A theoretical and computational study of MHD natural convection in an isotropic non-Darcian porous medium saturated with electrically conducting helium gas in an enclosure in the presence of heat generation is presented. A Brinkman extended Darcy-Forchheimer model is employed and the working fluid is assumed to be incompressible. The model is non-dimensionalised and converted into pressure-velocity form. The Harlow-Welch marker and cell (MAC) finite difference technique is employed to solve the nonlinear boundary value problem via pressure-vorticity coupling. A parametric investigation of the influence of Grashof number (Gr), Hartmann magnetic number (Ha), Darcy number (Da), and the internal heat generation parameter (Γ) on streamline and isotherm distributions with Prandtl number (Pr) is 0.71 (Helium) is conducted. The variation in local Nusselt number along the left and right walls of the computational 2 D enclosure is also studied. Validation house-computational numerical MATLAB code is tests are included. Local Nusselt number is elevated at both left and right walls with greater Darcy number (higher medium permeability) and Grashof number. However, with greater internal heat generation, local Nusselt number magnitudes are enhanced at the left (cold) wall only but suppressed at the right (hot) wall. Increasing magnetic field reduces local Nusselt number at both left and right walls. With increasing magnetic field, the single vortex is strongly distorted and skewed towards the top left and lower right corners of the enclosure. Temperature contours at the left and right wall are however less intense with greater magnetic field effect. The simulations are of relevance to hybrid electromagnetic gaseous fuel cells, magnetic field control of filtration processes and porous media materials processing systems.
SinghS.Experimental and numerical investigations of a single and double pass porous serpentine wavy wire mesh packed bed solar air heater. Renew Energy2020; 145: 1361–1387.
2.
DukhanN.Analysis of Brinkman-extended Darcy flow in porous media and experimental verification using metal foam. ASME J Fluids Eng2012; 134: 071201.
3.
BégOAMotsaSSKadirA, et al. Spectral quasilinear numerical simulation of micropolar convective wall plumes in high permeability porous media. J Eng Thermophys2016; 25: 1–24.
4.
ChoiWOokaR.Effect of natural convection on thermal response test conducted in saturated porous formation: comparison of gravel-backfilled and cement-grouted borehole heat exchangers. Renew Energy2016; 96: 891–903.
5.
BégOAMotsaSSBégTA, et al. Numerical study of nonlinear heat transfer from a wavy surface to a high permeability medium with pseudo-spectral and smoothed particle methods. Int J Appl Comput Math2017; 3: 3593–3613.
6.
BelabidJ.Impact of wall waviness on the convection patterns inside a horizontal porous annulus. ASME J Fluids Eng2020; 142: 071304.
7.
VafaiK.Porous media:aApplications in biological systems and biotechnology. Boca Raton, FL: CRC Press, 2010.
8.
TripathiDBégOA.A numerical study of oscillating peristaltic flow of generalized Maxwell viscoelastic fluids through a porous medium. Transp Porous Med2012; 95: 337–348.
9.
BégOAPrasadVRVasuB.Numerical study of mixed bioconvection in porous media saturated with nanofluid and containing oxytactic micro-organisms. J Mech Med Biol2013; 13: 1350067–1350025.
10.
CaltagironeJP.Thermoconvective instabilities in a porous medium bounded by two concentric horizontal cylinders. J Fluid Mech1976; 76: 337–362.
11.
Martins-CostaMLSampaioR andSaldanha da GamaRM.Modelling and simulation of natural convection flow in a saturated porous cavity. Meccanica1994; 29: 1–13.
12.
SalehHHashimI.Conjugate natural convection in a porous enclosure with non-uniform heat generation. Transp Porous Med2012; 94: 759–774.
13.
SiddheshwarPGSiddabasappaC.Unsteady natural convection in a liquid-saturated porous enclosure with local thermal non-equilibrium effect. Meccanica2020; 55: 1763–1780.
14.
BasakTRoySBabuSK.Natural convection and flow simulation in differentially heated isosceles triangular enclosures filled with porous medium. Chem Eng Sci2008; 63: 3328–3340.
15.
ChenYLiBZhangJ.Spectral collocation method for natural convection in a square porous cavity with local thermal equilibrium and non-equilibrium models. Int J Heat Mass Transfer2016; 96: 84–96.
16.
