Numerical simulation of Darcy–Brinkman oscillatory flow of dissipative fluid: Utilization of finite difference method

References

• H. Darcy, “Les fontaines publiques de la ville de Dijon: exposition et application des principes à suivre et des formules à employer dans les questions de distribution d’eau,” Victor Dalmont, vol. 1, 1856.
   Google Scholar
• H. C. Brinkman, “A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles,” Flow, Turbul. Combust., vol. 1, no. 1, pp. 27–34, 1949.
   Google Scholar
• P. Saxena and L. Kumar, “Flow of a viscous fluid through different porous structures embedded in porous medium,” J. Porous Media, vol. 15, no. 12, pp. 1125–1135, 2012.
   PubMed Web of Science ®Google Scholar
• W. Williams, “Constitutive equations for flow of an incompressible viscous fluid through a porous medium,” Q. Appl. Math., vol. 36, no. 3, pp. 255–267, 1978. DOI: 10.1090/qam/99640.
   Web of Science ®Google Scholar
• A. Nabizadeh, M. Abbasi, J. Siavashi, M. Sharifi and M. R. K. Movaghar, “Fluid flow modeling through pressure-dependent porous media: an analytical solution and a computational fluid dynamics approach,” Groundw. Sustain. Dev., vol. 18, pp. 100776, 2022. DOI: 10.1016/j.gsd.2022.100776.
   Google Scholar
• S. Jamshed, R. Kharbanda and A. K. Dhiman, “Study of flow through and around a pair of porous cylinders covering steady and unsteady regimes,” Phys. Fluids, vol. 34, no. 10, pp. 103601, Oct. 2022. DOI: 10.1063/5.0113660.
   Web of Science ®Google Scholar
• M. R. Shahnazari, M. H. Moosavi and A. J. Chamkha, “Investigation of nonlinear fluid flow equation in a porous media and evaluation of convection heat transfer coefficient, by taking the forchheimer term into account,” J. Nanofluids, vol. 11, no. 4, pp. 598–603, Aug. 2022. DOI: 10.1166/jon.2022.1867.
   Web of Science ®Google Scholar
• T. Karmakar, M. Alam and G. P. Raja Sekhar, “Analysis of Brinkman-Forchheimer extended Darcy’s model in a fluid saturated anisotropic porous channel,” CPAA, vol. 21, no. 3, pp. 845, 2022. DOI: 10.3934/cpaa.2022001.
   Google Scholar
• M. S. Kausar, A. Hussanan, M. Mamat and B. Ahmad, “Boundary layer flow through darcy–brinkman porous medium in the presence of slip effects and porous dissipation,” Symmetry (Basel), vol. 11, no. 5, pp. 659, May 2019. DOI: 10.3390/sym11050659.
   Google Scholar
• M. Hajipour and A. M. Dehkordi, “Transient behavior of fluid flow and heat transfer in vertical channels partially filled with porous medium: effects of inertial term and viscous dissipation,” Energy Convers. Manag., vol. 61, pp. 1–7, Sep 2012. DOI: 10.1016/j.enconman.2012.03.001.
   Web of Science ®Google Scholar
• M. M. Bhatti, L. Phali and C. M. Khalique, “Heat transfer effects on electro-magnetohydrodynamic Carreau fluid flow between two micro-parallel plates with Darcy–Brinkman–Forchheimer medium,” Arch. Appl. Mech., vol. 91, no. 4, pp. 1683–1695, Apr 2021. DOI: 10.1007/s00419-020-01847-4.
   Web of Science ®Google Scholar
• C. Y. Wang, “Darcy-Brinkman flow in channels of arbitrary curvature,” J. Porous Media, vol. 25, no. 3, pp. 1–10, 2022. DOI: 10.1615/JPorMedia.2021033843.
   Web of Science ®Google Scholar
• R. Surendar, M. Muthtamilselvan and R. Rakkiyappan, “LMI based sampled-data controller for synchronization on the time-delay Darcy-Brinkman model,” J. Franklin Inst., vol. 359, no. 12, pp. 5865–5890, Aug 2022. DOI: 10.1016/j.jfranklin.2022.06.020.
