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The Effect of Heat and Mass Transfer on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel

Received: 7 April 2022    Accepted: 27 April 2022    Published: 10 May 2022
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Abstract

This paper investigates the effects of heat and mass transfer on unsteady MHD Nanofluid flow (silver-water) through convergent-divergent channel. The governing equations of this study are non-linear partial differential equations and these partial differential equations were reduced to ordinary differential equations. The resulting non-linear ordinary differential equations have been reduced to a system of first order of ordinary differential equations and solved using collocation method via the bvp4c in MATLAB. It is found that the nanoparticle volume fraction reduces the velocity of the fluid for silver nanoparticle in the case of divergent channel. For a convergent, the increase in the volume fraction increases the velocity. Stretching divergent channel increases the flow near the walls of the channel. Shrinking convergent channel reduces the velocity of the fluid near the walls of the channel. The Grashof number increases the temperature in divergent channel and reduces the temperature in convergent channel. The Eckert number increases temperature of the fluid for all the cases. The heat generation parameter increases the velocity and temperature for both convergent and divergent channel. The heat generation parameter decreases the concentration of Nanofluid flow for both divergent and convergent. This kind of Nanofluid flow has a variety of applications such as the transportation of chemotherapy drug directly to cancerous growth as well as to deliver drugs to areas of arteries that are damaged in order to fight cardiovascular diseases.

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 8, Issue 1)
DOI 10.11648/j.ijfmts.20220801.12
Page(s) 10-22
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Unsteadiness, MHD Nanofluid Flow, Heat and Mass Transfer, Divergent-Convergent Channel

References
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[2] Hartmann. (1937). Hydrodynamic waves. Math.-fys. Medd. Vol 15, no. 6, pp. 405-406.
[3] Ella, R., (2013). The effects of MHD and Temperature Dependent Viscosity on the flow of non-Newtonian Nanofluid in a pipe. Analytical solution, Appl. Math. Model. 37, 3, pp 1451-1467.
[4] Makinde O. D. (2013). Buoyancy Effects on MHD Stagnation Point Flow and Heat Transfer of Nanofluid Past a convectively Heated Stretching /Shrinking Sheet. International Journal of Heat and Mass Transfer. Volume 62. Pp 33 (1), 526-533.
[5] Sheikholeslami, M., Ganji, D. D., Ashorynejad, H. R. Rokni, H. B. (2012). Analytical Investigation of Jeffrey-Hamel Flow with High Magnetic Field and Nanoparticle by Adomian Decomposition Method. App. Math. Mech 33 (1), pp 25-36.
[6] Hey, Shira Zaki M, Liu H, Himeno R, Sun Z (2006). A Numerical Coupling Model to Analyze the Blood Flow, Temperature and Oxygen Transport in Human Breast Tumor Under Laser Irradiation. Com Biol Medi 36: pp 130-135.
[7] Szasz A. (2007). Hyperthermia, a Modality in the Wings. J Cancer Res ther 3: pp 56-66.
[8] Y. Pathat, (2009). Recent Development in Nanoparticle Drug Delivery System, in Drug Delivery Nanoparticle Formulation and Characterization, pp. 1-7, Informa Health Care USA, New York.
[9] Mburu. A. Njeri, Thomas T. M. Onyango, Jackson Kwanza (2016). Investigation on Magneto hydrodynamic Flow Through Converging-Diverging Channel Under Weak Magnetic Field. LAP LAMBERT Academic Publishing, Saarbrucken. ISBN (N978-3-330-33677-3).
[10] Muhammad U, Syed T. M. D, Tamour Z. Muhammad. H. W. W (2018). Fluid Flow and Heat Transfer Investigation of Blood with Nanoparticle through Porous Vessels in the presence of Magnetic Field. Journal of Algorithms Computational Technology Volume 13: 1-15.
[11] Virginia M. Kitetu, Thomas T. M. Onyango, Jackson Kwanza (2020). Control Volume Analysis of MHD Nanofluid Flow as a Result of a stretching Surface and Suction.
[12] Edward Onyango, Mathew N. Kinyanjwi, Mark Kimathi, Surindar M. Uppal (2020). Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection. Applied and Computational Mathematics; 9 (1): 1-13.
[13] Nidal H. Abu-Hamdel A. R. Bantan, Ferhand Aalizadeb, Ashkan Alimoradi (2020). Controlled Drug Delivery Using the Magnetic Nanoparticles in Non-Newtonian Blood Vessels, Alexandria Engineering Journal. Vol 59, pp 4049-4062.
[14] Ashish Mishra, Alok K. Pandey, Ali, Ali J. Chamkha Manoj Kumar (2020). Roles of Nanoparticle and Heat Generation/Absorption on MHD Flow of Silver-Water Nanofluid via Porous Stretching/Shrinking convergent/Divergent channel. Journal of the Egyptian Mathematical Society Volume 28. Article Number: 17.
[15] Misra JC, Sinha A, Shit GC. (2010). Flow of a Biomagnetic Viscoelastic Fluid. Application to Estimation of the Blood Flow in Arteries During Electromagnetic Hyperthermia, a Therapeutic Procedure for Cancer Treatment. Appl. Math Meth. Ed (31) pp 1401-1420.
[16] Jafari, A., Zamankhan, P., MO Usavi, S. M., Kolari. P (2009). Numerical Investigation of the Blood Flow. Part II: In Capillaries. Communication in non-Linear Science and Numerical simulation, 14 (4), 1396-1402.
[17] Wernet, V, Schaf, O., Ghobark, H, H, H., Denoyel, R (2005). Adsorption Properties of Zeolites for Artificial Kidney. Application Micro Porous Material 83 (1-3), 101-113.
[18] Brinkman, H. C. (1952). The Viscosity of Concentration Suspensions and Solutions. The Journal of Chemical Physics. 20 (4) 571-581.
Cite This Article
  • APA Style

