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MHD natural convection around “plus” shape of circular barriers under local thermal non-equilibrium condition inside a wavy porous cavity saturated with Al2O3-Cu/water

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Abstract

At the current model, MHD natural convection has been numerically inspected around five circular thermal gates subjected to the non-Fourier heat flux. Streamlines experience many twists due to the addressed heat sources. In other words, streamline vortices appear as agitated groups through the cavity. When the frequency of the wavy sides increases, streamlines heaviness disperses widely, and the convection is enforced. Besides, given that there is no leading line for the force’s action, the buoyancy force style exhibits peculiar behavior. Particularly, the convection regime is greatly supported by the heat generation parameter. In addition, the hybrid nanofluid provides a good chemical inertness for the electrical and thermal conductivity as to the molecular structure of the fluid particle. On the other hand, by lowering the heat exchange rate regardless of fluid flow behavior, the local thermal non-equilibrium condition maintains the system’s internal energy overall, keeps the system in a static thermodynamic case, and creates isolation zones through the cavity. Moreover, the average heat transfer at the relevant porous model is not entirely dependent on the average fluid flow because porosity is proportional to flow intensity but conversely proportional to the average Nusselt number on the left, right, and bottom sides. Incidentally, the fact that the isotherm summit is near the isolated surface even though it is not connected to the heat sources indicates that the heat sources release separate energy batches that float along specific paths inside the cavity. Furthermore, the mechanism of independent energy batches is confirmed by the fact that many isotherm groups share the same values as the undulation parameter increases.

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Abbreviations

\({H}^{*}\) :

Inter-phase heat transfer coefficient

B 0 :

Magnetic field strength

C :

Concentration

Da:

Darcy number

Gr:

Grashof number, \({\text{Gr}}=\frac{g{\beta }_{{\text{f}}}{H}^{4}{q}_{w}}{{{\nu }^{2}}_{{\text{f}}}.{k}_{{\text{f}}}}\)

H :

Length of cavity, m

Ha:

Hartmann number, \({B}_{0}H\sqrt{{\sigma }_{{\text{f}}}/{\mu }_{{\text{f}}}}\)

Nus :

Local Nusselt number

Pr:

Prandtl number,\({\upsilon }_{{\text{f}}}/{\alpha }_{{\text{f}}}\)

Q 0 :

Heat generation/absorption coefficient

Re:

Reynolds number,\({ U}_{0}H/{\upsilon }_{{\text{f}}}\)

Ri:

Richardson parameter

Sc:

Schmidt number

Sh:

Schorword number

T :

Temperature

X, Y :

Dimensionless coordinates/H, y/H

c p :

Specific heat at constant pressure, J. kg. K−1

g :

Acceleration due to gravity, m s−2

k r :

Modified conductivity ratio

q :

Constant heat flux

u, v :

Velocity components in x, y directions, ms−1

\({{\text{Nu}}}_{m}\) :

Average Nusselt number of heat source

\(P\) :

Dimensionless pressure, \(pH/\rho_{{{\text{nf}}}} \alpha_{{\text{f}}}^{2}\)

\(U,V\) :

Dimensionless velocity components

\(k\) :

Thermal conductivity, Wm−1K−1

\(n\) :

Normal vector

\(p\) :

Fluid pressure, Pa

\(x,y\) :

Cartesian coordinates

0:

Reference

c :

Cold

f :

Pure fluid

h :

Hot

hnf:

Hybrid nanofluid

hnfs:

Inter-phase heat transfer Coeff.

m :

Mean value

s :

Solid phase (within porous medium)

α :

Thermal diffusivity, m2.s−1, \(k/\rho {c}_{p}\)

β :

Thermal expansion coefficient, k−1

μ :

Dynamic viscosity, N.s.m−2

ν :

Kinematic viscosity, m2.s−1

ϕ:

Solid volume fraction

Φ:

Magnetic field inclination angle

ρ :

Density, kg.m−3

σ:

Effective electrical conductivity, \(\mu S/{\text{cm}}\)

θ:

Dimensionless temperature

ε :

Porosity

φ:

