[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Mathematical Study on a Non-Darcian Flow of a Nanofluid

Journal of Applied Nonlinear Dynamics 15(1) (2026) 111--123 | DOI:10.5890/JAND.2026.03.007

B. Sathyapriya$^1$, M. Subha$^2$, S. Sivasankari$^3$, V. Ananthaswamy$^4$

$^1$ Research Scholar, Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India

$^2$ Department of Mathematics, Fatima College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India

$^3$ Research Scholar, Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India

$^4$ Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India

Download Full Text PDF

 

Abstract

The flow of two dimensional Buogiorno nanofluid across an extending sheet having magnetic effect with a non-Darcy porous medium is explored analytically. By applying the transformation of similarity, the associated dimensional equations are simplified into dimensionless equations. With the aid of Ananthaswamy-Sivasankari approach and Modified Homotopy Analysis Technique, the expressions regarding the corresponding non-dimensional temperature, velocity, and concentration equations are attained. When the outcomes are compared to the numerical solution, a very excellent fit is found. Numerous controlling parameters including magnetic, porosity and thermophoresis are graphically depicted to reveal how they affect the flow. Furthermore, the physical parameters, especially~the reduced number of Sherwood, and the reduced number of Nusselt are visually displayed.

References

  1. [1]  Ellahi, R., Zeeshan, A., Shehzad, N., and Alamri, S.Z. (2018), Structural impact of kerosene-Al2O3 nanoliquid on MHD Poiseuille flow with variable thermal conductivity: Application of cooling process, Journal of Molecular Liquids, 264, 607-615.
  2. [2]  Bezi, S., Souayeh, B., Ben-Cheikh, N., and Ben-Beya, B. (2018), Numerical simulation of entropy generation due to unsteady natural convection in a semi-annular enclosure filled with nanofluid, International Journal of Heat and Mass Transfer, 124, 841-859.
  3. [3]  Choi, S.U. and Eastman, J.A. (1995), Enhancing thermal conductivity of fluids with nanoparticles, ANL/MSD/CP-84938; CONF-951135-29, Argonne National Laboratory, Argonne, IL, United States.
  4. [4]  Batool, S., Rasool, G., Alshammari, N., Khan, I., Kaneez, H., and Hamadneh, N. (2022), Numerical analysis of heat and mass transfer in micropolar nanofluids flow through lid driven cavity: Finite volume approach, Case Studies in Thermal Engineering, 37, 102233.
  5. [5]  Souayeh, B. and Ramesh, K. (2023), Numerical scrutinization of ternary nanofluid flow over an exponentially stretching sheet with gyrotactic microorganisms, Mathematics, 11(4), 981.
  6. [6]  Patil, P.M. and Momoniat, E. (2020), Transport phenomena in MHD mixed convective nanofluid flow, International Journal of Numerical Methods for Heat and Fluid Flow, 30(2), 769-791.
  7. [7]  Khan, N.S., Shah, Q., Bhaumik, A., Kumam, P., Thounthong, P., and Amiri, I. (2020), Entropy generation in bioconvection nanofluid flow between two stretchable rotating disks, Scientific Reports, 10(1), 4448.
  8. [8]  Oreyeni, T., Shah, N.A., Popoola, A.O., Elzahar, E.R., and Yook, S.J. (2022), The significance of exponential space-based heat generation and variable thermophysical properties on the dynamics of Casson fluid over a stratified surface with non-uniform thickness, Waves in Random and Complex Media, 1-19.
  9. [9]  Ghasemi, S.E. and Hatami, M. (2021), Solar radiation effects on MHD stagnation point flow and heat transfer of a nanofluid over a stretching sheet, Case Studies in Thermal Engineering, 25, 100898.
  10. [10]  Alfvén, H. (1942), Existence of electromagnetic-hydrodynamic waves, Nature, 150(3805), 405-406.
  11. [11]  Haque, M.M. (2021), Heat and mass transfer analysis on magneto micropolar fluid flow with heat absorption in induced magnetic field, Fluids, 6(3), 126.
  12. [12]  Tarakaramu, N., Narayana, P.S., and Venkateswarlu, B. (2020), Numerical simulation of variable thermal conductivity on 3D flow of nanofluid over a stretching sheet, Nonlinear Engineering, 9(1), 233-243.
  13. [13]  Hdhiri, N., Souayeh, B., Alfannakh, H., and Beya, B.B. (2019), Natural convection study with internal heat generation on heat transfer and fluid flow within a differentially heated square cavity filled with different working fluids and porous media, BioNanoScience, 9, 702-722.
