• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2024, Volume: 17, Issue: 11, Pages: 990-1002

Original Article

Impacts of Thermal Radiation and Viscous Dissipation on the Boundary Layer Flow of Ferrofluid Past a Non-Flat Stretching Sheet in a Permeable Medium: Darcy-Forchheimer’s Model

Received Date:27 November 2023, Accepted Date:07 February 2024, Published Date:29 February 2024


Objectives: The current research explores the impacts of thermal radiation and viscous dissipation on MHD ferrofluid boundary layer flow past a non-flat stretching sheet in a permeable medium utilizing a Darcy-Forchheimer model. Methods: Magnetite nanoparticles ( ) disintegrate in base fluids using the Tiwari-Das model of nanofluids. The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) using the relevant similarity variables. These nonlinear ODEs are solved numerically using the bvp4c- technique in MATLAB software. The effects of pertinent parameters such as the magnetic parameter, porosity parameter, Forchheimer parameter, Prandtl number, Eckert number, and radiation parameter on velocity and temperature fields are plotted graphically. The influence of physical factors on Skin friction coefficient and local Nusselt number are computed and examined. Findings: An augmentation in values of porosity parameter ( ), magnetic field , and Forchheimer number ( ) reduce the momentum boundary layer thickness although increases the thermal boundary layer thickness. An increase in the fluid’s temperature is due to an increase either in the radiation parameter ( ) or in the Eckert number ( ). Escalation in Prandtl number ( ) lowers the compactness of the thermal boundary layer. Novelty: The current work focuses on the innovative investigation of the impact of heat radiation and viscous dissipation on the boundary layer flow of MHD ferrofluid via a stretched sheet with varying thickness and no research on the topic covered in this article has yet to be reported. The study also incorporates the use of the Darcy-Forchheimer model. Here, water ( ) is used as the base fluid, and magnetite ( ) is used as nanoparticles for the present study. The results coincide very well with previous published works that authenticate the validity of the current work.

Keywords: Ferrofluid, MHD, Stretching sheet with variable thickness, Thermal radiation, Viscous dissipation


  1. Alabdulhadi S, Bakar SA, Ishak A, Waini I, Ahmed SE. Effect of Buoyancy Force on an Unsteady Thin Film Flow of Al2O3/Water Nanofluid over an Inclined Stretching Sheet. Mathematics. 2023;11(3):1–16. Available from: https://doi.org/10.3390/math11030739
  2. Zeb H, Wahab HA, Khan U, Juhani ASA, Andualem M, Khan I. The Velocity Slip Boundary Condition Effects on Non-Newtonian Ferrofluid over a Stretching Sheet. Mathematical Problems in Engineering. 2022;2022:1–20. Available from: https://doi.org/10.1155/2022/1243333
  3. Abbas Z, Mushtaq T, Shehzad SA, Rauf A, Kumar R. Slip flow of hydromagnetic micropolar nanofluid between two disks with characterization of porous medium. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2019;41(10):1–3. Available from: https://doi.org/10.1007/s40430-019-1974-6
  4. Rauf A, Shehzad SA, Abbas Z, Hayat T. Unsteady three-dimensional MHD flow of the micropolar fluid over an oscillatory disk with Cattaneo-Christov double diffusion. Applied Mathematics and Mechanics. 2019;40(10):1471–1486. Available from: https://doi.org/10.1007/s10483-019-2530-6
  5. Shah SAGA, Hassan A, Karamti H, Alhushaybari A, Eldin SM, Galal AM. Effect of thermal radiation on convective heat transfer in MHD boundary layer Carreau fluid with chemical reaction. Scientific Reports. 2023;13(1):1–11. Available from: https://doi.org/10.1038/s41598-023-31151-4
  6. Umavathi JC, Hemavathi K. Flow and heat transfer of composite porous medium saturated with nanofluid. Propulsion and Power Research. 2019;8(2):173–181. Available from: https://doi.org/10.1016/j.jppr.2019.01.010
  7. Bejawada SG, Reddy YD, Jamshed W, Nisar KS, Alharbi AN, Chouikh R. Radiation effect on MHD Casson fluid flow over an inclined non-linear surface with chemical reaction in a Forchheimer porous medium. Alexandria Engineering Journal. 2022;61(10):8207–8220. Available from: https://doi.org/10.1016/j.aej.2022.01.043
  8. Khashi'ie NS, Waini I, Kasim ARM, Zainal NA, Ishak A, Pop I. Magnetohydrodynamic and viscous dissipation effects on radiative heat transfer of non-Newtonian fluid flow past a nonlinearly shrinking sheet: Reiner–Philippoff model. Alexandria Engineering Journal. 2022;61(10):7605–7617. Available from: https://doi.org/10.1016/j.aej.2022.01.014
  9. Dharmaiah G, Mebarek-Oudina F, Kumar MS, Kala KC. Nuclear reactor application on Jeffrey fluid flow with Falkner-skan factor, Brownian and thermophoresis, non linear thermal radiation impacts past a wedge. Journal of the Indian Chemical Society. 2023;100(2):100907. Available from: https://doi.org/10.1016/j.jics.2023.100907
  10. Abderrahmane A, Mourad A, Mohammed S, Smaisim GF, Toghraie D, Koulali A, et al. Second law analysis of a 3D magnetic buoyancy-driven flow of hybrid nanofluid inside a wavy cubical cavity partially filled with porous layer and non-Newtonian layer. Annals of Nuclear Energy. 2023;181:109511. Available from: https://doi.org/10.1016/j.anucene.2022.109511
  11. Sharma S. MHD Boundary Layer Flow Past an Exponentially Stretching Sheet with Darcy-Forchheimer Flow of Nanofluids. Indian Journal Of Science And Technology. 2022;15(33):1594–1604. Available from: https://doi.org/10.17485/IJST/v15i33.607
  12. Kierzenka J, Shampine LF. A BVP solver based on residual control and the Maltab PSE. ACM Transactions on Mathematical Software. 2001;27(3):299–316. Available from: https://doi.org/10.1145/502800.502801
  13. Shampine LF. Singular boundary value problems for ODEs. Applied Mathematics and Computation. 2003;138(1):99–112. Available from: https://doi.org/10.1016/S0096-3003(02)00111-X


© 2024 Prasad et al.  This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


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