Thermal energy analysis of multi-walled carbon nanotubes-Fe <sub>3</sub> O <sub>4</sub> /H <sub>2</sub> O flow over non-uniformed surface with Darcy–Forchheimer model
Chibani Lotfi, Fares Redouane, Chikr Djaoutsi Zineb, Wasim Jamshed, Mohamed R. Eid, Rabha W. Ibrahim, Siti Suzilliana Putri Mohamed Isa, Haifa Alqahtani, Syed M. Hussain
Abstract
In this study, a new cavity shape was filled with an extension multi-walled carbon nanotubes-Fe 2 O 3 /H 2 O nanofluid under a constant magnetic field. The Darcy–Forchheimer model is used to account for the inertial impact of advection in the porous layer while maintaining the laminar and incompressible nature of the nanofluid flow. The dimensionless version of the governing equations is used to describe the issue and the finite element approach is used to resolve it. Through this complex geometry, various thermophysical factors such as Rayleigh number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>≤</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">Ra</mml:mi> </mml:mrow> <mml:mo>≤</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>5</mml:mn> </mml:msup> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:math> , Hartmann number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">Ha</mml:mi> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mn>100</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:math> , and nanoparticle concentration are considered <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <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:mo stretchy="false">)</mml:mo> </mml:math> . The porous layer's numerous characteristics are also explored. For example, its porosity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <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:mo stretchy="false">)</mml:mo> </mml:math> and Darcy number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> <mml:mo>≤</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">Da</mml:mi> </mml:mrow> <mml:mspace width="0.25em"/> <mml:mo>≤</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:math> , which indicates the permeability of the porous medium. The content of the hybrid nanofluid is considered to be Newtonian, stable, incompressible, and following a constant Prandtl number for the base fluid <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Pr</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>6.2</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:math> . Calculations are made according to the finite element method. The results of this work are presented in terms of rheology, isotherms, entropy generation, and mean Nusselt numbers. They have demonstrated that increasing the Rayleigh and Darcy numbers improve heat transfer in the enclosure.