Study of Conducting Fluid Flow in Composite Regions Past an Impermeable Sphere in the Presence of Magnetic Field

Jump To References Section

Authors

  • R. Umadevi
     Department of Mathematics, Channabasaveshwara Institute of Technology, Tumkur – 572 216, Karnataka ,IN
  • D. V. Chandrashekhar
     Department of Mathematics, Vivekananda Institute of Technology, Bengaluru – 560 074, Karnataka ,IN
  • P. A. Dinesh
     Department of Mathematics, Ramaiah Institute of Technology, Bengaluru – 560 054, Karnataka ,IN
  • D. V. Jayalakshmamma
     Department of Mathematics, Vemana Institute of Technology, Bengaluru – 560 034, Karnataka ,IN

DOI:

https://doi.org/10.18311/jmmf/2023/41761

Keywords:

Brinkman Equation, Porosity, Stokes Equation.

Abstract

A steady, two dimensional, incompressible, viscous and conducting fluid flow over a fixed rigid sphere has been considered under the effect of magnetic force applied normal to flow direction. The fluid flow occurs in three multiple regions namely fluid, porous and fluid region respectively. The governing equations are reduced into linear PDEs in terms of dimensionless parameters which intern converted into linear ODEs by similarity transformation method. The impact of Hartmann number and porosity on the fluid flow has been analyzed graphically. It is observed that as the Hartmann number increases for fixed porosity, the flow of fluid is well controlled in porous and non-porous regions. Further, as porosity increases for fixed Hartmann number, fluid flow over a porous region is observed. Also, diminishes the fluid velocity in the porous region due to the suppression of the fluid flow as ‘σ’ increases when magnetic field is fixed to finite constant. The same observation is made when the Hartmann number is intensified for the fixed porosity ‘σ’.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2023-12-30

How to Cite

Umadevi, R., Chandrashekhar, D. V., Dinesh, P. A., & Jayalakshmamma, D. V. (2023). Study of Conducting Fluid Flow in Composite Regions Past an Impermeable Sphere in the Presence of Magnetic Field. Journal of Mines, Metals and Fuels, 71(12), 2699–2707. https://doi.org/10.18311/jmmf/2023/41761

Issue

Volume 71, Issue 12, December 2023

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC

 

References

Chandrashekara BC, Rudraiah N. Magnetohydrodynamics laminar flow between porous disks for large injection. Reynolds number - Bulletin of Accd. Sci. Georgian SSR. 1969; 53(2):286-9.

Rudraiah N, Chandrashekara BC. Flow of conducting fluid between porous disks for large suction. Reynolds number - J. Phys. SOC, Japan. 1969; 27(4):1041-5. https://doi.org/10.1143/JPSJ.27.1041 DOI: https://doi.org/10.1143/JPSJ.27.1041

Rudraiah N, Chandrashekara BC. MHD laminar flow between porous disks. Applied Sci. Res. 1970; 23:42-52. https://doi.org/10.1007/BF00413186 DOI: https://doi.org/10.1007/BF00413186

Chandrashekara BC, Rudraiah N. Three-dimensional magnetohydrodynamic flow between a rotating and stationary disk with uniform suction at the stationary disk. Archives of Mechanics. 1971; 23(1):27-36. https://doi. org/10.1007/BF01593206 DOI: https://doi.org/10.1007/BF01593206

Anjali Devi SP, Raghavachar MR. Magneto hydrodynamic stratified flow past a sphere. Int. J. Engng. 1982; 20(10):1169-77. https://doi.org/10.1016/0020- 7225(82)90097-0 DOI: https://doi.org/10.1016/0020-7225(82)90097-0

Chandrashekhar DV, Rudraiah N. Electrically conducting fluid flow past an impermeable sphere embedded in a sparsely packed porous medium in the presence of transverse magnetic field. Proc. of 12th A. C. Fluid Mech. 2008; 1-4.