Dimensionless concentration

References

  1. Ghadikolaei, S.S., Yassari, M., Sadeghi, H., Hosseinzadeh, K., Ganji, D.D.: Investigation on thermophysical properties of Tio2–Cu/H2O hybrid nanofluid transport dependent on shape factor in MHD stagnation point flow. Powder Technol. 322, 428 (2017)

    Article  CAS  Google Scholar 

  2. Syazana, N., Bachok, N., Arifin, N., Rosali, H.: MHD flow past a nonlinear stretching/shrinking sheet in carbon nanotubes Stability analysis. Chin. J. Phys. 65, 436 (2020)

    Article  MathSciNet  Google Scholar 

  3. Reddy, P.B.A., Bhaskar Reddy, N., Suneetha, S.: Radiation effects on MHD flow past an exponentially accelerated isothermal vertical plate with uniform mass diffusion in the presence of heat source. J. Appl. Fluid Mech. 5, 119 (2012)

    Google Scholar 

  4. Rashidi, M.M., Bagheri, S., Momoniat, E., Freidoonimehr, N.: Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet. Ain Shams Eng. J. 8, 77 (2017)

    Article  Google Scholar 

  5. S. Jakeer, B.A.R. Polu, P.B.A. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. 95440892110489 (2021)

  6. Rudraiah, N., Barron, R.M., Venkatachalappa, M., Subbaraya, C.K.: Effect of a magnetic field on free convection in a rectangular enclosure. Int. J. Eng. Sci. 33, 1075–1084 (1995). https://doi.org/10.1016/0020-7225(94)00120-9

    Article  Google Scholar 

  7. Ashorynejad, H.R., Mohamad, A.A., Sheikholeslami, M.: Magnetic field effects on natural convection flow of a nanofluid in a horizontal cylindrical annulus using lattice Boltzmann method. Int. J. Therm. Sci. 64, 240–250 (2013). https://doi.org/10.1016/j.ijthermalsci.2012.08.006

    Article  CAS  Google Scholar 

  8. Sheikholeslami, M., Gorji-Bandpy, M., Ganji, D.D., Rana, P., Soleimani, S.: Magnetohydrodynamic free convection of Al2O3–water nanofluid considering thermophoresis and Brownian motion effects. Comput. Fluids 94, 147–160 (2014). https://doi.org/10.1016/j.compfluid.2014.01.036

    Article  MathSciNet  CAS  Google Scholar 

  9. Bakar, N.A., Karimipour, A., Roslan, R.: Effect of magnetic field on mixed convection heat transfer in a lid-driven square cavity. J. Thermodyn. (2016). https://doi.org/10.1155/2016/3487182

    Article  Google Scholar 

  10. Hoseinpour, B., Ashorynejad, H.R., Javaherdeh, K.: Entropy generation of nanofluid in a porous cavity by lattice Boltzmann method. J. Thermophys. Heat Transf. 31, 20–27 (2017). https://doi.org/10.2514/1.T4652

    Article  CAS  Google Scholar 

  11. Ismael, M.A., Mansour, M.A., Chamkha, A.J., Rashad, A.M.: Mixed convection in a nanofluid filled-cavity with partial slip subjected to constant heat flux and inclined magnetic field. J. Magn. Magn. Mater. 416, 25–36 (2016). https://doi.org/10.1016/j.jmmm.2016.05.006

    Article  ADS  CAS  Google Scholar 

  12. Ashorynejad, H.R., Hoseinpour, B.: Investigation of different nanofluids effect on entropy generation on natural convection in a porous cavity. Eur. J. Mech. B. Fluids 62, 86–93 (2017). https://doi.org/10.1016/j.euromechflu.2016.11.016

    Article  ADS  MathSciNet  Google Scholar 

  13. Aly, A.M., Raizah, Z.A.: Incompressible smoothed particle hydrodynamics method for natural convection of a ferrofluid in a partially layered porous cavity containing a sinusoidal wave rod under the effect of a variable magnetic field. AIP Adv. 9, 105210 (2019)

    Article  ADS  Google Scholar 

  14. Ahmed, S.E., Mansour, M.A., Alwatban, A.M., Aly, A.M.: Finite element simulation for MHD ferro-convective flow in an inclined double-lid driven L-shaped enclosure with heated corners. Alex. Eng. J. 59, 217–226 (2020). https://doi.org/10.1016/j.aej.2019.12.026