  14. [14]  Rasool, G., Shah, N.A., El-Zahar, E.R., and Wakif, A. (2022), Numerical investigation of EMHD nanofluid flows over a convectively heated Riga pattern positioned horizontally in a Darcy-Forchheimer porous medium: Application of passive control strategy and generalized transfer laws, Waves in Random and Complex Media, 1-20.
  15. [15]  Darcy, H. (1856), Les Fontaines Publiques de Dijon, Victor Dalmont, Paris.
  16. [16]  Forchheimer, P. (1901), Wasserbewegung durch Boden, Zeitschrift des Vereins Deutscher Ingenieure, 45, 1782-1788.
  17. [17]  Pop, I. and Ingham, D.B. (2001), Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media, Elsevier.
  18. [18]  Vafai, K. (2015), Handbook of Porous Media, 3rd ed., CRC Press, Boca Raton.
  19. [19]  Hayat, T., Aziz, A., Muhammad, T., and Alsaedi, A. (2019), Effects of binary chemical reaction and Arrhenius activation energy in Darcy–Forchheimer three-dimensional flow of nanofluid subject to rotating frame, Journal of Thermal Analysis and Calorimetry, 136, 1769-1779.
  20. [20]  Ahmad, S., Ali, K., Rizwan, M., and Ashraf, M. (2021), Heat and mass transfer attributes of copper–aluminum oxide hybrid nanoparticles flow through a porous medium, Case Studies in Thermal Engineering, 25, 100932.
  21. [21]  Kareem, R.S. and Abdulhadi, A.M. (2020), A study of MHD and Darcy-Forchheimer effects on third-grade flow with Cattaneo-Christov heat flux, in AIP Conference Proceedings, Vol. 2292, AIP Publishing, 020004.
  22. [22]  Jawad, M., Saeed, A., Khan, A., and Islam, S. (2021), MHD bioconvection Darcy–Forchheimer flow of Casson nanofluid over a rotating disk with entropy optimization, Heat Transfer, 50(3), 2168-2196.
  23. [23]  Sheremet, M.A. and Pop, I. (2018), Effect of local heater size and position on natural convection in a tilted nanofluid porous cavity using LTNE and Buongiorno's models, Journal of Molecular Liquids, 266, 19-28.
  24. [24]  Hameed, S. and Saha, S. (2023), Analysis of mixed convecto-magnetic Buongiorno nanofluid flow in a non-Darcy porous medium, Journal of Taibah University for Science, 17(1), 2233755.
  25. [25]  Reddy Gorla, R.S. and Sidawi, I. (1994), Free convection on a vertical stretching surface with suction and blowing, Applied Scientific Research, 52, 247-257.
  26. [26]  Khan, W.A. and Pop, I. (2010), Boundary-layer flow of a nanofluid past a stretching sheet, International Journal of Heat and Mass Transfer, 53(11-12), 2477-2483.
  27. [27]  Makinde, O.D. and Aziz, A. (2011), Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, International Journal of Thermal Sciences, 50(7), 1326-1332.
  28. [28]  Kuznetsov, A.V. and Nield, D.A. (2011), Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences, 50(5), 712-717.
  29. [29]  Nield, D.A. and Kuznetsov, A.V. (2009), The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid, International Journal of Heat and Mass Transfer, 52(25-26), 5792-5795.
  30. [30]  Liao, S. and Campo, A. (2002), Analytic solutions of the temperature distribution in Blasius viscous flow problems, Journal of Fluid Mechanics, 453, 411-425.
  31. [31]  Liao, S.J. (1999), A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate, Journal of Fluid Mechanics, 385, 101-128.
  32. [32]  Chitra, J., Ananthaswamy, V., Sivasankari, S., and Sivasundaram, S. (2023), A new approximate analytical method (ASM) for solving non-linear boundary value problem in heat transfer through porous fin, Mathematics in Engineering, Science and Aerospace, 14(1), 1-14.
  33. [33]  Sivasankari, S., Ananthaswamy, V., and Sivasundaram, S. (2023), A new approximate analytical method for solving some non-linear initial value problems in physical sciences, Mathematics in Engineering, Science and Aerospace, 14(1), 15-28.
  34. [34]  Ananthaswamy, V., Subanya, R.R., and Sivasankari, S. (2023), A mathematical study on a steady MHD flow in double stratification medium, CFD Letters, 15(10), 34-51.
  35. [35]  Lone, S.A., Anwar, S., Raizah, Z., Kumam, P., Seangwattana, T., and Saeed, A. (2023), Analysis of the time-dependent magnetohydrodynamic Newtonian fluid flow over a rotating sphere with thermal radiation and chemical reaction, Heliyon, 9(7), e17555.
  36. [36]  Raza, J., Mebarek-Oudina, F., and Mahanthesh, B. (2019), Magnetohydrodynamic flow of nano Williamson fluid generated by stretching plate with multiple slips, Multidiscipline Modeling in Materials and Structures, 15(5), 871-894.

Copyright © 2011-2026 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates