Mathematical model on magneto-hydrodynamic dispersion in a porous medium under the influence of bulk chemical reaction

Ashis Kumar Roy; Apu Kumar Saha; R. Ponalagusamy; Sudip Debnath

Korea-Australia Rheology Journal, Vol.32, No.4, 287-299, November, 2020

DOI10.1007/s13367-020-0027-0 Export Citation

Mathematical model on magneto-hydrodynamic dispersion in a porous medium under the influence of bulk chemical reaction

Ashis Kumar Roy^†, Apu Kumar Saha¹, R. Ponalagusamy², and Sudip Debnath³

Department of Science & Humanities, Tripura Institute of Technology, Agartala, Tripura-799009, India
¹Department of Mathematics, National Institute of Technology, Agartala, 799046, Tripura, India
²Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620015, Tamil Nadu, India
³Center for Theoretical Studies, Indian Institute of Technology Kharagpur, 721302, West Bengal, India

E-mail:

The mathematical model of hydrodynamic dispersion through a porous medium is developed in the presence of transversely applied magnetic fields and axial harmonic pressure gradient. The solute introduce into the flow is experienced a first-order chemical reaction with flowing liquid. The dispersion coefficient is numerically determined using Aris’s moment equation of solute concentration. The numerical technique employed here is a finite difference implicit scheme. Dispersion coefficient behavior with Darcy number, Hartmann number and bulk flow reaction parameter is investigated. This study highlighted that the dependency of Hartmann number and Darcy number on dispersion shows different natures in different ranges of these parameters.

Keywords:Darcy number;Hartmann number;Taylor-Aris dispersion;bulk flow reaction

[References]