SongMViskantaR.Natural convection flow and heat transfer within a rectangular enclosure containing a vertical porous layer. Int J Heat Mass Transfer1994; 37: 2425–2438.
17.
BégOAUddinMJBégT, et al. Numerical simulation of self-similar thermal convection from a spinning cone in anisotropic porous medium. J Hydrodyn2016; 28: 184–194.
18.
ScheideggerAE.Physics of flow through porous media. New York: Macmillan Book Co., 1960.
19.
BégTARashidiMMBégOA, et al. Differential transform semi-numerical simulation of biofluid-particle suspension flow and heat transfer in non-Darcian porous media. Comput Methods Biomech Biomed Eng2013; 16: 896–907.
20.
ChandraPSatyamurtyVV.Non-Darcian and anisotropic effects on free convection in a porous enclosure. Transp Porous Med2011; 90: 301–320.
21.
KumarPTopinF.Investigation of fluid flow properties in open cell foams: Darcy and weak inertia regimes. Chem Eng Sci2014; 116: 793–805.
22.
UmavathiJCO. AnwarB.Numerical study of double-diffusive dissipative reactive convective flow in an open vertical duct containing a non-Darcy porous medium with Robin boundary conditions. J Eng Math2019; 119: 135–147.
23.
SultanaZHyderMN.Non-Darcy free convection inside a wavy enclosure. Int Commun Heat Mass Transfer2007; 34: 136–146.
24.
BaytasAC.Thermal non‐equilibrium natural convection in a square enclosure filled with a heat‐generating solid phase, non‐Darcy porous medium. Int J Energy Res2013; 27: 975–988.
25.
BaytaşAFBaytaşAC.Thermal non-equilibrium natural convection in a square enclosure with heat-generating porous layer on inner walls. Transp Porous Med2017; 120: 167–182.
26.
BaytasACBaytasAFInghamDB, et al. Double diffusive natural convection in an enclosure filled with a step type porous layer: non-Darcy flow. Int J Therm Sci2009; 48: 665–673.
27.
RashadAMElsayed AhmedSAhmed MansourM.Effects of chemical reaction and thermal radiation on unsteady double diffusive convection. Int J Numer Methods Heat Fluid Flow2014; 24: 1124–1140.
28.
RashadAMChamkhaAJIsmaelMA, et al. Magnetohydrodynamics natural convection in a triangular cavity filled with a Cu-Al2O3/water hybrid nanofluid with localized heating from below and internal heat generation. J Heat Transf2018; 140: 072502.
29.
MansourMASiddiqaSGorlaRSR, et al. Effects of heat source and sink on entropy generation and MHD natural convection of Al 2 O 3 -Cu/water hybrid nanofluid filled with square porous cavity. Therm Sci Eng Prog2018; 6: 57–71.
30.
Abdel-NourZAissaAMebarek-OudinaF, et al. Magnetohydrodynamic natural convection of hybrid nanofluid in a porous enclosure: numerical analysis of the entropy generation. J Therm Anal Calorim2020; 141: 1981–1992.
31.
RashadAMArmaghaniTChamkhaAJ, et al. Entropy generation and MHD natural convection of a nanofluid in an inclined square porous cavity: effects of a heat sink and source size and location. Chinese J Phys2018; 56: 193–211.
32.
AhmedSEMansourMARashadAM, et al. Natural convection from two heating modes in fined triangular enclosures filled with porous media using nanofluids. J Therm Anal Calorim2020; 139: 3133–3149.
33.
AhmedSE.Mixed convection in thermally anisotropic non-Darcy porous medium in double lid-driven cavity using Bejan’s heatlines. Alexandria Eng J2016; 55: 299–309.
34.
AhmedSERashedZZ.MHD natural convection in a heat generating porous medium-filled wavy enclosures using Buongiorno's nanofluid model. Case Stud Therm Eng2019; 14: 100430.
35.
MansourMAAhmedSE.Mixed convection flows in a square lid-driven cavity with heat source at the bottom utilising nanofluid. Can J Chem Eng2012; 90: 100–110.
36.
LiSLeeACMitchellRE, et al. Direct carbon conversion in a helium fluidized bed fuel cell. Solid State Ionics2008; 179: 1549–1552.
FaghriAGuoZ.Challenges and opportunities of thermal management issues related to fuel cell technology and modeling. Int J Heat Mass Transf2005; 48: 3891–3920.
39.
