of nanofluid (J kg−1 K−1)


Total drag coefficient, dimensionless


Diameter of the outer domain (m)


Diameter of the nanoparticle (nm)


Total drag force (N)


Heat transfer coefficient (W m−2 K−1)


Thermal conductivity of base fluid (W m−1 K−1)


Thermal conductivity of nanoparticle (W m−1 K−1)


Thermal conductivity of nanofluid, (W m−1 K−1)


Unit normal vector, dimensionless


Local Nusselt number, dimensionless


Average Nusselt number, dimensionless


Pressure, dimensionless


Prandtl number, dimensionless


Reynolds number, dimensionless


Surface area of the cylinder, m2


Temperature, K


Temperature difference, (= Tw − T), K


Velocity vector, dimensionless


Velocity at the inlet (ms−1)

List of Greek symbols


Boltzmann constant (m2 kg s−2 K−1)


Density of base fluid (kg m−3)


Density of nanoparticle (kg m−3)


Density of nanofluid (kg m−3)


Viscosity of base fluid (Pa s)


Viscosity of nanofluid (Pa s)


Temperature, dimensionless


Volume fraction of nanoparticle, dimensionless



Condition at the cylinder surface

Condition corresponds to far away from the cylinder surface


Base fluid






  1. 1.
    Zukauskas A. Heat transfer from tubes in crossflow. Adv Heat Transf. 1972;8:93–160.CrossRefGoogle Scholar
  2. 2.
    Morgan VT. The overall convective heat transfer from smooth circular cylinders. Adv Heat Transf. 1975;11:199–264.CrossRefGoogle Scholar
  3. 3.
    Chhabra RP. Fluid flow and heat transfer from circular and non-circular cylinders submerged in non-Newtonian liquids. Adv Heat Transf. 2011;43:289–417.CrossRefGoogle Scholar
  4. 4.
    Choi SUS, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. ASME. 1995;231:99–106.Google Scholar
  5. 5.
    Huminic G, Huminic A. Application of nanofluids in heat exchangers: a review. Renew Sustain Energy Rev. 2012;16:5625–38.CrossRefGoogle Scholar
  6. 6.
    Saidur R, Leong KY, Mohammad HA. A review on applications and challenges of nanofluids. Renew Sustain Energy Rev. 2011;15:1646–68.CrossRefGoogle Scholar
  7. 7.
    Rashidi S, Mahian O, Languri EM. Applications of nanofluids in condensing and evaporating systems. J Therm Anal Calorim. 2018;131(3):2027–39.CrossRefGoogle Scholar
  8. 8.
    Das SK, Choi SU, Yu W, Pradeep T. Nanofluids: science and technology. New York: Wiley; 2007.CrossRefGoogle Scholar
  9. 9.
    Khan WA, Culham RJ, Yovanovich MM. Fluid flow around and heat transfer from elliptical cylinders: analytical approach. J Thermophys Heat Transf. 2005;19:178–85.CrossRefGoogle Scholar
  10. 10.
    Ota T, Nishiyama H, Taoka Y. Heat transfer and flow around an elliptic cylinder. Int J Heat Mass Transf. 1984;27:1771–9.CrossRefGoogle Scholar
  11. 11.
    D’alessio SJD, Dennis SCR. Steady laminar forced convection from an elliptic cylinder. J Eng Math. 1995;29(2):181–93.CrossRefGoogle Scholar
  12. 12.
    Badr HM. Forced convection from a straight elliptical tube. Heat Mass Transf. 1998;34(2):229–36.CrossRefGoogle Scholar
  13. 13.
    Patel SA, Chhabra RP. Forced convection from an inclined elliptical cylinder with constant heat flux: effect of Prandtl number. New Delhi: Springer; 2017.Google Scholar
  14. 14.
    Patel SA, Chhabra RP. Effect of the angle of incidence on laminar forced convection from an elliptical cylinder in Bingham plastic fluids. Num Heat Transf Part A Appl. 2016;70(8):917–37.CrossRefGoogle Scholar
  15. 15.
    Patel SA, Chhabra RP. Heat transfer in Bingham plastic fluids from a heated elliptical cylinder. Int J Heat Mass Transf. 2014;73:671–92.CrossRefGoogle Scholar
  16. 16.
    Bharti RP, Sivakumar P, Chhabra RP. Forced convection heat transfer from an elliptical cylinder to power-law fluids. Int J Heat Mass Transf. 2008;51(7):1838–53.CrossRefGoogle Scholar
