Numerical study of MHD mixed convection in an oriented elliptic geometry under the influence of some selected geometrical variables and fluid flow properties saturated with Al2O3-water nanofluid
Corresponding Author(s) : T. Adekeye
Future Energy,
Vol. 5 No. 1 (2026): February 2026 Issue
Abstract
This study numerically investigated the effects of some selected geometrical parameters, such as inclination angles, eccentricity, and some fluid flow properties, such as nanoparticle volume fractions, Grashof, Hartmann, Reynolds, Prandtl, and Richardson numbers, on fluid flow pattern (velocity profiles), temperature history, and heat transfer rate in an inclined elliptic configuration filled with Al2O3-H2O nanofluid. The non-dimensional governing equations were developed for the elliptic geometry. The lower wall of the configuration was subjected to continual heat flux, and the top wall was retained at a persistent cold temperature (Tc) while the cross-sectional ends of the configuration were presumed to be insulated. The normalized controlling equations were explained using a 4th order Alternating Direction Implicit (ADI) scheme with the Gauss-Seidel iteration technique. A computer code was written with Python 3.X version to simulate the fluid flow and heat transfer in the enclosure. The numerical results obtained exhibited that fluid flow circulation deteriorated with increasing Hartmann number and increasing nanoparticle volume fraction individually. The rate of heat transfer (Nu) augmented with fluid flow circulation for the range of Grashof at 104-106 and φ=0.0-0.045, respectively. The temperature field decreased with increasing nanoparticle volume fractions (0.00, 0.025, and 0.045). It was revealed from the outcomes that the optimum heat transfer rates were attained in the configuration for eccentricity, e value at 0.866, and inclination angle in the range , correspondingly. The average rate of heat transfer is elevated with increasing Reynolds number under laminar conditions. The results obtained could be applied in metallurgical industries where a magnetic field is used to regulate the flow of hot fluid. It could also be useful in the development of a model for designing a compact MHD heat exchanger for industrial applications.
Keywords
Download Citation
Endnote/Zotero/Mendeley (RIS)BibTeX
- S.O. Oyedepo. Toward achieving energy for sustainable development in Nigeria. Renewable and Sustainable Energy Review, 34, (2014) ,255-273
- D. Ruchika, R. Puneet, and K. Lokendra . MHD mixed convection over an inclined cylinder subjected to velocity and thermal slip effect. Powder Technology, (2016). 288, 140 – 150.
- Al-Salem K., Ozto, H.R.,Pop,I, Varol, Y. (2012). Effects of moving lid direction on MHD
- convection in a linearly heated cavity. Int. Journal Heat and Mass Transfer, 55, 1103-1112.
- M. Fateh, and B. Rachid. Numerical modelling of MHD stability in a cylindrical configuration. Journal of the Franklin Institute, (2014) 351, 667-681.
- F.H. Ali, H.K. Hamzah and A. Abdulkadhim. Numerical study of mixed convection nanofluild in an annulus enclosure between outer rotating cylinder and inner corrugated cylinder.Heat transfer Asian res,(2019);48(1):343-360
- N. Morley, S.,Smolentser, and M. Abdan. MHD and Thermal issue on the SICF/SIC flow channel. Insent, Fusion Science and Technology, (2006) 50, 107-119
- S. Aberkane, M. Ihdere, M. Moderas, and A. Ghezal. Effect of an axial magnetic field on the heat and mass transfer in rotating annulus. Int. Journal. of Physical Science, (2014) 9, 368-379
- E.S. Ahmed, A. K., Hussein., H.A. Mohammad, I.K. Adegun, X. Zhang, L. Kolsi, A.Hasanpow, and S. Sivasankaran. Viscous dissipation and radiation effects on MHD natural convection in a square enclosure filled with a porous medium. Nuclear Engineering and Design, (2014), 266, 34-42
- M. Hasanuzzaman, F.O. Hakan, M. M., Raham, N.A. Rahim, R.,Saidur, and Y. Varol. Magnetohydrodynamics natural convection in trapezoidal cavities. Int. Comm Heat Mass Transfer, (2012) 31,606-612.
- T. Hussein, A. Tuga, S. Kaz, A. ,Baoarudiw, A .A. ,Kadhim, and E. Sadeghinezhad. A review of studies on forced, natural and mixed heat transfer to fluid and nanofluid flow in an annular passage, Renewable and Sustainable Energy, (2014)39,835-856.
