A A Computational Investigation of a Non-Singular Fractional Operator for an Unsteady MHD Flow Problem

A Computational Investigation

  • Bhaskar Jyoti Bhuyan
  • Utpal Kumar Saha Saha National Institute of Technology Arunachal Pradesh
  • G.C. Hazarika
  • Dipen Saikia

Abstract

This paper analyzes the impacts of thermal conductivity and variable viscosity on unsteady magnetohydrodynamic (MHD) fluid flow over an infinite vertical plate embedded in a porous medium, including thermal diffusion effects. Atangana–Baleanu (AB) and Caputo–Fabrizio (CF) fractional derivatives are applied in this work to model the system, including the effects of nonlocal and nonsingular kernels. A dimensionless formulation of the governing partial differential equations (PDEs) has been established. The equations are then discretized by using the ordinary finite difference approach and then numerically solved
by adopting the Gauss-Seidel iteration process. The influences of different parameters involved in the problems have been illustrated graphically and numerically. The variation of AB and CF fractional derivatives is obtained through a MATLAB based computational approach for the different values of velocity, temperature, and concentration distributions with respect to time under various parameters. A tabular comparison between AB and CF methods have been shown. It has been found that both approaches exhibit a significant level of consistency.

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References

H. Alfven, Existence of electromagnetic-hydrodynamic waves, Nature 150 (1942), no. 3805, 405–406. doi:10.1038/150405d0.

V. C. Ferraro and C. Plumpton, Introduction to magneto-fluid mechanics, 1966.

K. R. Cramer and S. I. Pai, Magnetofluid dynamics for engineers and applied physicists, 1973.

D. A. Nield and A. Bejan, Convection in porous media, vol. 3, Springer, New York, 2006.

P. S. Hiremath and P. M. Patil, Free convection effects on the oscillatory flow of a couple stress fluid through a porous medium, Acta Mech. 98 (1993), 143–158. https://doi.org/10.1007/BF01174299.

B. Shankar Goud, P. Srilatha, T. Srinivasulu, Y. D. Reddy, and K. S. Kumar, Induced by heat source on unsteady MHD free convective flow of Casson fluid past a vertically oscillating plate through porous medium utilizing finite difference method, Mater. Today Proc. (2023). https://doi.org/10.1016/j.matpr.2023.01.378.

N. Gulle and R. Kodi, Soret radiation and chemical reaction effect on MHD Jeffrey fluid flow past an inclined vertical plate embedded in porous medium, Mater. Today Proc. 50 (2022), 2218–2226.

A. Sandhya, G. Reddy, and G. V. S. R. Deekshitulu, Radiation and chemical reaction effects on MHD Casson fluid flow past a semi-infinite vertical moving porous plate, 2020. https://doi.org/10.56042/ijpap.v58i7.31001.

R. Srinivasa Raju, Unsteady MHD boundary layer flow of Casson fluid over an inclined surface embedded in a porous medium with thermal radiation and chemical reaction, J. Nanofluids 7 (2018), no. 4, 694–703. https://doi.org/10.1166/jon.2018.1500.

S. Srinivas, P. B. A. Reddy, and B. S. R. V. Prasad, Effects of chemical reaction and thermal radiation on MHD flow over an inclined permeable stretching surface with non-uniform heat source/sink: An application to the dynamics of blood flow, J. Mech. Med. Biol. 14 (2014), no. 5, 1450067. https://doi.org/10.1142/S0219519414500675.

E. Omamoke and E. Amos, Chemical reaction, radiation and heat source effects on unsteady MHD blood flow over a horizontal porous surface in the presence of an inclined magnetic field, Int. J. Sci. Eng. Res. 11 (2020), no. 4.

D. Pal and B. Talukdar, Buoyancy and chemical reaction effects on MHD mixed convection heat and mass transfer in a porous medium with thermal radiation and Ohmic heating, Commun. Nonlinear Sci. Numer. Simul. 15 (2010), no. 10, 2878–2893. https://doi.org/10.1016/j.cnsns.2009.10.029.

N. S. Wahid, N. M. Arifin, N. S. Khashi’ie, I. Pop, N. Bachok, and M. E. H. Hafidzuddin, MHD mixed convection flow of a hybrid nanofluid past a permeable vertical flat plate with thermal radiation effect, Alex. Eng. J. 61 (2022), no. 4, 3323–3333. https://doi.org/10.1016/j.cjph.2023.07.016.

K. Suneetha, S. M. Ibrahim, and G. V. Ramana Reddy, The effects of radiation and chemical reaction on MHD mixed convective flow and mass transfer from a vertical surface with Ohmic heating and viscous dissipation, Multidiscip. Model. Mater. Struct. 16 (2020), no. 1, 191–207. https://doi.org/10.1108/MMMS-02-2018-0021.

O. Aydın and A. Kaya, Radiation effect on MHD mixed convection flow about a permeable vertical plate, Heat Mass Transf. 45 (2008), 239–246. https://doi.org/10.1007/s00231-008-0428-y.

S. Naramgari, S. Vangala, and M. Penem, Aligned magnetic field, radiation, and rotation effects on unsteady hydromagnetic free convection flow past an impulsively moving vertical plate in a porous medium, Int. J. Eng. Math. (2014), no. 1, 565162. https://doi.org/10.1155/2014/565162.

N. Sandeep and V. Sugunamma, Radiation and inclined magnetic field effects on unsteady hydromagnetic free convection flow past an impulsively moving vertical plate in a porous medium, J. Appl. Fluid Mech. 7 (2014), no. 2, 275–286. https://doi.org/10.36884/jafm.7.02.19431.

A. Kumar, MHD free convective fluctuating flow through a porous effect with variable permeability parameter, Int. J. Eng. 23 (2010), no. 3, 313–322.

B. K. Sharma, R. C. Chaudhary, and P. K. Sharma, Fluctuating mass transfer on three-dimensional flow through a porous medium with variable permeability, Adv. Theor. Appl. Math. 2 (2007), no. 3, 257–267.

M. V. Krishna and K. Jyothi, Heat and mass transfer on MHD rotating flow of a visco-elastic fluid through porous medium with time-dependent oscillatory permeability, J. Anal. 27 (2019), no. 2, 643–662. https://doi.org/10.1007/s41478-018-0099-0.

R. N. Barik, G. C. Dash, and M. Kar, Unsteady free convective MHD flow and mass transfer through porous medium in a rotating system with fluctuating heat source/sink and chemical reaction, J. Appl. Anal. Comput. 4 (2014), no. 3, 231–244.

J. R. Pattnaik, G. C. Dash, and S. Singh, Radiation and mass transfer effects on MHD free convection flow through porous medium past an exponentially accelerated vertical plate with variable temperature, Ann. Fac. Eng. Hunedoara 10 (2012), no. 3, 175.

B. S. Goud, B. S. Babu, M. N. Raja Shekar, and G. Srinivas, Mass transfer effects on MHD flow through porous medium past an exponentially accelerated inclined plate with variable temperature and thermal radiation, Int. J. Thermofluid Sci. Technol. 6 (2019), 19060402. http://dx.doi.org/10.36963/IJTST.19060402.

G. S. Seth, R. Sharma, and B. Kumbhakar, Heat and mass transfer effects on unsteady MHD natural convection flow of a chemically reactive and radiating fluid through a porous medium past a moving vertical plate with arbitrary ramped temperature, J. Appl. Fluid Mech. 9 (2015), no. 1, 103–117. https://doi.org/10.18869/acadpub.jafm.68.224.23961.

U. S. Rajput and S. Kumar, Radiation effects on MHD flow past an impulsively started vertical plate with variable heat and mass transfer, Int. J. Appl. Math. Mech. 8 (2012), no. 1, 66–85.

A. Selvaraj and E. Jothi, Heat source impact on MHD and radiation absorption fluid flow past an exponentially accelerated vertical plate with exponentially variable temperature and mass diffusion through a porous medium, Mater. Today Proc. 46 (2021), 3490–3494. https://doi.org/10.1016/j.matpr.2020.11.919.

