Non-Newtonian Casson pulsatile fluid flow influenced by Lorentz force in a porous channel with multiple constrictions: A numerical study

Amjad Ali; Attia Fatima; Zainab Bukhari; Hamayun Farooq; Zaheer Abbas

Korea-Australia Rheology Journal, Vol.33, No.1, 79-90, February, 2021

DOI10.1007/s13367-021-0007-z Export Citation

Non-Newtonian Casson pulsatile fluid flow influenced by Lorentz force in a porous channel with multiple constrictions: A numerical study

Amjad Ali, Attia Fatima^†, Zainab Bukhari, Hamayun Farooq, and Zaheer Abbas¹

Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
¹Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

E-mail:

In this paper, we investigate non-Newtonian Casson fluid flow with pulsation in a channel having symmetrical constriction bumps on the upper and lower walls. The medium is assumed to be porous, following Darcy’s law. The fluid is modeled as electrically low conducting, and the pulsatile flow is subjected to a transverse magnetic field of uniform strength to study the impact of the resulting Lorentz force. We transform the mathematical model using the vorticity-stream function form for obtaining the solution. We analyze influence of the Hartman, Strouhal, Casson fluid, and porosity parameters on various flow profiles. It is revealed that the region of flow separation in the wake of a constriction bump tends to vanish with increasing the magnetic field parameter as well as Casson fluid parameter. The wall shear stress has higher values at the first constriction bump than that at the second constriction bump on a wall. It is also noticed that wall shear stress decreases with increasing the value of the porosity parameter during the pulsation cycle.

Keywords:double constricted channel;Casson fluid;pulsatile flow;vorticity-stream function;finite difference method

[References]

Afifi NAS, Gad NS, Acta Mech., 149, 229 (2001)
Ahmed SA, Giddens DP, J. Biomech., 16, 505 (1983)
Ali A, Syed KS, Adv. Comput., 91, 87 (2013)
Ali A, Farooq H, Abbas Z, Bukhari Z, Fatima A, Sci. Rep., 10, 10629 (2020)
Alimohamadi H, Sadeghy K, Nihon Reoroji Gakkaishi, 43, 135 (2015)
Amlimohamadi H, Akram M, Sadeghy K, Korea-Aust. Rheol. J., 28(2), 129 (2016)
Bandyopadhyay S, Layek GC, Commun. Nonlinear Sci. Numer. Simul., 16, 252 (2011)
Bandyopadhyay S, Layek GC, Commun. Nonlinear Sci. Numer. Simul., 17, 2434 (2012)
Batra RL, Jena B, Int. J. Eng. Sci., 29, 1245 (1991)
Casson N, Rheology of Disperse Systems, 84 1959.
Chakarvarty S, Mandal PK, Int. J. Non-Linear Mech., 35, 779 (2000)
Dash RK, Mehta KN, Jayaraman G, Int. J. Eng. Sci., 134, 1145 (1996)
Deplano V, Siouffi M, J. Biomech., 32, 1081 (1999)
Devi R, Poply V, Manimala, Int. J. Adv. Trends Comput. Appl., 1, 32 (2019)
El-Dabe N, Ghaly AY, Rizkallah RR, Ewis KM, Al-Bareda AS, J. Appl. Math. Phys., 3, 649 (2015)
Haghighi AR, Kabdool AA, Asl MS, Kiyasatfar M, Int. J. Appl. Comput. Math., 2, 649 (2016)
Haldar K, Ghosh SN, Indian J. Pure Appl. Math., 25, 345 (1994)
Hamid M, Usman U, Khan ZH, Haq RU, Wang W, Int. Commun. Heat Mass Transf., 108, 104284 (2019)
Ismail Z, Abdullah I, Mustapha N, Amin N, Appl. Math. Comput., 195, 669 (2008)
Khair A, Wang BC, Kuhn DCS, Int. J. Comput. Fluid Dyn., 29, 447 (2015)
Makanda G, Shaw S, Sibanda P, Math. Probl. Eng., 2015, 724596 (2015)
Mallik BB, Nanda S, Das B, Saha D, Das DS, Paul K, Sch. J. Eng. Tech., 1, 27 (2013)
Midya C, Layek GC, Gupta AS, Mahapatra TR, J. Fluids Eng.-Trans. ASME, 125, 952 (2003)
Mittal AS, Patel HR, Physica A, 537, 122710 (2020)
Mukhopadhyay S, De PR, Bhattacharyya K, Layek GC, Ain Shams Eng. J., 4, 933 (2013)
Mustapha N, Mandal PR, Johnston PR, Amin N, Appl. Math. Model., 34, 1559 (2010)
Nadeem S, Haq RU, Lee C, Sci. Iran., 19, 1550 (2012)
Nadeem S, Haq RU, Akbar NS, Khan ZH, Alex. Eng. J., 52, 577 (2013)
Nagarani P, Sebastian BT, Acta Mech., 224, 571 (2013)
Ramesh K, Devakar M, Ain Shams Eng. J., 6, 967 (2015)
Sankar DS, Nagar AK, J. Appl. Math., 2012, 950323 (2012)
Sankar DS, Lee U, Commun. Nonlinear Sci. Numer. Simul., 15, 2086 (2010)
Sarifuddin S, Chakravarty, Mandal PK, Z. Angew. Math. Phys., 65, 767 (2014)
Sarkar T, Reza-E-Rabbi S, Arifuzzaman SM, Ahmed R, Khan MS, Ahmmed SF, Int. J. Heat Technol., 37, 1117 (2019)
Srinivas S, Kumar CK, Reddy AS, Nonlinear Anal.-Model Control, 23, 213 (2018)

