Influence of entropy on Brinkman–Forchheimer model of MHD hybrid nanofluid flowing in enclosure containing rotating cylinder and undulating porous stratum
Fares Redouane, Wasim Jamshed, S. Suriya Uma Devi, Belhadj Mahammed Amine, Rabia Safdar, Khaled Al‐Farhany, Mohamed R. Eid, Kottakkaran Sooppy Nisar, Abdel‐Haleem Abdel‐Aty, I.S. Yahia
Abstract
Abstract The current article aims to discuss the natural convection heat transfer of Ag/Al 2 O 3 -water hybrid filled in an enclosure subjected to a uniform magnetic field and provided with a rotating cylinder and an inner undulated porous layer. The various thermo-physical parameters are investigated such as Rayleigh number ( $$100 \le Ra \le 100000$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>100</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>R</mml:mi> <mml:mi>a</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>100000</mml:mn> </mml:mrow> </mml:math> ), Hartmann number ( $$0 \le Ha \le 100$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>H</mml:mi> <mml:mi>a</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>100</mml:mn> </mml:mrow> </mml:math> ), and the nanoparticles concentration ( $$0.02 \le \phi \le 0.08$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.02</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>0.08</mml:mn> </mml:mrow> </mml:math> ). Likewise, the rotational speed of the cylinder ( $$- 4000 \le \omega \le + 4000$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>4000</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>≤</mml:mo> <mml:mo>+</mml:mo> <mml:mn>4000</mml:mn> </mml:mrow> </mml:math> ), as well as several characteristics related to the porous layer, are examined li its porosity ( $$0.2 \le \varepsilon \le 0.8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.2</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>ε</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>0.8</mml:mn> </mml:mrow> </mml:math> ), Darcy number ( $$- 100000 \le Da \le - 100$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>100000</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>D</mml:mi> <mml:mi>a</mml:mi> <mml:mo>≤</mml:mo> <mml:mo>-</mml:mo> <mml:mn>100</mml:mn> </mml:mrow> </mml:math> ) which indicates the porous medium permeability and the number of undulations ( $$0 \le N \le 4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>N</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> ). The calculations are carried out based on the Galerkin Finite element method (GFEM) to present the streamlines, isotherms, entropy generation, and average Nusselt numbers in details. The main results proved that increment of Rayleigh number and Darcy number enhances heat transfer convection within the enclosure. Whilst, the porosity presents a minimal impact. Also, the rotational speed in a positive direction has a favorable influence on the heat transfer dispersion across the cavity.