  17. 17.
    Sasmal C. Effects of axis ratio, nanoparticle volume fraction and its size on the momentum and heat transfer phenomena from an elliptic cylinder in water-based CuO nanofluids. Powder Technol. 2017;313:272–86.CrossRefGoogle Scholar
  18. 18.
    Selvakumar RD, Dhinakaran S. Nanofluid flow and heat transfer around a circular cylinder: a study on effects of uncertainties in effective properties. J Mol Liq. 2016;223:572–88.CrossRefGoogle Scholar
  19. 19.
    Valipour MS, Ghadi AZ. Numerical investigation of fluid flow and heat transfer around a solid circular cylinder utilizing nanofluid. Int Commun Heat Mass Transf. 2011;38:1296–304.CrossRefGoogle Scholar
  20. 20.
    Etminan-Farooji V, Ebrahimnia-Bajestan E, Niazmand H, Wongwises S. Uncon- fined laminar nanofluid flow and heat transfer around a square cylinder. Int J Heat Mass Transf. 2012;55:1475–85.CrossRefGoogle Scholar
  21. 21.
    Bovand M, Rashidi S, Esfahani JA. Enhancement of heat transfer by nanofluids and orientations of the equilateral triangular obstacle. Energy Convers Manag. 2015;97:212–23.CrossRefGoogle Scholar
  22. 22.
    Sasmal C, Nirmalkar N. Momentum and heat transfer characteristics from heated spheroids in water based nanofluids. Int J Heat Mass Transf. 2016;96:582–601.CrossRefGoogle Scholar
  23. 23.
    Behroyan I, Vanaki SM, Ganesan P, Saidur R. A comprehensive comparison of various CFD models for convective heat transfer of Al2O3 nanofluid inside a heated tube. Int Commun Heat Mass Transf. 2016;70:27–37.CrossRefGoogle Scholar
  24. 24.
    Kalteh M, Abbassi A, Saffar-Avval M, Harting J. Eulerian-Eulerian two-phase numerical simulation of nanofluid laminar forced convection in a microchannel. Int J Heat Fluid Flow. 2011;32(1):107–16.CrossRefGoogle Scholar
  25. 25.
    Kalteh M, Abbassi A, Saffar-Avval M, Frijns A, Darhuber A, Harting J. Experimental and numerical investigation of nanofluid forced convection inside a wide microchannel heat sink. Appl Therm Eng. 2012;36:260–8.CrossRefGoogle Scholar
  26. 26.
    Toosi MH, Siavashi M. Two-phase mixture numerical simulation of natural convection of nanofluid flow in a cavity partially filled with porous media to enhance heat transfer. J Mol Liq. 2017;238:553–69.CrossRefGoogle Scholar
  27. 27.
    Alinia M, Ganji DD, Gorji-Bandpy M. Numerical study of mixed convection in an inclined two-sided lid driven cavity filled with nanofluid using two-phase mixture model. Int Commun Heat Mass Transf. 2011;38(10):1428–35.CrossRefGoogle Scholar
  28. 28.
    Kumar N, Puranik BP. Numerical study of convective heat transfer with nanofluids in turbulent flow using a Lagrangian-Eulerian approach. Appl Therm Eng. 2017;111:1674–81.CrossRefGoogle Scholar
  29. 29.
    Mirzaei M, Saffar-Avval M, Naderan H. Heat transfer investigation of laminar developing flow of nanofluids in a microchannel based on Eulerian–Lagrangian approach. Can J Chem Eng. 2014;92(6):1139–49.CrossRefGoogle Scholar
  30. 30.
    Buongiorno J. Convective transport in nanofluids. J Heat Transf. 2006;128(3):240–50.CrossRefGoogle Scholar
  31. 31.
    Sheremet MA, Pop I. Free convection in a porous horizontal cylindrical annulus with a nanofluid using Buongiorno’s model. Comput Fluids. 2015;118:182–90.CrossRefGoogle Scholar
  32. 32.
    Motlagh SY, Soltanipour H. Natural convection of al 2 o 3-water nanofluid in an inclined cavity using Buongiorno’s two-phase model. Int J Therm Sci. 2017;111:310–20.CrossRefGoogle Scholar
  33. 33.
    Sheremet MA, Groşan T, Pop I. Steady-state free convection in right-angle porous trapezoidal cavity filled by a nanofluid: Buongiorno’s mathematical model. Eur J Mech B/Fluids. 2015;53:241–50.CrossRefGoogle Scholar
  34. 34.
    Garoosi F, Garoosi S, Hooman K. Numerical simulation of natural convection and mixed convection of the nanofluid in a square cavity using Buongiorno model. Powder Technol. 2014;268:279–92.CrossRefGoogle Scholar
  35. 35.
    Alsabery AI, Armaghani T, Chamkha AJ, Hashim I. Conjugate heat transfer of Al2O3–water nanofluid in a square cavity heated by a triangular thick wall using Buongiorno’s two-phase model. J Therm Anal Calorim. 2018. Scholar
  36. 36.
    Moshizi SA, Malvandi A. Different modes of nanoparticle migration at mixed convection of al 2 o 3–water nanofluid inside a vertical microannulus in the presence of heat generation/absorption. J Therm Anal Calorim. 2016;126(3):1947–62.CrossRefGoogle Scholar
  37. 37.
    Esfe MH, Saedodin S, Malekshah EH, Babaie A, Rostamian H. Mixed convection inside lid-driven cavities filled with nanofluids. J Therm Anal Calorim. 2018. Scholar
  38. 38.
    Selimefendigil F, Ismael MA, Chamkha AJ. Mixed convection in superposed nanofluid and porous layers in square enclosure with inner rotating cylinder. Int J Mech Sci. 2017;124:95–108.CrossRefGoogle Scholar
  39. 39.
    Selimefendigil F, Oztop HF, Chamkha AJ. Analysis of mixed convection of nanofluid in a 3d lid-driven trapezoidal cavity with flexible side surfaces and inner cylinder. Int Commun Heat Mass Transf. 2017;87:40–51.CrossRefGoogle Scholar
  40. 40.
    Selimefendigil F, Oztop HF. Conjugate natural convection in a nanofluid filled partitioned horizontal annulus formed by two isothermal cylinder surfaces under magnetic field. Int J Heat Mass Transf. 2017;108:156–71.CrossRefGoogle Scholar
  41. 41.
    Shehzad N, Zeeshan A, Ellahi R, Vafai K. Convective heat transfer of nanofluid in a wavy channel: Buongiorno’s mathematical model. J Mol Liq. 2016;222:446–55.CrossRefGoogle Scholar
  42. 42.
    Heyhat MM, Kowsary F. Effect of particle migration on flow and convective heat transfer of nanofluids flowing through a circular pipe. J Heat Transf. 2010;132(6):062401.CrossRefGoogle Scholar
  43. 43.
    Alvariño PF, Jabardo JMS, Arce A, Galdo ML. A numerical investigation of laminar flow of a water/alumina nanofluid. Int J Heat Mass Transf. 2013;59:423–32.CrossRefGoogle Scholar
  44. 44.
    Alvarino PF, Jabardo JMS, Arce A, Galdo ML. Heat transfer enhancement in nanofluids. A numerical approach. J Phys Conf Ser. 2012;395(1):012116.CrossRefGoogle Scholar
  45. 45.
    Selimefendigil F, Oztop HF. Forced convection and thermal predictions of pulsating nanofluid flow over a backward facing step with a corrugated bottom wall. Int J Heat Mass Transf. 2017;110:231–47.CrossRefGoogle Scholar
  46. 46.
    Pak BC, Cho YI. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transf. 1998;11:151–70.CrossRefGoogle Scholar
  47. 47.
    Xuan Y, Roetzel W. Conceptions for heat transfer correlation of nanofluids. Int J Heat Mass Transf. 2000;43:3701–7.CrossRefGoogle Scholar
  48. 48.
    Corcione M. Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids. Energy Convers Manag. 2011;52(1):789–93.CrossRefGoogle Scholar
  49. 49.
    Park JK, Park SO, Hyun JM. Flow regimes of unsteady laminar flow past a slender elliptic cylinder at incidence. Int J Heat Fluid Flow. 1989;10:311–7.CrossRefGoogle Scholar
  50. 50.
    Ghanbarpour M, Haghigi EB, Khodabandeh R. Thermal properties and rheo- logical behavior of water based Al2O3 nanofluid as a heat transfer fluid. Exp Therm Fluid Sci. 2014;53:227–35.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Department of Chemical EngineeringIndian Institute of TechnologyRoparIndia

Personalised recommendations