Skip to main content
SpringerLink
Log in

The effects of buoyancy force on mixed convection heat transfer of MHD nanofluid flow and entropy generation in an inclined duct with separation considering Brownian motion effects

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

In this paper, an attempt is made to study the buoyancy force influences on the MHD mixed convection nanofluid flow and entropy generation over an inclined step in an inclined duct. This inclined step leads to the flow separation in duct and affects the hydrodynamic and thermal behaviors. Influences of Brownian motion on the effective viscosity and thermal conductivity of Cu-water nanofluid are considered. The second law of thermodynamics is used to calculate the entropy generation number that is an applied criterion to compute the flow irreversibility. The interaction effects of Grashof number \( \left( {0 \le Gr \le 10,000} \right) \), duct inclination angle \( \left( {0^\circ \le \beta \le 90^\circ } \right) \), Hartmann number \( \left( {0 \le Ha \le 60} \right) \) and concentration of \( Cu \) nanoparticles \( \left( {0 \le \phi \le 0.06} \right) \) on the flow pattern, heat transfer rates and the amount of flow irreversibility are studied with all details. The results show that the Hartmann number has a large influence on the trends of the fiction coefficient, Nusselt number and entropy generation number along the bottom wall. Also, the highest values of average friction coefficient and average Nusselt number occur in the absence of magnetic field and for the vertical duct with highest values of \( Gr \) and \( \phi \). In addition, an increase in the amounts of flow irreversibility is registered by enhancing the buoyancy force, magnetic field strength and nanoparticles concentration.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Abbreviations

B :

Magnetic field strength

\( C_{\text{f}} \) :

Friction coefficient

\( C_{\text{p}} \) :

Specific heat (J kg−1 K−1)

\( d_{\text{s}} \) :

Diameter of nanoparticle (nm)

H :

Duct height upstream of the step (m)

H :

Duct height downstream of the step (m)

Ha :

Hartmann number

K :

Thermal conductivity (W m−1 K−1)

L 1 :

Duct length upstream of the step (m)

L 2 :

Duct length downstream of the step (m)

\( Ns \) :

Entropy generation number

\( Nu \) :

Nusselt number

\( p \) :

Pressure (N m−2)

\( P \) :

Dimensionless pressure

Pr :

Prandtl number

Re :

Reynolds number

\( S_{\text{g}} \) :

Entropy generation rate

\( T \) :

Temperature (K)

\( T_{\text{Ave}} \) :

Average temperature (K)

\( X_{\text{r}} \) :

Length of the primary recirculation zone on the bottom wall (reattachment length)

\( X_{\text{S}} \) :

Length of the secondary recirculation zone on the top wall

\( \left( {u, v} \right) \) :

x- and y-components of velocity (m s−1)

\( \left( {U, V} \right) \) :

Dimensionless X- and Y-component of velocity

\( \beta \) :

Duct inclination angle

\( \phi \) :

Nanoparticles volume fraction

\( \mu \) :

Dynamic viscosity (N s m−2)

\( \rho \) :

Density (kg m−3)

\( \sigma \) :

Electrical conductivity

\( \varTheta \) :

Dimensionless temperature

\( \gamma \) :

Thermal expansion coefficient (K−1)

C:

Cold wall

f:

Fluid

H:

Heat transfer and hot wall

In:

Inlet section

M:

Magnetic field

nf:

Nanofluid

s:

Solid nanoparticles

t:

Total

V:

Viscous shear stresses

References

  1. Oztop HF, Al-Salem K, Pop I. MHD mixed convection in a lid-driven cavity with corner heater. Int J Heat Mass Transf. 2011;54:3494–504.

    Google Scholar 

  2. Shirvan KM, Mamourian M, Mirzakhanlari S, Moghiman M. Investigation on effect of magnetic field on mixed convection heat transfer in a ventilated square cavity. Procedia Engineering. 2015;127:1181–8.

    Google Scholar 

  3. Jha BK, Aina B, Ajiya AT. MHD natural convection flow in a vertical parallel plate microchannel. Ain Shams Eng J. 2015;6(1):289–95.