Ananthakrishnan V, Gill WN, Barduhn AJ, AIChE J., 11, 1063 (1965)
Anastasiou AD, Spyrogianni AS, Koskinas KC, Giannoglou GD, Paras SV, Med. Eng. Phys., 34, 211 (2012)
Annapurna N, Gupta A, ACI Mater. J., 367, 281 (1979)
Aris R, Proc. R. Soc. London, Ser. A, 235, 67 (1956)
Bailey HR, Gogarty WB, Proc. R. Soc. London, Ser. A., 269, 352 (1962)
Balakotaiah V, Chang HC, Smith F, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci., 351, 39 (1995)
Bandyopadhyay S, Mazumder BS, Int. J. Eng. Sci., 37, 1407 (1999)
Barton N, J. Fluid Mech., 126, 205 (1983)
Berger SA, Jou LD, Annu. Rev. Fluid Mech., 32, 347 (2000)
Bhargava R, Rawat S, Takhar HS, Beg OA, Meccanica, 42, 247 (2007)
Chatwin P, Allen C, Annu. Rev. Fluid Mech., 17, 119 (1985)
Das K, Saha GC, Bulletin of Society of Mathematicians Banja Luka, 16, 21 2009.
Dash R, Mehta K, Jayaraman G, Int. J. Eng. Sci., 3, 1145 (1996)
Debnath S, Paul S, Roy AK, J. Appl. Fluid Mech., 11, 405 (2018)
Debnath S, Saha AK, Mazumder B, Roy AK, Phys. Fluids, 29, 097107 (2017)
El-Shahed M, Appl. Math. Comput., 138, 2003
Fallon MS, Howell BA, Chauhan A, Math. Med. Biol., 26, 263 (2009)
Gill WN, Sankarasubramanian R, Proc. R. Soc. London, Ser. A., 322, 101 (1971)
Grotberg J, Annu. Rev. Fluid Mech., 26, 529 (1994)
Gupta A, Chatterjee A, Math. Proc. Cambridge Philos. Soc., 64, 1209 (1968)
Gupta P, Gupta A, Proc. R. Soc. London, Ser. A., 330, 59 (1972)
Haldar K, Ghosh S, Indian J. Pure Appl. Math., 25, 345 (1994)
Jiang W, Chen G, Phys. Fluids, 31, 043303 (2019)
Mazumder BS, Paul S, Int. J. Flu id Mech. Res., 35, 475 (2008)
Mazumder BS, Das SK, J. Fluid Mech., 239, 523 (1992)
Mehmood OU, Mustapha N, Shafie S, Transport Porous Med., 92, 259 (2012)
Mekheimer KS, El Kot M, Indian J. Pure Appl. Math., 36, 393 (2007)
Midya C, Layek G, Gupta A, Mahapatra TR, J. Fluids Eng., 125, 952 (2003)
Mondal KK, Mazumder BS, ZAMM - J. Appl. Math. Mech., 85, 422 (2005)
Motta M, Haik Y, Gandhari A, Chen CJ, Bioelectrochem. Bioenerg., 47, 297 (1998)
Ng CO, Fluid Dyn. Res., 34, 335 (2004)
Ng CO, Proc. R. Soc. London, Ser. A., 462, 481 (2006)
Pal D, Appl. Math. Modell., 23, 557 (1999)
Paul S, ZAMM - J. Appl. Math. Mech., 91, 23 (2010)
Paul S, Mazumder B, Eur. J. Mech. B. Fluids, 28, 411 (2009)
Pedley TJ, The fluid mechanics of large blood vessels, Cambridge University Press Cambridge, 1980.
Ponalagusamy R, Priyadharshini S, J. Mech. Med. Biol., 17, 175010 (2017)
Rao AR, Deshikachar K, J. Indian Inst. Sci., 68, 247 (2013)
Roy AK, Saha AK, Debnath S, J. Appl. Fluid Mech., 10, 1487 (2017)
Roy AK, Saha AK, Debnath S, Int. J. Heat Technol., 37, 387 (2019)
Roy AK, Saha AK, Debnath S, Int. Commun. Heat Mass Transfer, 110, 104369 (2020)
Sankarasubramanian R, Gill WN, Proc. R. Soc. London, Ser. A, 329, 479 (1972)
Sankarasubramanian, Gill RWN, Proc. R. Soc. London. Ser. A, 333, 115 (1973)
Taylor G, Proc. R. Soc. London, Ser. A, 219, 186 (1953)
Tu C, Deville M, J. Biomech., 29, 899 (1996)
Voltairas P, Fotiadis D, Michalis L, J. Biomech., 35, 813 (2002)
Wang P, Chen G, Commun. Nonlinear Sci. Numer. Simul., 22, 348 (2015)
Wang P, Li Z, Wu X, An Y, Int. J. Heat Mass Transfer, 91, 89 (2015)
Yadav P, Jaiswal S, Sharma B, Appl. Math. Mech., 39, 993 (2018)
Zeng L, Chen G, Ecol. Modell., 222, 293 (2011)

[1] Ananthakrishnan V, Gill WN, Barduhn AJ, AIChE J., 11, 1063 (1965)

[2] Anastasiou AD, Spyrogianni AS, Koskinas KC, Giannoglou GD, Paras SV, Med. Eng. Phys., 34, 211 (2012)

[3] Annapurna N, Gupta A, ACI Mater. J., 367, 281 (1979)

[4] Aris R, Proc. R. Soc. London, Ser. A, 235, 67 (1956)

[5] Bailey HR, Gogarty WB, Proc. R. Soc. London, Ser. A., 269, 352 (1962)

[6] Balakotaiah V, Chang HC, Smith F, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci., 351, 39 (1995)

[7] Bandyopadhyay S, Mazumder BS, Int. J. Eng. Sci., 37, 1407 (1999)

[8] Barton N, J. Fluid Mech., 126, 205 (1983)

[9] Berger SA, Jou LD, Annu. Rev. Fluid Mech., 32, 347 (2000)

[10] Bhargava R, Rawat S, Takhar HS, Beg OA, Meccanica, 42, 247 (2007)

[11] Chatwin P, Allen C, Annu. Rev. Fluid Mech., 17, 119 (1985)

[12] Das K, Saha GC, Bulletin of Society of Mathematicians Banja Luka, 16, 21 2009.

