Mathematical Study on a Non-Darcian Flow of a Nanofluid
DOI:
https://doi.org/10.5890/JAND.2026.03.007Abstract
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] 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] 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] 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] 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] 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] 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] 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] 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] 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] Alfvén, H. (1942), Existence of electromagnetic-hydrodynamic waves, Nature, 150(3805), 405-406.
[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] 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] 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] 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] Darcy, H. (1856), Les Fontaines Publiques de Dijon, Victor Dalmont, Paris.
[16] Forchheimer, P. (1901), Wasserbewegung durch Boden, Zeitschrift des Vereins Deutscher Ingenieure, 45, 1782-1788.
[17] Pop, I. and Ingham, D.B. (2001), Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media, Elsevier.
[18] Vafai, K. (2015), Handbook of Porous Media, 3rd ed., CRC Press, Boca Raton.
[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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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.
Article Metrics
Usage tracking begins September 1, 2026.