    Felicien Habiyaremye, Mary Wainaina, Mark Kimathi. (2022). The Effect of Heat and Mass Transfer on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel. International Journal of Fluid Mechanics & Thermal Sciences, 8(1), 10-22. https://doi.org/10.11648/j.ijfmts.20220801.12

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    ACS Style

    Felicien Habiyaremye; Mary Wainaina; Mark Kimathi. The Effect of Heat and Mass Transfer on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel. Int. J. Fluid Mech. Therm. Sci. 2022, 8(1), 10-22. doi: 10.11648/j.ijfmts.20220801.12

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    AMA Style

    Felicien Habiyaremye, Mary Wainaina, Mark Kimathi. The Effect of Heat and Mass Transfer on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel. Int J Fluid Mech Therm Sci. 2022;8(1):10-22. doi: 10.11648/j.ijfmts.20220801.12

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  • @article{10.11648/j.ijfmts.20220801.12,
      author = {Felicien Habiyaremye and Mary Wainaina and Mark Kimathi},
      title = {The Effect of Heat and Mass Transfer on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel},
      journal = {International Journal of Fluid Mechanics & Thermal Sciences},
      volume = {8},
      number = {1},
      pages = {10-22},
      doi = {10.11648/j.ijfmts.20220801.12},
      url = {https://doi.org/10.11648/j.ijfmts.20220801.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20220801.12},
      abstract = {This paper investigates the effects of heat and mass transfer on unsteady MHD Nanofluid flow (silver-water) through convergent-divergent channel. The governing equations of this study are non-linear partial differential equations and these partial differential equations were reduced to ordinary differential equations. The resulting non-linear ordinary differential equations have been reduced to a system of first order of ordinary differential equations and solved using collocation method via the bvp4c in MATLAB. It is found that the nanoparticle volume fraction reduces the velocity of the fluid for silver nanoparticle in the case of divergent channel. For a convergent, the increase in the volume fraction increases the velocity. Stretching divergent channel increases the flow near the walls of the channel. Shrinking convergent channel reduces the velocity of the fluid near the walls of the channel. The Grashof number increases the temperature in divergent channel and reduces the temperature in convergent channel. The Eckert number increases temperature of the fluid for all the cases. The heat generation parameter increases the velocity and temperature for both convergent and divergent channel. The heat generation parameter decreases the concentration of Nanofluid flow for both divergent and convergent. This kind of Nanofluid flow has a variety of applications such as the transportation of chemotherapy drug directly to cancerous growth as well as to deliver drugs to areas of arteries that are damaged in order to fight cardiovascular diseases.},
     year = {2022}
    }
    

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  • TY  - JOUR
    T1  - The Effect of Heat and Mass Transfer on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel
    AU  - Felicien Habiyaremye
    AU  - Mary Wainaina
    AU  - Mark Kimathi
    Y1  - 2022/05/10
    PY  - 2022
    N1  - https://doi.org/10.11648/j.ijfmts.20220801.12
    DO  - 10.11648/j.ijfmts.20220801.12
    T2  - International Journal of Fluid Mechanics & Thermal Sciences
    JF  - International Journal of Fluid Mechanics & Thermal Sciences
    JO  - International Journal of Fluid Mechanics & Thermal Sciences
    SP  - 10
    EP  - 22
    PB  - Science Publishing Group
    SN  - 2469-8113
    UR  - https://doi.org/10.11648/j.ijfmts.20220801.12
    AB  - This paper investigates the effects of heat and mass transfer on unsteady MHD Nanofluid flow (silver-water) through convergent-divergent channel. The governing equations of this study are non-linear partial differential equations and these partial differential equations were reduced to ordinary differential equations. The resulting non-linear ordinary differential equations have been reduced to a system of first order of ordinary differential equations and solved using collocation method via the bvp4c in MATLAB. It is found that the nanoparticle volume fraction reduces the velocity of the fluid for silver nanoparticle in the case of divergent channel. For a convergent, the increase in the volume fraction increases the velocity. Stretching divergent channel increases the flow near the walls of the channel. Shrinking convergent channel reduces the velocity of the fluid near the walls of the channel. The Grashof number increases the temperature in divergent channel and reduces the temperature in convergent channel. The Eckert number increases temperature of the fluid for all the cases. The heat generation parameter increases the velocity and temperature for both convergent and divergent channel. The heat generation parameter decreases the concentration of Nanofluid flow for both divergent and convergent. This kind of Nanofluid flow has a variety of applications such as the transportation of chemotherapy drug directly to cancerous growth as well as to deliver drugs to areas of arteries that are damaged in order to fight cardiovascular diseases.
    VL  - 8
    IS  - 1
    ER  - 

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Author Information
  • Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya

  • Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya

  • Department of Mathematics, Statistics and Actuarial Science, Machakos University, Machakos, Kenya

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