[13] Dash R, Mehta K, Jayaraman G, Int. J. Eng. Sci., 3, 1145 (1996)

[14] Debnath S, Paul S, Roy AK, J. Appl. Fluid Mech., 11, 405 (2018)

[15] Debnath S, Saha AK, Mazumder B, Roy AK, Phys. Fluids, 29, 097107 (2017)

[16] El-Shahed M, Appl. Math. Comput., 138, 2003

[17] Fallon MS, Howell BA, Chauhan A, Math. Med. Biol., 26, 263 (2009)

[18] Gill WN, Sankarasubramanian R, Proc. R. Soc. London, Ser. A., 322, 101 (1971)

[19] Grotberg J, Annu. Rev. Fluid Mech., 26, 529 (1994)

[20] Gupta A, Chatterjee A, Math. Proc. Cambridge Philos. Soc., 64, 1209 (1968)

[21] Gupta P, Gupta A, Proc. R. Soc. London, Ser. A., 330, 59 (1972)

[22] Haldar K, Ghosh S, Indian J. Pure Appl. Math., 25, 345 (1994)

[23] Jiang W, Chen G, Phys. Fluids, 31, 043303 (2019)

[24] Mazumder BS, Paul S, Int. J. Flu id Mech. Res., 35, 475 (2008)

[25] Mazumder BS, Das SK, J. Fluid Mech., 239, 523 (1992)

[26] Mehmood OU, Mustapha N, Shafie S, Transport Porous Med., 92, 259 (2012)

[27] Mekheimer KS, El Kot M, Indian J. Pure Appl. Math., 36, 393 (2007)

[28] Midya C, Layek G, Gupta A, Mahapatra TR, J. Fluids Eng., 125, 952 (2003)

[29] Mondal KK, Mazumder BS, ZAMM - J. Appl. Math. Mech., 85, 422 (2005)

[30] Motta M, Haik Y, Gandhari A, Chen CJ, Bioelectrochem. Bioenerg., 47, 297 (1998)

[31] Ng CO, Fluid Dyn. Res., 34, 335 (2004)

[32] Ng CO, Proc. R. Soc. London, Ser. A., 462, 481 (2006)

[33] Pal D, Appl. Math. Modell., 23, 557 (1999)

[34] Paul S, ZAMM - J. Appl. Math. Mech., 91, 23 (2010)

[35] Paul S, Mazumder B, Eur. J. Mech. B. Fluids, 28, 411 (2009)

[36] Pedley TJ, The fluid mechanics of large blood vessels, Cambridge University Press Cambridge, 1980.

[37] Ponalagusamy R, Priyadharshini S, J. Mech. Med. Biol., 17, 175010 (2017)

[38] Rao AR, Deshikachar K, J. Indian Inst. Sci., 68, 247 (2013)

[39] Roy AK, Saha AK, Debnath S, J. Appl. Fluid Mech., 10, 1487 (2017)

[40] Roy AK, Saha AK, Debnath S, Int. J. Heat Technol., 37, 387 (2019)

[41] Roy AK, Saha AK, Debnath S, Int. Commun. Heat Mass Transfer, 110, 104369 (2020)

[42] Sankarasubramanian R, Gill WN, Proc. R. Soc. London, Ser. A, 329, 479 (1972)

[43] Sankarasubramanian, Gill RWN, Proc. R. Soc. London. Ser. A, 333, 115 (1973)

[44] Taylor G, Proc. R. Soc. London, Ser. A, 219, 186 (1953)

[45] Tu C, Deville M, J. Biomech., 29, 899 (1996)

[46] Voltairas P, Fotiadis D, Michalis L, J. Biomech., 35, 813 (2002)

[47] Wang P, Chen G, Commun. Nonlinear Sci. Numer. Simul., 22, 348 (2015)

[48] Wang P, Li Z, Wu X, An Y, Int. J. Heat Mass Transfer, 91, 89 (2015)

[49] Yadav P, Jaiswal S, Sharma B, Appl. Math. Mech., 39, 993 (2018)

[50] Zeng L, Chen G, Ecol. Modell., 222, 293 (2011)