- S.K. Farid, M.M. Billah, M.M. Rahman, and U.Md.Sharif. MHD mixed convection in a lid-driven cavity having a heated circular hollow cylinder. Proceeding Engineering, (2013), 56, 474 – 479
- K.H. Wisam, and J. S. Gregory, J.S. Heat transfer in a high Hartmann number MHD duct flow with a circular cylinder around the heated wall. Int. J. of Heat and Mass Transfer, (2013) 67,944-954
- S. Fatih, and F.O. Hakan, Numerical study of MHD mixed convection in a nanofluid filled lid-driven square enclosure with a rotating cylinder. Int. J. of Heat and Mass Transfer, (2014). 78, 744-754
- M. S. Alam and M.A.H. Khan, M.A.H. (2014). MHD effects on mixed convection flow through a diverging channel with circular obstacles. 10th Int. Conference in Mechanical Engineering ICME 2013, Procedia Engineering, 90, 403-410.
- S. H. Muhammad, M. A. Alim, and H.K. Kazi.. Numerical analysis on MHD natural
- convection within trapezoidal cavity having circular block. American J. of Applied Mathematics and Statistics,(2016) 4(5),161-168
- E. Sourtiji, M. Gorji-Bandipy. D.D. Gangui, and S.M. Seyyedi. MHD buoyancy driven heat transfer in a cylindrical-triangular cavity filled with Cu-water nanofluid. Journal of Molecular Liquid, (2014), 196, 370 – 380
- B. Mahfoud, B. (2014). Swirling flow with heat transfer in a cylindrical under axial magnetic field. Recent Advances in Environmental Science and Biomedicine, 9, 45-50.
- B. R. Sharma, and H. Konwa,. MHD flow, heat and mass transfer about a horizontal cylinder in porous medium. Int. J. of Innovative Research in Science Engineering and Technology (IJIRSET), (2014) 3,1- 10.
- W. Xiang, and S. M Arun. A review on nanofluids part II, experiments and applications. Brazilian Journal of Chemical Engineering, (2008) ,25 (4), 631-648
- U .S. Choi. Enhancing thermal conductivity of fluid with nanoparticles. Development and applications of non-newtonian flows. ASME, N/York, FED, (1995), 66, 99-105.
- T. Adekeye, I. K. Adegun, P. O. Okekunle, A.K. Hussein, S.O. Oyedepo, E. Adetiba, and O.S.I. Fayomi, Numerical analysis of the effects of selected geometrical parameters and fluid properties on MHD natural convection flow in an inclined elliptic porous enclosure with localized heating. Heat Transfer Asian Research, 46(3),(2017) 261-293.
- J.A. Chamkha, F. Salimefenchgil, and H.F. Oztop.. Effects of rotating cone on the mixed convection in a double lid-driven 3D porous trapezoidal nanofluid filled cavity, under the influence of magnetic field-nanomaterials,(2020) 10:1-17.
- T. Armaghani, H Esmaeli, Y.A. Mohammadpoor, I. Pop. MHD mixed convection flow and heat transfer in an open C-shaped enclosure using water-copper oxide nanofluid. Heat and mass transfer, (2018) 1-11
- N.Shukla, P. Rana, O. AnwarBeg, B. Singh, and A. Kadir, Homotopy study of MHD mixed convection nanofluid multiple slip flow as heat transfer over a vertical cylinder with entropy generation. Propulsion and power research, (2019), 8(2):147-162.
- A.J. Chamkha, A.M Rasheed, M.A, Ameghem, M.A. Mansour. Effect of partial slope on entropy generation and MHD combined convection in a lid-driven porous enclosure saturated with a Cu-water nanofluid of thermal. (2020), 132(2):1291-1306
- I K.,Adegun,. T.S. Jolayemi, O. A. Olayemi, and A.M Adebisi .Numerical simulation of forced convective heat transfer in inclined eliptic ducts with multiple internal longitudinal fins.Alexandra Engineering Journal,57,(2018) 2485-2496.
- R. B. Bird W. E. Stewart and E. N. Light foot. Transport phenomena 2nd edition, John Wiley, New York (2006). ISBN: 978-0-470-11539-8
- X. Wang, X. Xu, and S. U.S. Choi. Thermal conductivity of nanoparticles fluid mixture. Journal of Thermophysics and Heat Transfer,(1999) 13(4), 474-480.