    Google Scholar 

  4. Sajjadi H, Kefayati GR. MHD turbulent and laminar natural convection in a square cavity utilizing lattice Boltzmann method. Heat Transfer Asian Res. 2016;45(8):795–814.

    Google Scholar 

  5. Rashidi S, Esfahani JA, Maskaniyan M. Applications of magnetohydrodynamics in biological systems-a review on the numerical studies. J Magn Magn Mater. 2017;439:358–72.

    CAS  Google Scholar 

  6. Babu MJ, Sandeep N, Saleem S. Free convective MHD Cattaneo-Christov flow over three different geometries with thermophoresis and Brownian motion. Alex Eng J. 2017;56(4):659–69.

    Google Scholar 

  7. Kumar MS, Sandeep N, Kumar BR, Saleem S. Effect of aligned magnetic field on MHD squeezing flow of Casson fluid between parallel plates. Defect Diffus Forum. 2018;384:1–11.

    Google Scholar 

  8. Sajjadi H, Delouei AA, Sheikholeslami M, Atashafrooz M, Succi S. Simulation of three dimensional MHD natural convection using double MRT lattice Boltzmann method. Phys A. 2019;515:474–96.

    CAS  Google Scholar 

  9. Sheikholeslami M, Ganji DD. Heat transfer of Cu–water nanofluid flow between parallel plates. Powder Technol. 2013;235:873–9.

    CAS  Google Scholar 

  10. Sidik NAC, Mohammed HA, Alawi OA, Samion S. A review on preparation methods and challenges of nanofluids. Int Commun Heat Mass Transfer. 2014;54:115–25.

    CAS  Google Scholar 

  11. Yang YT, Wang YH, Tseng PK. Numerical optimization of heat transfer enhancement in a wavy channel using nanofluids. Int Commun Heat Mass Transfer. 2014;51:9–17.

    CAS  Google Scholar 

  12. Rashidi S, Bovand M, Esfahani JA, Ahmadi G. Discrete particle model for convective AL2O3–water nanofluid around a triangular obstacle. Appl Therm Eng. 2016;100:39–54.

    CAS  Google Scholar 

  13. Sidik NAC, Yazid MNAWM, Samion S, Musa MN, Mamat R. Latest development on computational approaches for nanofluid flow modeling: Navier-Stokes based multiphase models. Int Commun Heat Mass Transf. 2016;74:114–24.

    Google Scholar 

  14. Bovand M, Rashidi S, Ahmadi G, Esfahani JA. Effects of trap and reflect particle boundary conditions on particle transport and convective heat transfer for duct flow—a two-way coupling of Eulerian-Lagrangian model. Appl Therm Eng. 2016;108:368–77.

    CAS  Google Scholar 

  15. Sheikholeslami M, Rokni HB. Free convection of CuO–H2O nanofluid in a curved porous enclosure using mesoscopic approach. Int J Hydrogen Energy. 2017;42(22):14942–9.

    CAS  Google Scholar 

  16. Maskaniyan M, Rashidi S, Esfahani JA. A two-way couple of Eulerian-Lagrangian model for particle transport with different sizes in an obstructed channel. Powder Technol. 2017;312:260–9.

    CAS  Google Scholar 

  17. Upadhyaa SM, Rajub CSK, Maheshac, Saleem S. Nonlinear unsteady convection on micro and nanofluids with Cattaneo-Christov heat flux. Results Phys. 2018;9:779–86.

    Google Scholar 

  18. Rashidi S, Mahian O, Languri EM. Applications of nanofluids in condensing and evaporating systems. J Therm Anal Calorim. 2018;131(3):2027–39.

    CAS  Google Scholar 

  19. Shah Z, Gul T, Islam S, Khan MA, Bonyah E, Hussain F, Mukhtar S, Ullah M. Three dimensional third grade nanofluid flow in a rotating system between parallel plates with Brownian motion and thermophoresis effects. Results in Physics. 2018;10:36–45.