    Article  Google Scholar 

  15. Armaghani, T., Chamkha, A., Rashad, A.M., Mansour, M.A.: Inclined magneto: convection, internal heat, and entropy generation of nanofluid in an I-shaped cavity saturated with porous media. J. Therm. Anal. Calorim. 142, 2273–2285 (2020). https://doi.org/10.1007/s10973-020-09449-6

    Article  CAS  Google Scholar 

  16. Aly, A.M., Aldosary, A., Mohamed, E.M.: Double diffusion in a nanofluid cavity with a wavy hot source subjected to a magnetic field using ISPH method. Alex. Eng. J. 60, 1647–1664 (2021)

    Article  Google Scholar 

  17. Dogonchi, A.S., Asghar, Z., Waqas, M.: CVFEM simulation for Fe3O4-H2O nanofluid in an annulus between two triangular enclosures subjected to magnetic field and thermal radiation. Int. Commun. Heat Mass Transf. 112, 104449 (2020). https://doi.org/10.1016/j.icheatmasstransfer.019.104449

    Article  CAS  Google Scholar 

  18. Sadeghi, M.S., Tayebi, T., Dogonchi, A.S., Nayak, M.K., Waqas, M.: Analysis of thermal behavior of magnetic buoyancy-driven flow in ferrofluid–filled wavy enclosure furnished with two circular cylinders. Int. Commun. Heat Mass Transf. 120, 104951 (2021). https://doi.org/10.1016/j.icheatmasstransfer.2020.104951

    Article  CAS  Google Scholar 

  19. Dogonchi, A.S., Tayebi, T., Karimi, N., Chamkha, A.J., Alhumade, H.: Thermal-natural convection and entropy production behavior of hybrid nanoliquid flow under the effects of magnetic field through a porous wavy cavity embodies three circular cylinders. J. Taiwan Inst. Chem. Eng. (2021). https://doi.org/10.1016/j.jtice.2021.04.033

    Article  Google Scholar 

  20. Scott, D., Anderson, R., Figliola, R.: Blockage of natural convection boundary layer flow in a multizone enclosure. Int. J. Heat Fluid Flow 9(2), 208–214 (1988)

    Article  Google Scholar 

  21. Chang, L.C., Lloyd, J.R., Yang, K.T. A finite difference study of natural convection in complex enclosures. In: 7th international heat transfer conferences, Munich, Germany, (1982)

  22. Nansteel, M.W., Greif, R.: Natural convection in undivided and partially divided rectangular enclosures. J. Heat Transfer. 104, 527–532 (1982)

    Google Scholar 

  23. Lin, N.N., Bejan, A.: Natural convection in a partially divided enclosure. Int. J. Heat Mass Transf. 26, 1867–1878 (1983)

    Article  Google Scholar 

  24. Alsabery, A.I., Ismael, M.A., Chamkha, A.J., Hashim, I.: Mixed convection of Al2O3-water nanofluid in a double lid-driven square cavity with a solid inner insert using Buongiorno’s two-phase model. Int. J. Heat Mass Transf. 119, 939–961 (2018)

    Article  CAS  Google Scholar 

  25. Ghalambaz, M., Mehryan, S.A.M., Izadpanahi, E., Chamkha, A.J., Wen, D.: MHD natural convection of Cu–Al2O3 water hybrid nanofluids in a cavity equally divided into two parts by a vertical flexible partition membrane. J Therm Anal Calorim 138(2), 1723–1743 (2019). https://doi.org/10.1007/s10973-019-08258-w

    Article  CAS  Google Scholar 

  26. Sahoo, R.K., Sarkar, A., Sastri, V.M.K.: Effect of an obstruction on natural convection heat transfer in vertical channels-A finite element analysis. Int. J. Numer. Methods Heat Fluid Flow 3, 267–276 (1993)

    Article  CAS  Google Scholar 

  27. Said, S.A., Krane, R.J.: An analytical and experimental investigation of natural convection heat transfer in vertical channel with a single obstruction. Int. J. Heat Mass Transf. 33, 1121–1134 (1990)