[1] Afifi NAS, Gad NS, Acta Mech., 149, 229 (2001)

[2] Ahmed SA, Giddens DP, J. Biomech., 16, 505 (1983)

[3] Ali A, Syed KS, Adv. Comput., 91, 87 (2013)

[4] Ali A, Farooq H, Abbas Z, Bukhari Z, Fatima A, Sci. Rep., 10, 10629 (2020)

[5] Alimohamadi H, Sadeghy K, Nihon Reoroji Gakkaishi, 43, 135 (2015)

[6] Amlimohamadi H, Akram M, Sadeghy K, Korea-Aust. Rheol. J., 28(2), 129 (2016)

[7] Bandyopadhyay S, Layek GC, Commun. Nonlinear Sci. Numer. Simul., 16, 252 (2011)

[8] Bandyopadhyay S, Layek GC, Commun. Nonlinear Sci. Numer. Simul., 17, 2434 (2012)

[9] Batra RL, Jena B, Int. J. Eng. Sci., 29, 1245 (1991)

[10] Casson N, Rheology of Disperse Systems, 84 1959.

[11] Chakarvarty S, Mandal PK, Int. J. Non-Linear Mech., 35, 779 (2000)

[12] Dash RK, Mehta KN, Jayaraman G, Int. J. Eng. Sci., 134, 1145 (1996)

[13] Deplano V, Siouffi M, J. Biomech., 32, 1081 (1999)

[14] Devi R, Poply V, Manimala, Int. J. Adv. Trends Comput. Appl., 1, 32 (2019)

[15] El-Dabe N, Ghaly AY, Rizkallah RR, Ewis KM, Al-Bareda AS, J. Appl. Math. Phys., 3, 649 (2015)

[16] Haghighi AR, Kabdool AA, Asl MS, Kiyasatfar M, Int. J. Appl. Comput. Math., 2, 649 (2016)

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

[18] Hamid M, Usman U, Khan ZH, Haq RU, Wang W, Int. Commun. Heat Mass Transf., 108, 104284 (2019)

[19] Ismail Z, Abdullah I, Mustapha N, Amin N, Appl. Math. Comput., 195, 669 (2008)

[20] Khair A, Wang BC, Kuhn DCS, Int. J. Comput. Fluid Dyn., 29, 447 (2015)

[21] Makanda G, Shaw S, Sibanda P, Math. Probl. Eng., 2015, 724596 (2015)

[22] Mallik BB, Nanda S, Das B, Saha D, Das DS, Paul K, Sch. J. Eng. Tech., 1, 27 (2013)

[23] Midya C, Layek GC, Gupta AS, Mahapatra TR, J. Fluids Eng.-Trans. ASME, 125, 952 (2003)

[24] Mittal AS, Patel HR, Physica A, 537, 122710 (2020)

[25] Mukhopadhyay S, De PR, Bhattacharyya K, Layek GC, Ain Shams Eng. J., 4, 933 (2013)

[26] Mustapha N, Mandal PR, Johnston PR, Amin N, Appl. Math. Model., 34, 1559 (2010)

[27] Nadeem S, Haq RU, Lee C, Sci. Iran., 19, 1550 (2012)

[28] Nadeem S, Haq RU, Akbar NS, Khan ZH, Alex. Eng. J., 52, 577 (2013)

[29] Nagarani P, Sebastian BT, Acta Mech., 224, 571 (2013)

[30] Ramesh K, Devakar M, Ain Shams Eng. J., 6, 967 (2015)

[31] Sankar DS, Nagar AK, J. Appl. Math., 2012, 950323 (2012)

[32] Sankar DS, Lee U, Commun. Nonlinear Sci. Numer. Simul., 15, 2086 (2010)

[33] Sarifuddin S, Chakravarty, Mandal PK, Z. Angew. Math. Phys., 65, 767 (2014)

[34] Sarkar T, Reza-E-Rabbi S, Arifuzzaman SM, Ahmed R, Khan MS, Ahmmed SF, Int. J. Heat Technol., 37, 1117 (2019)

[35] Srinivas S, Kumar CK, Reddy AS, Nonlinear Anal.-Model Control, 23, 213 (2018)