   Web of Science ®Google Scholar
• M. M. Bhatti and E. E. Michaelides, “Oldroyd 6-constant Electro-magneto-hydrodynamic fluid flow through parallel micro-plates with heat transfer using Darcy-Brinkman-Forchheimer model: a parametric investigation,” MINE, vol. 5, no. 3, pp. 1–19, 2023. DOI: 10.3934/mine.2023051.
   Google Scholar
• K. N. Sneha, U. S. Mahabaleshwar, R. Bennacer and M. E. Ganaoui, “Darcy Brinkman equations for hybrid dusty nanofluid flow with heat transfer and mass transpiration,” Computation, vol. 9, no. 11, pp. 118, Nov 2021. DOI: 10.3390/computation9110118.
   Web of Science ®Google Scholar
• M. S. Khan, M. A. Siddiqui and M. I. Afridi, “Finite difference simulation of nonlinear convection in magnetohydrodynamic flow in the presence of viscous and joule dissipation over an oscillating plate,” Symmetry (Basel), vol. 14, no. 10, pp. 1988, Sep 2022. DOI: 10.3390/sym14101988.
   Google Scholar
• A. O. Nyakebogo, J. M. Kerongo and R. K. Obogi, “Stability and consistency analysis of FTCS scheme for unsteady magnetohydrodynamic fluid flow over a vertical stretching sheet,” Int. J. Sci. Res. Math. Stat. Sci, vol. 8, no. 4, pp. 38-43, 2021.
   Google Scholar
• S. Li, M. I. Khan, F. Alzahrani and S. M. Eldin, “Heat and mass transport analysis in radiative time dependent flow in the presence of Ohmic heating and chemical reaction, viscous dissipation: an entropy modeling,” Case Stud. Therm. Eng., vol. 42, pp. 102722, Feb 2023. DOI: 10.1016/j.csite.2023.102722.
   Web of Science ®Google Scholar
• K. Muhammad, K. A. M. Alharbi, N. Fatima and A. Alhowaity, “Squeezed flow of MHNF (modified hybrid nanofluid) with thermal radiation and C-C (Cattaneo-Christov) heat flux: a numerical study via FDM,” Mater. Sci. Eng. B, vol. 289, pp. 116268, Mar 2023. DOI: 10.1016/j.mseb.2023.116268.
   Web of Science ®Google Scholar
• M. Qasim and B. Ahmad, “Numerical solution for the blasius flow in a Casson fluid with viscous dissipation and convective boundary conditions,” Heat Transf. Res., vol. 46, no. 8, pp. 689–697, 2015. DOI: 10.1615/HeatTransRes.2015007148.
   Web of Science ®Google Scholar
• S. Noreen and M. Qasim, “Influence of Hall current and viscous dissipation on pressure driven flow of pseudoplastic fluid with heat generation: a mathematical study,” PLoS One, vol. 10, no. 6, pp. e0129588, Jun 2015. DOI: 10.1371/journal.pone.0129588.
   PubMed Web of Science ®Google Scholar
• Z. Iqbal, M. Qasim, M. Awais, T. Hayat and S. Asghar, “Stagnation-point flow by an exponentially stretching sheet in the presence of viscous dissipation and thermal radiation,” J. Aerosp. Eng., vol. 29, no. 2, pp. 2016, Mar 2016. DOI: 10.1061/(ASCE)AS.1943-5525.0000546.
   Web of Science ®Google Scholar
• K. Ganesh Kumar, G. K. Ramesh, B. J. Gireesha and R. S. R. Gorla, “Characteristics of Joule heating and viscous dissipation on three-dimensional flow of Oldroyd B nanofluid with thermal radiation,” Alexandria Eng. J, vol. 57, no. 3, pp. 2139–2149, Sep 2018. DOI: 10.1016/j.aej.2017.06.006.
   Web of Science ®Google Scholar
• B. K. Swain, B. C. Parida, S. Kar and N. Senapati, “Viscous dissipation and joule heating effect on MHD flow and heat transfer past a stretching sheet embedded in a porous medium,” Heliyon, vol. 6, no. 10, pp. e05338, Oct 2020. DOI: 10.1016/j.heliyon.2020.e05338.