BaoCOuyangMYiB.Analysis of the air and thermal management in insulated heat exchange membrane fuel cell systems. Int J Hydrogen Energy2006; 31: 1040–1057.
40.
KanawkaKOthmanMHDDroushiotisN, et al. NI/NI-YSZ current collector/anode dual layer hollow fibers for micro-tubular solid oxide fuel cells. Fuel Cells2011; 11: 690–696.
41.
GuidottiR.Evaluation of MHD materials for use in high-temperature fuel cells, topical report I - SAN-1485-1. The Montana Energy and MHD Research and Development Institute, Inc. 'Bune, Montana, USA, 1978.
42.
FerraroVCAPlumptonC.An introduction to magneto-fluid mechanics. Oxford: Oxford University Press, 1961.
43.
MaqboolKBégOA.Ayesha Sohail, ShafaqIdreesa, analytical solutions for magnetohydrodynamic oscillatory rotating plate and channel flows in porous media using a fractional Burgers viscoelastic model. Eur Phys J Plus2016; 131: 140–157.
44.
Anwar BégOPrasadVRVasuB, et al. Computational modelling of magnetohydrodynamic convection from a rotating cone in orthotropic Darcian porous media. J Braz Soc Mech Sci Eng2017; 39: 2035–2054.
45.
JiangCFengWZhongH, et al. Magnetic and gravitational convection of air in a porous cubic enclosure with a coil inclined around the Y axis. Transp Porous Med2014; 102: 167–183.
46.
BegumASNithyadeviNÖztopHF, et al. Numerical simulation of MHD mixed convection in a nanofluid filled non-Darcy porous enclosure. Int J Mech Sci2017; 130: 154–166.
47.
IliutaILarachiF.Magnetohydrodynamics of trickle bed reactors: mechanistic model, experimental validation and simulations. Chem Eng Sci2003; 58: 297–307.
48.
AllouiZVasseurPCostaVAF, et al. Effect of a non-constant magnetic field on natural convection in a horizontal porous layer heated from the bottom. J Eng Math2013; 81: 141–155.
49.
HarlowFH. The marker-and-cell method. In: Numerical methods in fluid dynamics. Von Karman Inst. for Fluid Dynamics, Belgium, 1972.
50.
SiavashiMBordbarVRahnamaP.Heat transfer and entropy generation study of non-Darcy double-diffusive natural convection in inclined porous enclosures with different source configurations. Appl Therm Eng2017; 110: 1462–1475.
51.
Ahmed SE. Non-Darcian natural convection of a nanofluid due to triangular fins within trapezoidal enclosures partially filled with a thermal non-equilibrium porous layer. J Therm Anal Calorim 2020.
52.
VenkatadriKGaffarSAPrasad VR, et al. Simulation of natural convection heat transfer in a 2-D trapezoidal enclosure. Int J Autom Mech Eng2019; 16: 7375–7390.
53.
VenkatadriKBégOAPrasadVR.Numerical simulation of thermal radiation influence on natural convection in a trapezoidal enclosure: heat flow visualization through energy flux vectors. Int J Mech Sci2020; 171.
54.
BégOAVenkatadriKRamachandra PrasadV, et al. Numerical simulation of hydromagnetic Marangoni convection flow in a Darcian porous semiconductor melt enclosure with buoyancy and heat generation effects. Mater Sci Eng B2020; 261: 114722.
55.
TannehillJCAndersonDAPletcherRH.Computational fluid mechanics and heat transfer. Boca Raton, FL: Taylor & Francis Ltd., 1997.
56.
de Vahl DavisD.Natural convection of air in a square cavity: a benchmark solution. Int J Numer Methods Fluids1983; 3: 249–264.
57.
ManzariMT.An explicit finite element algorithm for convective heat transfer problems. Int J Numer Methods Heat Fluid Flow1999; 9: 860–877.
58.
WanDCPatnaikBSVWeiGW.A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution. Numer Heat Transf B2001; 40: 199–228.
59.
DybbsAEdwardsRV. A new look at porous media fluid mechanics - Darcy to turbulent. In: Bear J (ed.) Fundamentals of transport phenomena in porous media. NATO Series, Netherlands, 1984, pp. 199–256.
60.
UddinMJKhanWABégOA.Bioconvection nanofluid slip flow past a wavy surface with applications in nano-biofuel cells. ChineseJ Phys2017; 55: 2048–2063.