    CAS  Google Scholar 

  20. Sheikholeslami M, Rokni HB. Numerical simulation for impact of Coulomb force on nanofluid heat transfer in a porous enclosure in presence of thermal radiation. Int J Heat Mass Transf. 2018;118:823–31.

    CAS  Google Scholar 

  21. Nasiri H, Jamalabadi MYA, Sadeghi R, Safaei MR, Nguyen TK, Shadloo MS. A smoothed particle hydrodynamics approach for numerical simulation of nano-fluid flows. Journal of Thermal Analysis and Calorimetry. 2019. https://doi.org/10.1007/s10973-018-7022-4.

    Article  Google Scholar 

  22. Rashidi S, Karimi N, Mahian O, Esfahani JA. A concise review on the role of nanoparticles upon the productivity of solar desalination systems. J Therm Anal Calorim. 2019;135(2):1145–59.

    CAS  Google Scholar 

  23. Rashidi S, Eskandarian M, Mahian O, Poncet S. Combination of nanofluid and inserts for heat transfer enhancement. J Therm Anal Calorim. 2019;135(1):437–60.

    CAS  Google Scholar 

  24. Ellahi R. The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: analytical solutions. Appl Math Model. 2013;37(3):1451–67.

    Google Scholar 

  25. Rashidi S, Bovand M, Esfahani JA. Opposition of Magnetohydrodynamic and AL2O3–water nanofluid flow around a vertex facing triangular obstacle. J Mol Liq. 2016;215:276–84.

    CAS  Google Scholar 

  26. Bovand M, Rashidi S, Esfahani JA. Optimum interaction between magnetohydrodynamics and nanofluid for thermal and drag management. J Thermophys Heat Transfer. 2016;31(1):218–29.

    Google Scholar 

  27. Sajjadi H, Delouei AA, Atashafrooz M, Sheikholeslami M. Double MRT lattice Boltzmann simulation of 3-D MHD natural convection in a cubic cavity with sinusoidal temperature distribution utilizing nanofluid. Int J Heat Mass Transf. 2018;126:489–503.

    CAS  Google Scholar 

  28. Sheikholeslami M, Sajjadi H, Delouei AA, Atashafrooz M, Li Z. Magnetic force and radiation influences on nanofluid transportation through a permeable media considering Al2O3 nanoparticles. J Thermal Anal Calorim. 2018. https://doi.org/10.1007/s10973-018-7901-8.

    Article  Google Scholar 

  29. Mehryan SAM, Izadi M, Namazian Z, Chamkha AJ, Li Z. Natural convection of multi-walled carbon nanotube–Fe3O4/water magnetic hybrid nanofluid flowing in porous medium considering the impacts of magnetic field-dependent viscosity. J Thermal Anal Calorim. 2018. https://doi.org/10.1007/s10973-019-08164-1.

    Article  Google Scholar 

  30. Animasaun IL, Mahanthesh B, Jagun AO, Bankole TD, Sivaraj R, Shah NA, Saleem S. Significance of Lorentz force and thermoelectric on the flow of 29 nm CuO–water nanofluid on an upper horizontal surface of a paraboloid of revolution. J Heat Transf. 2019;141(2):022402.

    CAS  Google Scholar 

  31. Izadi M, Mohebbi R, Delouei AA, Sajjadi H. Natural convection of a magnetizable hybrid nanofluid inside a porous enclosure subjected to two variable magnetic fields. Int J Mech Sci. 2019;151:154–69.

    Google Scholar 

  32. Sajjadi H, Delouei AA, Izadi M, Mohebbi R. Investigation of MHD natural convection in a porous media by double MRT lattice Boltzmann method utilizing MWCNT–Fe3O4/water hybrid nanofluid. Int J Heat Mass Transf. 2019;132:1087–104.

    CAS  Google Scholar 

  33. Mehryan SAM, Sheremet MA, Soltani M, Izadi M. Natural convection of magnetic hybrid nanofluid inside a double-porous medium using two-equation energy model. J Mol Liq. 2019;277:959–70.