B. K. Taid, N. Ahmed, and S. Sarma, Heat source and radiation absorption on unsteady MHD fluid flow over an infinite vertical plate embedded in a porous medium in presence of Soret effect, J. Math. Comput. Sci. 11 (2021), no. 6, 7154–7169. https://doi.org/10.28919/jmcs/6149.

S. Sarma and N. Ahmed, Thermal diffusion effect on unsteady MHD free convective flow past a semi-infinite exponentially accelerated vertical plate in a porous medium, Can. J. Phys. 100 (2022), no. 10, 437–451. https: //doi.org/10.1139/cjp-2021-0361.

S. F. Ahmmed, R. Biswas, and M. Afikuzzaman, Unsteady magnetohydrodynamic free convection flow of nanofluid through an exponentially accelerated inclined plate embedded in a porous medium with variable thermal conductivity in the presence of radiation, J. Nanofluids 7 (2018), no. 5, 891–901. https://doi.org/10.1166/jon.2018.1520.

G. S. Seth, Md S. Ansari, and R. Nandkeolyar, MHD natural convection flow with radiative heat transfer past an impulsively moving plate with ramped wall temperature, Heat Mass Transfer 47 (2011), 551–561. https://doi.org/10.1007/s00231-010-0740-1.

N. Ghara, S. Das, S. L. Maji, and R. N. Jana, Effect of radiation on MHD free convection flow past an impulsively moving vertical plate with ramped wall temperature, Amer. J. Sci. Ind. Res. 3 (2012), no. 6, 376–386. https://doi.org/10.5251/AJSIR.2012.3.6.376.386.

R. Srinivasa Raju, K. Sudhakar, and M. Rangamma, The effects of thermal radiation and heat source on an unsteady MHD free convection flow past an infinite vertical plate with thermal diffusion and diffusion thermo, J. Inst. Eng. (India): Ser. C 94 (2013), 175–186. https://doi.org/10.1007/s40032-013-0063-3.

F. S. Ibrahim, A. M. Elaiw, and A. A. Bakr, Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi-infinite vertical permeable moving plate with heat source and suction, Commun. Nonlinear Sci. Numer. Simul. 13 (2008), no. 6, 1056–1066. https://doi.org/10.1016/j.cnsns.2006.09.007.

N. Ahmed, Soret and radiation effects on transient MHD free convection from an impulsively started infinite vertical plate, (2012), 062701. https://doi.org/10.1115/1.4005749.

N. Ahmed, MHD convection with Soret and Dufour effects in a three-dimensional flow past an infinite vertical porous plate, Can. J. Phys. 88 (2010), no. 9, 663–674. https://doi.org/10.1139/P10-056.

N. Ahmed, H. Kalita, and D. P. Barua, Unsteady MHD free convective flow past a vertical porous plate immersed in a porous medium with Hall current, thermal diffusion and heat source, Int. J. Eng. Sci. Technol. 2 (2010), no. 6. http://dx.doi.org/10.4314/ijest.v2i6.63699.

N. A. Sheikh, F. Ali, M. Saqib, I. Khan, S. A. A. Jan, A. S. Alshomrani, and M. S. Alghamdi, Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction, Results Phys. 7 (2017), 789–800. https://doi.org/10.1016/j.rinp.2017.01.025.

D. Saikia, U. K. Saha, and G. C. Hazarika, A numerical study of Atangana-Baleanu and Caputo-Fabrizio for MHD flow problem over a vertical hot stretching sheet with variable viscosity and thermal conductivity, IAENG Int. J. Appl. Math. 50 (2020), no. 3.

M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl. 1 (2015), no. 2, 73–85.

F. C. Lai and F. A. Kulacki, The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium, Int. J. Heat Mass Transfer 33 (1990), no. 5, 1028–1031. https://doi.org/10.1016/0017-9310(90)90084-8.

Published
2025-08-13
Section
Advances in Nonlinear Analysis and Applications