AUTHOR=Mahmood Rashid , Khan Y. , Rahman Nusrat , Majeed Afraz Hussain , Alameer A. , Faraz N. 

TITLE=Numerical Computations of Entropy Generation and MHD Ferrofluid Filled in a Closed Wavy Configuration: Finite Element Based Study

JOURNAL=Frontiers in Physics

VOLUME=10

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.916394

DOI=10.3389/fphy.2022.916394

ISSN=2296-424X

ABSTRACT=<p>In this article, the thermal flow effects of inclined magnetohydrodynamics ferrofluid filled in a wavy cavity are studied by adopting the finite element method (FEM). The non-dimensional governing equations and model for different parameters are evaluated. The system of non-linear algebraic equations is computed by adopting the Newton method. A space involving quadratic polynomials (<inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi mathvariant="normal">ℙ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) has been selected to compute for the velocity profile, while the pressure and temperature profiles are approximated by linear (<inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi mathvariant="normal">ℙ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) finite element space of functions. The discrete systems of non-linear algebraic equations are computed by utilizing the Newton method. The vertical walls are considered cold, whereas the bottom wavy surface is considered hot and the top wavy surface is insulated. The effect of the pertinent parameters, like <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo> </mml:mo><mml:mi>R</mml:mi><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mn>5</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, volume fraction <inline-formula id="inf4"><mml:math id="m4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0.00</mml:mn><mml:mo>≤</mml:mo><mml:mi>ϕ</mml:mi><mml:mo>≤</mml:mo><mml:mn>0.06</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mo> </mml:mo></mml:mrow></mml:math></inline-formula> inclination angle <inline-formula id="inf5"><mml:math id="m5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mn>0</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>≤</mml:mo><mml:mi>γ</mml:mi><mml:mo>≤</mml:mo><mml:msup><mml:mrow><mml:mn>90</mml:mn></mml:mrow><mml:mo>∘</mml:mo></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, and amplitude of the wavy surface <inline-formula id="inf6"><mml:math id="m6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mn>0.02</mml:mn><mml:mo>≤</mml:mo><mml:mi>A</mml:mi><mml:mi>R</mml:mi><mml:mo>≤</mml:mo><mml:mn>0.08</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is investigated. Computational results are addressed as streamlines out, isotherms, and proper graphs for substantial amounts of interest. Increasing Hartmann number (<inline-formula id="inf7"><mml:math id="m7" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>H</mml:mi><mml:mi>a</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> leads to an increase in Bejan number <inline-formula id="inf8"><mml:math id="m8" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi><mml:mi>e</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, while opposite behavior can be observed in the case of viscous, magnetic, and thermal irreversibility, that is, curves are decreased by increasing <inline-formula id="inf9"><mml:math id="m9" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>H</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:math></inline-formula>. Under the influence of an inclined magnetic field, the mathematical structuring of the problem is manifested by continuity, momentum, and energy equations. These equations are solved by using the finite element method computation. The graphs of velocity and isotherm are compared to the relevant parameters. To predict the flow characteristics at different locations, cross-sectional lines representing the velocity field in the horizontal and vertical directions are also drawn. Magnetization’s impact on flow control, heat transfer, and various irreversibilities are also discussed. The <inline-formula id="inf10"><mml:math id="m10" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>N</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>a</mml:mi><mml:mi>v</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> progressively declined with the enhancement in the amplitude of the wavy surface <inline-formula id="inf11"><mml:math id="m11" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>A</mml:mi><mml:mi>R</mml:mi></mml:mrow></mml:math></inline-formula>.</p>