    CAS  Google Scholar 

  34. Raza J, Rohni AM, Omar Z. MHD flow and heat transfer of Cu–water nanofluid in a semi porous channel with stretching walls. Int J Heat Mass Transf. 2016;103:336–40.

    CAS  Google Scholar 

  35. Rashidi MM, Nasiri M, Khezerloo M, Laraqi N. Numerical investigation of magnetic field effect on mixed convection heat transfer of nanofluid in a channel with sinusoidal walls. J Magn Magn Mater. 2016;401:159–68.

    CAS  Google Scholar 

  36. Sheikholeslami M, Rokni HB. Simulation of nanofluid heat transfer in presence of magnetic field: a review. Int J Heat Mass Transf. 2017;115:1203–33.

    CAS  Google Scholar 

  37. Öztop HF, Sakhrieh A, Abu-Nada E, Al-Salem K. Mixed convection of MHD flow in nanofluid filled and partially heated wavy walled lid-driven enclosure. Int Commun Heat Mass Transfer. 2017;86:42–51.

    Google Scholar 

  38. Sheikholeslami M, Gerdroodbary MB, Mousavi SV, Ganji DD, Moradi R. Heat transfer enhancement of ferrofluid inside an 90° elbow channel by non-uniform magnetic field. J Magn Magn Mater. 2018;460:302–11.

    CAS  Google Scholar 

  39. Nie JH, Chen YT, Hsieh HT. Effects of a baffle on separated convection flow adjacent to backward-facing step. Int J Therm Sci. 2009;48:618–25.

    CAS  Google Scholar 

  40. Ansari AB, Gandjalikhan Nassab SA. Combined gas radiation and laminar forced convection flow adjacent to a forward facing step in a duct. Int J Numer Method Heat Fluid Flow. 2011;23(2):320–35.

    Google Scholar 

  41. Oztop HF, Mushatet KS, Yılmaz İ. Analysis of turbulent flow and heat transfer over a double forward facing step with obstacles. Int Commun Heat Mass Transfer. 2012;39(9):1395–403.

    Google Scholar 

  42. Atashafrooz M, Gandjalikhan Nassab SA. Simulation of laminar mixed convection recess flow combined with radiation heat transfer. Iran J Sci Technol Trans Mech Eng. 2013;37(M1):71–5.

    Google Scholar 

  43. Selimefendigil F, Oztop HF. Numerical analysis of laminar pulsating flow at a backward facing step with an upper wall mounted adiabatic thin fin. Comput Fluids. 2013;88:93–107.

    Google Scholar 

  44. Atashafrooz M, Nassab SAG, Lari K. Application of full-spectrum k-distribution method to combined non-gray radiation and forced convection flow in a duct with an expansion. J Mech Sci Technol. 2015;29(2):845–59.

    Google Scholar 

  45. Ramšak M. Conjugate heat transfer of backward-facing step flow: a benchmark problem revisited. Int J Heat Mass Transf. 2015;84:791–9.

    Google Scholar 

  46. Atashafrooz M, Gandjalikhan Nassab SA, Lari K. Numerical analysis of interaction between non-gray radiation and forced convection flow over a recess using the full-spectrum k-distribution method. Heat Mass Transf. 2016;52(2):361–77.

    CAS  Google Scholar 

  47. Kherbeet AS, Safaei MR, Mohammed HA, Salman BH, Ahmed HE, Alawi OA, Al-Asadi MT. Heat transfer and fluid flow over microscale backward and forward facing step: a review. Int Commun Heat Mass Transfer. 2016;76:237–44.

    CAS  Google Scholar 

  48. Atashafrooz M, Gandjalikhan Nassab SA, Lari K. Coupled thermal radiation and mixed convection step flow of non-gray gas. J Heat Transf. 2016;138(7):072701-9.

    Google Scholar 

  49. Nouri-Borujerdi A, Moazezi A. Investigation of obstacle effect to improve conjugate heat transfer in backward facing step channel using fast simulation of incompressible flow. Heat Mass Transf. 2018;54(1):135–50.