- F. Selimefendigil and H. F. Oztop. MHD mixed convection of nanofluid filled partially heated triangular enclosure with a rotating adiabatic cylinder. Journal Taiwan Inst. Chem. Eng. In press.(2014) doi.org/10.1016/j.jtice
- M. Sheikholeslami, M, Gorji-Bandipy, D.D. Gangi. MHD influence in Al2O3-water based nanofluid in a concertic annulus Energy, (2013), 60, 501 – 510
- V.Javery,.Analysis of laminar thermal entrance region of elliptical and rectangular ducts with Kantorovish method, (1976) 85-98
- Sakalis,V.D., Hatzkonstaninoi,P.M.,Kafousias,N. (2002).Thermally developing flow in elliptic ducts with axially variable wall temperature distribution. International Journal of Meat and mass ransfer,45,25-35
- J. Amin. Numerical and experimental study of laminar forced convection heat transfer of TiO2-water nanofluid in triangular duct. Int. Journal of Artificial Intelligence and Mechatronics, (2014) 3(3), 107-111
- R.B. Mansour, N. Gelami, and C.T. Nguyen. Experimental investigation of mixed convection with water- Al2O3 nanofluid in inclined tube with uniform wall heat flux. Int. J. of Thermal Science, (2011), 50, 403 – 410.
References
S.O. Oyedepo. Toward achieving energy for sustainable development in Nigeria. Renewable and Sustainable Energy Review, 34, (2014) ,255-273
D. Ruchika, R. Puneet, and K. Lokendra . MHD mixed convection over an inclined cylinder subjected to velocity and thermal slip effect. Powder Technology, (2016). 288, 140 – 150.
Al-Salem K., Ozto, H.R.,Pop,I, Varol, Y. (2012). Effects of moving lid direction on MHD
convection in a linearly heated cavity. Int. Journal Heat and Mass Transfer, 55, 1103-1112.
M. Fateh, and B. Rachid. Numerical modelling of MHD stability in a cylindrical configuration. Journal of the Franklin Institute, (2014) 351, 667-681.
F.H. Ali, H.K. Hamzah and A. Abdulkadhim. Numerical study of mixed convection nanofluild in an annulus enclosure between outer rotating cylinder and inner corrugated cylinder.Heat transfer Asian res,(2019);48(1):343-360
N. Morley, S.,Smolentser, and M. Abdan. MHD and Thermal issue on the SICF/SIC flow channel. Insent, Fusion Science and Technology, (2006) 50, 107-119
S. Aberkane, M. Ihdere, M. Moderas, and A. Ghezal. Effect of an axial magnetic field on the heat and mass transfer in rotating annulus. Int. Journal. of Physical Science, (2014) 9, 368-379
E.S. Ahmed, A. K., Hussein., H.A. Mohammad, I.K. Adegun, X. Zhang, L. Kolsi, A.Hasanpow, and S. Sivasankaran. Viscous dissipation and radiation effects on MHD natural convection in a square enclosure filled with a porous medium. Nuclear Engineering and Design, (2014), 266, 34-42
M. Hasanuzzaman, F.O. Hakan, M. M., Raham, N.A. Rahim, R.,Saidur, and Y. Varol. Magnetohydrodynamics natural convection in trapezoidal cavities. Int. Comm Heat Mass Transfer, (2012) 31,606-612.
T. Hussein, A. Tuga, S. Kaz, A. ,Baoarudiw, A .A. ,Kadhim, and E. Sadeghinezhad. A review of studies on forced, natural and mixed heat transfer to fluid and nanofluid flow in an annular passage, Renewable and Sustainable Energy, (2014)39,835-856.
S.K. Farid, M.M. Billah, M.M. Rahman, and U.Md.Sharif. MHD mixed convection in a lid-driven cavity having a heated circular hollow cylinder. Proceeding Engineering, (2013), 56, 474 – 479
K.H. Wisam, and J. S. Gregory, J.S. Heat transfer in a high Hartmann number MHD duct flow with a circular cylinder around the heated wall. Int. J. of Heat and Mass Transfer, (2013) 67,944-954
S. Fatih, and F.O. Hakan, Numerical study of MHD mixed convection in a nanofluid filled lid-driven square enclosure with a rotating cylinder. Int. J. of Heat and Mass Transfer, (2014). 78, 744-754
M. S. Alam and M.A.H. Khan, M.A.H. (2014). MHD effects on mixed convection flow through a diverging channel with circular obstacles. 10th Int. Conference in Mechanical Engineering ICME 2013, Procedia Engineering, 90, 403-410.