   PubMed Web of Science ®Google Scholar
• M. Usman, O. D. Makinde, Z. H. Khan, R. Ahmad and W. A. Khan, “Applications of fractional calculus to thermodynamics analysis of hydromagnetic convection in a channel,” Int. Commun. Heat Mass Transf., vol. 149, pp. 107105, Dec 2023. DOI: 10.1016/j.icheatmasstransfer.2023.107105.
   Web of Science ®Google Scholar
• K. Govindarajulu, A. S. Reddy and A. J. Chamkha, “Entropy analysis on oscillating flow of third grade nanofluid in a channel with Joule heating: a Buongiorno model approach,” Eur. Phys. J. Plus, vol. 138, no. 5, pp. 416, May 2023. DOI: 10.1140/epjp/s13360-023-04061-7.
   Web of Science ®Google Scholar
• M. I. Afridi and M. Qasim, “Entropy generation and heat transfer in boundary layer flow over a thin needle moving in a parallel stream in the presence of nonlinear Rosseland radiation,” Int. J. Therm. Sci., vol. 123, pp. 117–128, 2018. DOI: 10.1016/j.ijthermalsci.2017.09.014.
   Web of Science ®Google Scholar
• M. I. Afridi and M. Qasim, “Comparative study and entropy generation analysis of Cu–H2O and Ag–H2O nanofluids flow over a slendering stretching surface,” J. Nanofluids, vol. 7, no. 4, pp. 783–790, Aug 2018. DOI: 10.1166/jon.2018.1488.
   Web of Science ®Google Scholar
• M. I. Afridi, M. Qasim and S. Shafie, “Entropy generation in hydromagnetic boundary flow under the effects of frictional and Joule heating: exact solutions,” Eur. Phys. J. Plus, vol. 132, no. 9, pp. 404, Sep 2017. DOI: 10.1140/epjp/i2017-11704-5.
   Web of Science ®Google Scholar
• M. I. Afridi, M. Qasim, N. A. Khan and O. D. Makinde, “Minimization of entropy generation in mhd mixed convection flow with energy dissipation and joule heating: utilization of sparrow-quack-boerner local non-similarity method,” DDF, vol. 387, pp. 63–77, 2018. DOI: 10.4028/www.scientific.net/DDF.387.63.
   Google Scholar
• M. I. Afridi, M. Qasim, S. Shafie and O. D. Makinde, “Entropy generation analysis of spherical and non-spherical Ag-water nanofluids in a porous medium with magnetic and porous dissipation,” J. Nanofluids, vol. 7, no. 5, pp. 951–960, Oct 2018. DOI: 10.1166/jon.2018.1519.
   Google Scholar
• M. I. Afridi, Z.-M. Chen, M. Qasim and O. D. Makinde, “Computational analysis of entropy generation minimization and heat transfer enhancement in magnetohydrodynamic oscillatory flow of ferrofluids,” J. Magn. Magn. Mater., vol. 594, pp. 171848, Mar 2024. DOI: 10.1016/j.jmmm.2024.171848.
   Web of Science ®Google Scholar
• M. I. Afridi and M. Qasim, “Second law analysis of Blasius flow with nonlinear Rosseland thermal radiation in the presence of viscous dissipation,” Propuls. Power Res., vol. 8, no. 3, pp. 234–242, Sep 2019. DOI: 10.1016/j.jppr.2018.06.001.
   Web of Science ®Google Scholar
• K. A. Hoffmann and S. T. Chiang, “Computational fluid dynamics volume I,” Eng. Educ. Syst., 2000.
   Google Scholar
• A. Wakif, M. Qasim, M. I. Afridi, S. Saleem and M. M. Al-Qarni, “Numerical examination of the entropic energy harvesting in a magnetohydrodynamic dissipative flow of Stokes’ second problem: utilization of the gear-generalized differential quadrature method,” J. Non-Equilibrium Thermodyn., vol. 44, no. 4, pp. 385–403, Oct 2019. DOI: 10.1515/jnet-2018-0099.
   Web of Science ®Google Scholar