    Article  CAS  Google Scholar 

  28. Shahriari, A., Ashorynejad, H.R., Pop, I.: Entropy generation of MHD nanofluid inside an inclined wavy cavity by lattice Boltzmann method. J. Therm. Anal. Calorim. 135, 283 (2019)

    Article  CAS  Google Scholar 

  29. Sheremet, M.A., Oztop, H.F., Pop, I., Al-Salem, K.: MHD free convection in a wavy open porous tall cavity filled with nanofluids under an effect of corner heater. Int. J. Heat Mass Transf. 103, 955–964 (2016). https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.006

    Article  CAS  Google Scholar 

  30. Li, C., Xiao, J., Zhang, Y., Chen, X.D.: Mixing in a soft-elastic reactor (SER): a simulation study. Can. J. Chem. Eng. 97, 676–686 (2019). https://doi.org/10.1002/cjce.23351

    Article  CAS  Google Scholar 

  31. Zou, J., Xiao, J., Zhang, Y., Li, C., Chen, X.D.: Numerical simulation of the mixing process in a soft elastic reactor with bionic contractions. Chem. Eng. Sci. 220, 115623 (2020). https://doi.org/10.1016/j.ces.2020.115623

    Article  CAS  Google Scholar 

  32. Shekaramiz, M., Fathi, S., Ataabadi, H.A., Kazemi-Varnamkhasti, H., Toghraie, D.: MHD nanofluid free convection inside the wavy triangular cavity considering periodic temperature boundary condition and velocity slip mechanisms. Int. J. Therm. Sci. 170, 107179 (2021)

    Article  CAS  Google Scholar 

  33. Dogonchi, A.S., Chamkha, A.J., Ganji, D.D.: A numerical investigation of magneto-hydrodynamic natural convection of Cu–water nanofluid in a wavy cavity using CVFEM. J. Therm. Anal. Calorim. 135, 2599–2611 (2019). https://doi.org/10.1007/s10973-018-7339-z

    Article  CAS  Google Scholar 

  34. Rashad, A.M., Ismael, M.A., Chamkha, A.J., Mansour, M.A.: MHD mixed convection of localized heat source/sink in a nanofluid-filled lid-driven square cavity with partial slip. J. Taiwan Inst. Chem. Eng. 68, 173 (2016)

    Article  CAS  Google Scholar 

  35. Jakeer, S., Reddy, P.B.A., Rashad, A.M., Nabwey, H.A.: Impact of heated obstacle position on magneto-hybrid nanofluid flow in a lid-driven porous cavity with Cattaneo-Christov heat flux pattern. Alex. Eng. J. 60, 821 (2021)

    Article  Google Scholar 

  36. 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 (2017)

    Article  CAS  Google Scholar 

  37. Aghaei, A., Khorasanizadeh, H., Sheikhzadeh, G.A.: A numerical study of the effect of the magnetic field on turbulent fluid flow, heat transfer and entropy generation of hybrid nanofluid in a trapezoidal enclosure. Eur. Phys. J. Plus 134, 1 (2019)

    Article  CAS  Google Scholar 

  38. Chamkha, A.J.: Non-darcy hydromagnetic free convection from a cone and awedge in porous media. Int. Comm. Heat Mass Transf. 23(6), 875–887 (1996)

    Article  MathSciNet  CAS  Google Scholar 

  39. Khanafer, K.M., Chamkha, A.J.: Hydromagnetic natural convection from an inclined porous square enclosure with heat generation. Numer. Heat Transf. Part A Appl. 33(8), 891–910 (1998). https://doi.org/10.1080/10407789808913972

    Article  ADS  CAS  Google Scholar 

  40. Chamkha, A.J.: Non-darcy fully developed mixed convection in a porous medium channel with heat generation/absorption and hydromagnetic effects. Numer. Heat Transf. Part A Appl. 32(6), 653–675 (1997). https://doi.org/10.1080/10407789708913911

    Article  ADS  Google Scholar 

  41. Izadi, S., Armaghani, T., Ghasemiasl, R., Chamkha, A.J., Molana, M.: A comprehensive review on mixed convection of nanofluids in various shapes of enclosures. Powder Technol. 343, 880–907 (2019)

    Article  CAS  Google Scholar 

  42. Khanafer, K., Vafai, K., Lightstone, M.: Buoyancy-driven heat transfer enhancement in two-dimensional enclosure utilizing nanofluids. Int. J. Heat Mass Transf. 46, 3639–3653 (2003)