    CAS  Google Scholar 

  50. Abu-Nada E. Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. Int J Heat Fluid Flow. 2008;29:242–9.

    CAS  Google Scholar 

  51. Al-aswadi AA, Mohammed HA, Shuaib NH, Campo A. Laminar forced convection flow over a backward facing step using nanofluids. Int Commun Heat Mass Transfer. 2010;37(8):950–7.

    CAS  Google Scholar 

  52. Mohammed HA, Golieskardi M, Munisamy KM, Wahid MA. Combined convection heat transfer of nanofluids flow over forward facing step in a channel having a blockage. Appl Mech Mater. 2013;388:185–91.

    Google Scholar 

  53. Safaei MR, Togun H, Vafai K, Kazi SN, Badarudin A. Investigation of heat transfer enhancement in a forward-facing contracting channel using FMWCNT Nanofluids. Numer Heat Transf Part A Appl. 2014;66(12):1321–40.

    CAS  Google Scholar 

  54. Togun H, Safaei MR, Sadri R, Kazi SN, Badarudin A, Hooman K, Sadeghinezhad E. Numerical simulation of laminar to turbulent nanofluid flow and heat transfer over a backward-facing step. Appl Math Comput. 2014;239:153–70.

    Google Scholar 

  55. Mohammed HA, Al-aswadi AA, Abu-Mulaweh HI, Shuaib NH. Influence of nanofluids on mixed convective heat transfer over a horizontal backward facing step. Heat Transf Asian Res. 2011;40(4):287–307.

    Google Scholar 

  56. Alawi OA, Sidik NAC, Kazi SN, Abdolbaqi MK. Comparative study on heat transfer enhancement and nanofluids flow over backward and forward facing steps. J Adv Res Fluid Mech Therm Sci. 2016;23(1):25–49.

    Google Scholar 

  57. Mohammed HA, Alawi OA, Wahid MA. Mixed convective nanofluid flow in a channel having backward-facing step with a baffle. Powder Technol. 2015;275:329–43.

    CAS  Google Scholar 

  58. Selimefendigil F, Oztop HF. Numerical study of forced convection of nanofluid flow over a backward facing step with a corrugated bottom wall in the presence of different shaped obstacles. Heat Transf Eng. 2016;37(15):1280–92.

    CAS  Google Scholar 

  59. Kherbeet AS, Mohammed HA, Salman BH, Ahmed HE, Alawi OA, Rashidi MM. Experimental study of nanofluid flow and heat transfer over microscale backward- and forward-facing steps. Exp Thermal Fluid Sci. 2015;65:13–21.

    CAS  Google Scholar 

  60. Kherbeet AS, Mohammed HA, Ahmed HE, Salman BH, Alawi OA, Safaei MR, Khazaal MT. Mixed convection nanofluid flow over microscale forward-facing step —effect of inclination and step heights. Int Commun Heat Mass Transf. 2016;78:145–54.

    CAS  Google Scholar 

  61. Atashafrooz M. Effects of Ag-water nanofluid on hydrodynamics and thermal behaviors of three-dimensional separated step flow. Alex Eng J. 2018;57:4277–85.

    Google Scholar 

  62. Abbassi H, Nassrallah SB. MHD flow and heat transfer in a backward-facing step. Int Commun Heat Mass Transfer. 2007;34(2):231–7.

    Google Scholar 

  63. Atashafrooz M, Sheikholeslami M, Sajjadi H, Delouei AA. Interaction effects of an inclined magnetic field and nanofluid on forced convection heat transfer and flow irreversibility in a duct with an abrupt contraction. J Magn Magn Mater. 2019;478:216–26.

    CAS  Google Scholar 

  64. Mehrez Z, Cafsi AE, Belghith A, Quéré PL. The entropy generation analysis in the mixed convective assisting flow of Cu-water nanofluid in an inclined open cavity. Adv Powder Technol. 2015;26(5):1442–51.

    CAS  Google Scholar 

  65. Nayak RK, Bhattacharyya S, Pop I. Heat transfer and entropy generation in mixed convection of a nanofluid within an inclined skewed cavity. Int J Heat Mass Transf. 2016;102:596–609.