S. H. Muhammad, M. A. Alim, and H.K. Kazi.. Numerical analysis on MHD natural
convection within trapezoidal cavity having circular block. American J. of Applied Mathematics and Statistics,(2016) 4(5),161-168
E. Sourtiji, M. Gorji-Bandipy. D.D. Gangui, and S.M. Seyyedi. MHD buoyancy driven heat transfer in a cylindrical-triangular cavity filled with Cu-water nanofluid. Journal of Molecular Liquid, (2014), 196, 370 – 380
B. Mahfoud, B. (2014). Swirling flow with heat transfer in a cylindrical under axial magnetic field. Recent Advances in Environmental Science and Biomedicine, 9, 45-50.
B. R. Sharma, and H. Konwa,. MHD flow, heat and mass transfer about a horizontal cylinder in porous medium. Int. J. of Innovative Research in Science Engineering and Technology (IJIRSET), (2014) 3,1- 10.
W. Xiang, and S. M Arun. A review on nanofluids part II, experiments and applications. Brazilian Journal of Chemical Engineering, (2008) ,25 (4), 631-648
U .S. Choi. Enhancing thermal conductivity of fluid with nanoparticles. Development and applications of non-newtonian flows. ASME, N/York, FED, (1995), 66, 99-105.
T. Adekeye, I. K. Adegun, P. O. Okekunle, A.K. Hussein, S.O. Oyedepo, E. Adetiba, and O.S.I. Fayomi, Numerical analysis of the effects of selected geometrical parameters and fluid properties on MHD natural convection flow in an inclined elliptic porous enclosure with localized heating. Heat Transfer Asian Research, 46(3),(2017) 261-293.
J.A. Chamkha, F. Salimefenchgil, and H.F. Oztop.. Effects of rotating cone on the mixed convection in a double lid-driven 3D porous trapezoidal nanofluid filled cavity, under the influence of magnetic field-nanomaterials,(2020) 10:1-17.
T. Armaghani, H Esmaeli, Y.A. Mohammadpoor, I. Pop. MHD mixed convection flow and heat transfer in an open C-shaped enclosure using water-copper oxide nanofluid. Heat and mass transfer, (2018) 1-11
N.Shukla, P. Rana, O. AnwarBeg, B. Singh, and A. Kadir, Homotopy study of MHD mixed convection nanofluid multiple slip flow as heat transfer over a vertical cylinder with entropy generation. Propulsion and power research, (2019), 8(2):147-162.
A.J. Chamkha, A.M Rasheed, M.A, Ameghem, M.A. Mansour. Effect of partial slope on entropy generation and MHD combined convection in a lid-driven porous enclosure saturated with a Cu-water nanofluid of thermal. (2020), 132(2):1291-1306
I K.,Adegun,. T.S. Jolayemi, O. A. Olayemi, and A.M Adebisi .Numerical simulation of forced convective heat transfer in inclined eliptic ducts with multiple internal longitudinal fins.Alexandra Engineering Journal,57,(2018) 2485-2496.
R. B. Bird W. E. Stewart and E. N. Light foot. Transport phenomena 2nd edition, John Wiley, New York (2006). ISBN: 978-0-470-11539-8
X. Wang, X. Xu, and S. U.S. Choi. Thermal conductivity of nanoparticles fluid mixture. Journal of Thermophysics and Heat Transfer,(1999) 13(4), 474-480.
F. Selimefendigil and H. F. Oztop. MHD mixed convection of nanofluid filled partially heated triangular enclosure with a rotating adiabatic cylinder. Journal Taiwan Inst. Chem. Eng. In press.(2014) doi.org/10.1016/j.jtice
M. Sheikholeslami, M, Gorji-Bandipy, D.D. Gangi. MHD influence in Al2O3-water based nanofluid in a concertic annulus Energy, (2013), 60, 501 – 510
V.Javery,.Analysis of laminar thermal entrance region of elliptical and rectangular ducts with Kantorovish method, (1976) 85-98
Sakalis,V.D., Hatzkonstaninoi,P.M.,Kafousias,N. (2002).Thermally developing flow in elliptic ducts with axially variable wall temperature distribution. International Journal of Meat and mass ransfer,45,25-35
J. Amin. Numerical and experimental study of laminar forced convection heat transfer of TiO2-water nanofluid in triangular duct. Int. Journal of Artificial Intelligence and Mechatronics, (2014) 3(3), 107-111
R.B. Mansour, N. Gelami, and C.T. Nguyen. Experimental investigation of mixed convection with water- Al2O3 nanofluid in inclined tube with uniform wall heat flux. Int. J. of Thermal Science, (2011), 50, 403 – 410.