    Article  CAS  Google Scholar 

  43. Chamkha, A.J., Selimefendigil, F., Ismael, M.A.: Mixed convection in a partially layered porous cavity with an inner rotating cylinder. Numer. Heat Transf. Part A: Appl. 69(6), 659–675 (2016)

    Article  ADS  Google Scholar 

  44. Aly, A.M., Raizah, Z.A.S.: Mixed convection in an inclined nanofluid filled-cavity saturated with a partially layered porous medium. J. Therm. Sci. Eng. Appl. 11(4), 041002–041011 (2019)

    Article  CAS  Google Scholar 

  45. Chamkha, A.J., Mansour, M.A., Rashad, A.M., Kargarsharifabad, H., Armaghani, T.: Magnetohydrodynamic mixed convection and entropy analysis of nanofluid in gamma-shaped porous cavity. J. Thermophys. Heat Transf. 34(4), 836–47 (2020)

    Article  CAS  Google Scholar 

  46. Chamkha, A.J., Armaghani, T., Mansour, M.A., Rashad, A.M., Kargarsharifabad, H.: MHD convection of an Al2O3–Cu/water hybrid nanofluid in an inclined porous cavity with internal heat generation/absorption. Iran. J. Chem. Chem. Eng. (IJCCE) 41(3), 936 (2021)

    Google Scholar 

  47. Tiwari, R., Das, M.: Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transf. 50, 2002–2018 (2007)

    Article  CAS  Google Scholar 

  48. Billah, M.M., Rahman, D.M., Razzak, M.A., Rahman, S., Mekhilef, S.: Unsteady buoyancy-driven heat transfer enhancement of nanofluids in an inclined triangular enclosure. Int. Commun. Heat Mass Transf. 49, 115–127 (2013)

    Article  CAS  Google Scholar 

  49. Suresh, S., Venkitaraj, K.P., Selvakumar, K.P., Chandrasekar, M.: Effect of Al2O3–Cu/water hybrid nanofluid in heat transfer. Exp. Thermal Fluid Sci. 38, 54–60 (2012)

    Article  CAS  Google Scholar 

  50. Jeena, P.K., Brocchi, E.A., Motta, M.S.: In-situ formation of Cu–Al2O3 nanoscale composites by chemical routes and studies on their microstructures. Mater. Sci. Eng. A 313, 180–186 (2001)

    Article  Google Scholar 

  51. Sung-Tag, Oh.: Jai-Sung Lee, Tohru Sekino, Koichi Niihara, Fabrication of Cu dispersed Al2O3 nanocomposite using Al2O3/CuO and Al2O3/Cu nitrate mixtures. Scripta Mater. 44, 2117–2120 (2001)

    Google Scholar 

  52. Toghraie, D., Chaharsoghi, V.A., Afrand, M.: Measurement of thermal conductivity of ZnO–TiO2/EG hybrid nanofluid. J. Thermal Anal. Calorim. 125, 527–535 (2016)

    Article  CAS  Google Scholar 

  53. Huang, D., Zan, Wu., Sunden, B.: Effects of hybrid nanofluid mixture in plate heat exchangers. Exp. Thermal Fluid Sci. 72, 190–196 (2016)

    Article  CAS  Google Scholar 

  54. Han, Z.H., Yang, B., Kim, S.H., Zachariah, M.R.: Application of hybrid sphere/carbon nanotube particles in naonofluids. Nanotechnology 18, 105701 (2007)

    Article  ADS  Google Scholar 

  55. Labib, M.N., Nine, Md.J., Afrianto, H., Chung, H., Jeong, H.: Numerical investigation on effect of base fluids and hybrid nanofluid in forced convective heat transfer. Int. J. Therm. Sci. 71, 163–171 (2013)

    Article  Google Scholar 

  56. Arefmanesh, A., Najafi, M., Nikfar, M.: MLPG application of nanofluid flow mixed convection heat transfer in a wavy wall cavity. Comput. Model. Eng. Sci. 69(2), 91 (2010). https://doi.org/10.3970/cmes.2010.069.091