    CAS  Google Scholar 

  66. Mamourian M, Shirvan KM, Ellahi R, Rahimi AB. Optimization of mixed convection heat transfer with entropy generation in a wavy surface square lid-driven cavity by means of Taguchi approach. Int J Heat Mass Transf. 2016;102:544–54.

    CAS  Google Scholar 

  67. Oztop HF, Kolsi L, Alghamdi A, Abu-Hamdeh N, Borjini MN, Aissia HB. Numerical analysis of entropy generation due to natural convection in three-dimensional partially open enclosures. J Taiwan Inst Chem Eng. 2017;75:131–40.

    CAS  Google Scholar 

  68. Rashidi S, Akbarzadeh M, Karimi N, Masoodi R. Combined effects of nanofluid and transverse twisted-baffles on the flow structures, heat transfer and irreversibilities inside a square duct—a numerical study. Appl Therm Eng. 2018;130:135–48.

    CAS  Google Scholar 

  69. Afridi MI, Qasim M, Saleem S. Second law analysis of three dimensional dissipative flow of hybrid nanofluid. J Nanofluids. 2018;7(6):1272–80.

    Google Scholar 

  70. Gul A, Khan I, Makhanov SS. Entropy generation in a mixed convection Poiseulle flow of molybdenum disulphide Jeffrey nanofluid. Results Phys. 2018;9:947–54.

    Google Scholar 

  71. Izadi M, Hashemi Pour SMR, Yasuri AK, Chamkha AJ. Mixed convection of a nanofluid in a three-dimensional channel. J Therm Anal Calorim. 2018. https://doi.org/10.1007/s10973-018-7889-0.

    Article  Google Scholar 

  72. Akbarzadeh M, Rashidi S, Karimi N, Omar N. First and second laws of thermodynamics analysis of nanofluid flow inside a heat exchanger duct with wavy walls and a porous insert. J Therm Anal Calorim. 2019;135(1):177–94.

    CAS  Google Scholar 

  73. Rashidi S, Javadi P, Esfahani JA. Second law of thermodynamics analysis for nanofluid turbulent flow inside a solar heater with the ribbed absorber plate. J Therm Anal Calorim. 2019;135(1):551–63.

    CAS  Google Scholar 

  74. Shamsabadi H, Rashidi S, Esfahani JA. Entropy generation analysis for nanofluid flow inside a duct equipped with porous baffles. J Therm Anal Calorim. 2019;135(2):1009–19.

    CAS  Google Scholar 

  75. Mahmoudi AH, Pop I, Shahi M, Talebi F. MHD natural convection and entropy generation in a trapezoidal enclosure using Cu–water nanofluid. Comput Fluids. 2013;72:46–62.

    CAS  Google Scholar 

  76. Rashidi MM, Abelman S, Mehr NF. Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid. Int J Heat Mass Transf. 2013;62:515–25.

    CAS  Google Scholar 

  77. Aghaei A, Khorasanizadeh H, Sheikhzadeh G, Abbaszadeh M. Numerical study of magnetic field on mixed convection and entropy generation of nanofluid in a trapezoidal enclosure. J Magn Magn Mater. 2016;403:133–45.

    CAS  Google Scholar 

  78. Afridi MI, Qasim M, Khan I, Tlili I. Entropy generation in MHD mixed convection stagnation-point flow in the presence of joule and frictional heating. Case Stud Therm Eng. 2018;12:292–300.

    Google Scholar 

  79. Mehryan SAM, Izadi M, Chamkha AJ, Sheremet MA. Natural convection and entropy generation of a ferrofluid in a square enclosure under the effect of a horizontal periodic magnetic field. J Mol Liq. 2018;263:510–25.

    CAS  Google Scholar 

  80. Rashid M, Khan MI, Hayat T, Khan MI, Alsaedi A. Entropy generation in flow of ferromagnetic liquid with nonlinear radiation and slip condition. J Mol Liq. 2019;276:441–52.