Blerlom RV. Magnetohydrodynamic flow of a viscous fluid past a sphere. J. Fluid. Mech. 2006; 8(3):438-41.

Jayalakshmamma DV, Dinesh PA and Sankar M. Analytical study of creeping flow past a composite sphere: solid core with porous shell in presence of magnetic field. Mapana J. of Sci. 2011; 10(2):11-24. https:// doi.org/10.12723/mjs.19.2 DOI: https://doi.org/10.12723/mjs.19.2

Shukla P, Das S. Effect of uniform magnetic field on the motion of porous sphere in spherical container. J. of Appl. Mathematics and Fluid Mechanics. 2015; 7(1): 51-6.

Ghosh S, Sarkar S, Sivakumar R, Sekhar TVS. Full magnetohydrodynamic flow past a circular cylinder considering the penetration of magnetic field. Physics of Fluids. 2018; 30(8):87-102. https://doi. org/10.1063/1.5040949 DOI: https://doi.org/10.1063/1.5040949

Pantokratoras A, Fang T. Flow of a weakly conducting fluid in a channel filled with a porous medium. Trans Porous med. 2010; 83:667-76. https://doi.org/10.1007/ s11242-009-9470-6 DOI: https://doi.org/10.1007/s11242-009-9486-y

Dhiman N, Awasthi M, Singh MP. Electro hydrodynamic Kelvin-Helmholtz instability of cylindrical interface through porous media. Int. J. Fluid Mechanics Research. 2013; 40(5):455-67. https://doi.org/10.1615/ InterJFluidMechRes.v40.i5.80 DOI: https://doi.org/10.1615/InterJFluidMechRes.v40.i5.80

Srivastava BG, Deo S. Effect of magnetic field on the viscous fluid flow in a channel filled with porous medium of variable permeability. Applied Mathematica and Computation. 2013; 219(17):8959-64. https://doi. org/10.1016/j.amc.2013.03.065 DOI: https://doi.org/10.1016/j.amc.2013.03.065

Yeh S, Tsai-Jung Chen, Leong JC. Analytical solution for MHD flow of a magnetic fluid within a thick porous annulus. J. Appl. Mathematics. 2014. https://doi. org/10.1155/2014/931732 DOI: https://doi.org/10.1155/2014/931732

Yadav S, Sharma PR. Effects of porous medium on MHD fluid flow along a stretching cylinder. Annals of Pure and Appl. Mathematics. 2014; 6(1):104-13.

Sharma MK, Singh K, Kumar A. MHD flow and heat transfer through a circular cylinder partially filled with non-Darcy porous media. IJITEE. 2014; 4(7).

Cauhan TS, Chauhan IS, Shikha. Flow of a viscous fluid through a porous circular pipe in the presence of magnetic field. Mathematica Aeterna. 2015; 5(2):395-402.

Verma VK, Gupta AK. Analytical solution of the flow in a composite cylindrical channel partially with a porous medium in the presence of magnetic field. Special topics and reviews in porous media. 2017; 8(1):39-48. https:// doi.org/10.1615/SpecialTopicsRevPorousMedia.v8.i1.30 DOI: https://doi.org/10.1615/SpecialTopicsRevPorousMedia.v8.i1.30

Ansari IA, Deo S. Magnetohydrodynamic viscous fluid flow past a porous sphere embedded in another porous medium. Special topics and reviews in porous media. 2018; 9(2):191-200. https://doi.org/10.1615/ SpecialTopicsRevPorousMedia.v9.i2.70 DOI: https://doi.org/10.1615/SpecialTopicsRevPorousMedia.v9.i2.70

Namdeo RP, Gupta BR. Slip at the surface of slightly deformed sphere in MHD flow. Special Topics & Reviews in Porous Media: An International Journal. 2022; 13(1):1-14. https://doi.org/10.1615/SpecialTopics RevPorousMedia.2021038694 DOI: https://doi.org/10.1615/SpecialTopicsRevPorousMedia.2021038694