    Article  MathSciNet  Google Scholar 

  57. Alsabery, A.I., Ismael, M.A., Chamkha, A.J., Hashim, I.: Impact of finite wavy wall thickness on entropy generation and natural convection of nanofluid in cavity partially filled with non-Darcy porous layer. Neural Comput. Appl. 32, 13679–13699 (2020)

    Article  Google Scholar 

  58. Das, P.K., Mahmud, S.: Numerical investigation of natural convection inside a wavy enclosure. Int. J. Therm. Sci. 42, 397–406 (2003)

    Article  Google Scholar 

  59. Kumar, B.R.: A study of free convection induced by a vertical wavy surface with heat flux in a porous enclosure. Numer. Heat Transf. Part A Appl. 37, 493–510 (2000)

    Article  ADS  CAS  Google Scholar 

  60. Alsabery, A.I., Tayebi, T., Chamkha, A.J., Hashim, I.: Natural convection of A’l2O3-water nanofluid in a non-Darcian wavy porous cavity under the local thermal non-equilibrium condition. Sci. Rep. 10, 18048 (2020). https://doi.org/10.1038/s41598-020-75095-5

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  61. Baytaş, A.C.: Thermal non-equilibrium natural convection in a square enclosure filled with a heat-generating solid phase, non-Darcy porous medium. Int. J. Energy Res. 27, 975–988 (2003)

    Article  Google Scholar 

  62. Sheremet, M.A., Pop, I., Nazar, R.: Natural convection in a square cavity filled with a porous medium saturated with a nanofluid using the thermal nonequilibrium model with a Tiwari and Das nanofluid model. Int. J. Mech. Sci. 100, 312–321 (2015)

    Article  Google Scholar 

  63. Zargartalebi, H., Ghalambaz, M., Sheremet, M.A., Pop, I.: Unsteady free convection in a square porous cavity saturated with nanofluid: the case of local thermal nonequilibrium and Buongiorno’s mathematical models. J. Porous Media 20, 999–1016 (2017)

    Article  Google Scholar 

  64. Tahmasebi, A., Mahdavi, M., Ghalambaz, M.: Local thermal nonequilibrium conjugate natural convection heat transfer of nanofluids in a cavity partially filled with porous media using Buongiorno’s model. Numer. Heat Transf. Part A 73(4), 254–276 (2018). https://doi.org/10.1080/10407782.2017.1422632

    Article  ADS  CAS  Google Scholar 

  65. Nield, D.A., Kuznetsov, A.V., Xiong, M.: Effect of local thermal non-equilibrium on thermally developing forced convection in a porous medium. Int. J. Heat Mass Transf. 45, 4949–4955 (2002)

    Article  Google Scholar 

  66. Kim, S.J., Jang, S.P.: Effects of the Darcy number, the Prandtl number, and the Reynolds number on local thermal non-equilibrium. Int. J. Heat Mass Transf. 45, 3885–3896 (2002)

    Article  CAS  Google Scholar 

  67. Amiri, A., Vafai, K., Kuzay, T.M.: Effects of boundary conditions on non-Darcian heat transfer through porous media and experimental comparisons. Numer. Heat Transf. Part A 27, 651–664 (1995)

    Article  ADS  CAS  Google Scholar 

  68. Mahmoudi, Y., Karimi, N.: Numerical investigation of heat transfer enhancement in a pipe partially filled with a porous material under local thermal non-equilibrium condition. Int. J. Heat Mass Transf. 68, 161–173 (2014)

    Article  Google Scholar 

  69. Izadi, M., Mehryan, S.A.M., Sheremet, M.A.: Natural convection of CuO-water micropolar nanofluids inside a porous enclosure using local thermal non-equilibrium condition. J. Taiwan Inst. Chem. Eng. 88, 89–103 (2018)

    Article  CAS  Google Scholar 

  70. Sivasankaran, S., Alsabery, A.I., Hashim, I.: Internal heat generation effect on transient natural convection in a nanofluid-saturated local thermal non-equilibrium porous inclined cavity. Physica A 509(1), 275–293 (2018)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  71. Cho, C.-C.: Heat transfer and entropy generation of mixed convection flow in Cu-water nanofluid-filled lid-driven cavity with wavy surface. Int. J. Heat Mass Transf. 119, 163–174 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.090