    CAS  Google Scholar 

  81. Mehrez Z, Cafsi AE, Belghith A, Quéré PL. MHD effects on heat transfer and entropy generation of nanofluid flow in an open cavity. J Magn Magn Mater. 2015;374:214–24.

    CAS  Google Scholar 

  82. Shirvan KM, Mirzakhanlari S, Öztop HF, Mamourian M, Al-Salem K. MHD heat transfer and entropy generation in inclined trapezoidal cavity filled with nanofluid: numerical investigation and sensitivity analysis. Int J Numer Meth Heat Fluid Flow. 2017;27(10):2174–202.

    Google Scholar 

  83. Sheikholeslami M. New computational approach for exergy and entropy analysis of nanofluid under the impact of Lorentz force through a porous media. Comput Methods Appl Mech Eng. 2019;344:319–33.

    Google Scholar 

  84. Abu-Nada E. Entropy generation due to heat and fluid flow in backward facing step flow with various expansion ratios. Int J Exergy. 2006;3:419–35.

    Google Scholar 

  85. Abu-Nada E. Investigation of entropy generation over a backward facing step under bleeding conditions. Energy Convers Manag. 2008;49:3237–42.

    Google Scholar 

  86. Atashafrooz M, Gandjalikhan Nassab SA, Ansari AB. Numerical study of entropy generation in laminar forced convection flow over inclined backward and forward facing steps in a duct. Int Rev Mech Eng. 2011;5(5):898–907.

    Google Scholar 

  87. Atashafrooz M, Gandjalikhan Nassab SA, Ansari AB. Numerical investigation of entropy generation in laminar forced convection flow over inclined backward and forward facing steps in a duct under bleeding condition. Therm Sci. 2014;8(2):479–92.

    Google Scholar 

  88. Khanafer K, Vafai K, Lightstone M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat MassTransf. 2003;46(19):3639–53.

    CAS  Google Scholar 

  89. Koo J, Kleinstreuer C. A new thermal conductivity model for nanofluids. J Nanopart Res. 2004;6(6):577–88.

    Google Scholar 

  90. Akbar NS, Raza M, Ellahi R. Peristaltic flow with thermal conductivity of H2O + Cu nanofluid and entropy generation. Results Phys. 2015;5:115–24.

    Google Scholar 

  91. Patankar SV, Spalding DB. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int J Heat Mass Transf. 1972;15(10):1787–806.

    Google Scholar 

  92. Atashafrooz M, Gandjalikhan Nassab SA. Simulation of three-dimensional laminar forced convection flow of a radiating gas over an inclined backward-facing step in a duct under bleeding condition. Inst Mech Eng Part C J Mech Eng Sci. 2012;227(2):332–45.

    Google Scholar 

  93. Atashafrooz M, Gandjalikhan Nassab SA. Numerical analysis of laminar forced convection recess flow with two inclined steps considering gas radiation effect. Comput Fluids. 2012;66(167–176):2012.

    Google Scholar 

  94. Atashafrooz M, Gandjalikhan Nassab SA. Combined heat transfer of radiation and forced convection flow of participating gases in a three-dimensional recess. J Mech Sci Technol. 2012;26(10):3357–68.

    Google Scholar 

  95. Kooshki MS, Nassab SAG, Ansari AB. Investigation of entropy generation in a 3D laminar forced convection flow over a backward facing step with bleeding. Int J Eng Trans A. 2012;25(4):379–88.

    Google Scholar 

  96. Aminossadati SM, Raisi A, Ghasemi B. Effects of magnetic field on nanofluid forced convection in a partially heated microchannel. Int J Non-Linear Mech. 2011;46:1373–82.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran

    M. Atashafrooz

Authors
  1. M. Atashafrooz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Atashafrooz.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Atashafrooz, M. The effects of buoyancy force on mixed convection heat transfer of MHD nanofluid flow and entropy generation in an inclined duct with separation considering Brownian motion effects. J Therm Anal Calorim 138, 3109–3126 (2019). https://doi.org/10.1007/s10973-019-08363-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-019-08363-w

Keywords

Search

Navigation