Thermodynamics of magnetohydrodynamic Brinkman fluid in porous medium

Applications to thermal science
  • Ambreen Siyal
  • Kashif Ali AbroEmail author
  • Muhammad Anwar Solangi


This research article investigates that how heat flow changes versus temperature or time on the rheology of magnetohydrodynamic Brinkman fluid embedded in porous medium for the oscillations of heated plate. A fractional approach namely Caputo–Fabrizio fractional operator is applied for developing the governing partial differential equations of Brinkman fluid flow. The fractional governing partial differential equations have been modeled for temperature distribution, mass concentration and velocity field along with imposed initial and boundary conditions. The solutions are obtained by integral transforms and presented in special and elementary functions. In the limiting sense, the analytical solutions are particularized in the presence and absence of heat and mass transfer, magnetic field and porous medium. The parametric graphs have been depicted for the influence of different embedded rheological parameters on fluid flow. The results show few interesting differences and similarities by comparative analysis for fractional and ordinary Brinkman fluid flow, such as physically higher Prandtl (Pr) number that leads to decay thermal diffusivity which results in the reduction in thermal field; this means that better quality of production can be achieved through proper choice of Prandtl (Pr) and Schmidt (Sc) numbers.


Caputo–Fabrizio fractional operator Brinkman fluid Porous medium Analytic solutions Parametric study 



The authors appreciate the constructive remarks and suggestions of the anonymous referees that helped to improve the quality of paper. The authors are highly thankful and grateful to Mehran University of Engineering and Technology, Jamshoro, Pakistan, for generous support and facilities of this research work.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Ambreen Siyal
    • 1
  • Kashif Ali Abro
    • 1
    Email author
  • Muhammad Anwar Solangi
    • 1
  1. 1.Department of Basic Sciences and Related StudiesMehran University of Engineering and TechnologyJamshoroPakistan

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