    Article  CAS  Google Scholar 

  72. Hussain, S., Oztop, H.F., Mehmood, K., Abu-Hamdeh, N.: Effects of inclined magnetic field on mixed convection in a nanofluid filled double lid-driven cavity with volumetric heat generation or absorption using finite element method. Chin. J. Phys. 56, 484–501 (2018). https://doi.org/10.1016/j.cjph.2018.02.002

    Article  CAS  Google Scholar 

  73. Madkhali, H.A., Nawaz, M., Saif, R.S., Afzaal, M.F., Alharbi, S.O., Alaoui, M.K.: Comparative analysis on the roles of different nanoparticles on mixed convection heat transfer in Newtonian fluid in Darcy-Forchheimer porous space subjected to convectively heated boundary. Int. Commun. Heat Mass Transf. 128, 105580 (2021)

    Article  CAS  Google Scholar 

  74. Maxwell, J.A.: Treatise on electricity and magnetism, 2nd edn. Oxford University Press, Cambridge (1904)

    Google Scholar 

  75. Maxwell, J.: A Treatise on electricity and magnetism, 2nd edn. Clarendon Press, Oxford (1881)

    Google Scholar 

  76. Brinkman, H.C.: The viscosity of concentrated suspensions and solution. J. Chem. Phys. 20, 571–581 (1952)

    Article  ADS  CAS  Google Scholar 

  77. Ahmed, S.E.: Mixed convection in thermally anisotropic non-Darcy porous medium in double lid-driven cavity using Bejan’s heatlines. Alex. Eng. J. 55, 299 (2016)

    Article  Google Scholar 

  78. Ahmed, S.E., Mansour, M.A., Rashad, A.M., Salah, T.: MHD natural convection from two heating modes in fined triangular enclosures filled with porous media using nanofluids. J. Therm. Anal. Calorim. 139, 3133 (2020)

    Article  CAS  Google Scholar 

  79. Cheong, H.T., Sivasankaran, S., Bhuvaneswari, M.: Natural convection in a wavy porous cavity with sinusoidal heating and internal heat generation. Int. J. Numer. Methods Heat Fluid Flow 27, 287 (2017)

    Article  Google Scholar 

  80. Abbaszadeh, M., Salehi, A., Abbassi, A.: Lattice Boltzmann simulation of heat transfer enhancement in an asymmetrically heated channel filled with random porous media. J. Porous Media 20(2), 175–191 (2017)

    Article  Google Scholar 

  81. Chamkha, A.J.: Double-diffusive convection in a porous enclosure with cooperating temperature and concentration gradients and heat generation or absorption effects. Numer. Heat Transf. Part A Appl. 41(1), 65–87 (2002). https://doi.org/10.1080/104077802317221447

    Article  ADS  Google Scholar 

  82. Chamkha, A.J., Al-Naser, H.: Double-diffusive convection in an inclined porous enclosure with opposing temperature and concentration gradients. Int. J. Therm. Sci. 40, 227–244 (2001)

    Article  CAS  Google Scholar 

  83. Mansour, M.A., Bakier, M.A.Y.: Magnetohydrodynamic mixed convection of TiO2–Cu/water between the double lid-driven cavity and a central heat source surrounding by a wavy tilted domain of porous medium under local thermal non-equilibrium. SN Appl. Sci. 5, 51 (2023). https://doi.org/10.1007/s42452-022-05260-0

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Assiut University, Assiut, 71515, Egypt

    M. A. Mansour & M. A. Y. Bakier

  2. Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt

    Sameh E. Ahmed

  3. Faculty of Science, King Khalid University, Abha, 62529, Saudi Arabia

    Sameh E. Ahmed

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  1. M. A. Mansour
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  2. Sameh E. Ahmed
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  3. M. A. Y. Bakier
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Correspondence to M. A. Y. Bakier.

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Mansour, M.A., Ahmed, S.E. & Bakier, M.A.Y. MHD natural convection around “plus” shape of circular barriers under local thermal non-equilibrium condition inside a wavy porous cavity saturated with Al2O3-Cu/water. Int J Adv Eng Sci Appl Math 16, 87–104 (2024). https://doi.org/10.1007/s12572-024-00369-4

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