Thermosolutal convection of nano–encapsulated phase change materials within a porous circular cylinder containing crescent with periodic side-wall temperature and concentration: ISPH simulation

Abstract

Abstract This work inspects the magnetic influences on the thermosolutal convection of nano–encapsulated phase change materials (NEPCMs) within a circular cylinder including crescent with periodic side-wall temperature and concentration. The incompressible smoothed particle hydrodynamics (ISPH) method based on a Grunwald- Letnikove time derivative is adopted to handle the current physical problem. The circular cylinder is suspended by NEPCM and saturated by a porous medium. Rotation of an inner crescent with a variable frequency has been conducted. The influences of a fractional time derivative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> </mml:math> from 0.95 to 1, Darcy parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>D</mml:mi> <mml:mi>a</mml:mi> </mml:math> from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> </mml:math> Rayleigh number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>R</mml:mi> <mml:mi>a</mml:mi> </mml:math> from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mn>6</mml:mn> </mml:msup> <mml:mo>,</mml:mo> </mml:math> Hartmann number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>H</mml:mi> <mml:mi>a</mml:mi> </mml:math> from 0 to 50, a fusion temperature from 0.05 to 0.9, rotation parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ω</mml:mi> </mml:math> from 1 to 5, amplitude parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>A</mml:mi> </mml:math> from 0.5 to 2, and frequency parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>f</mml:mi> </mml:math> from 5 to 100 on the heat capacity, isotherms, velocity field, isoconcentration, and mean Nusselt number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>u</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> and mean Sherwood number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>h</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> are investigated. It is found that an increase in the Hartmann number drops the velocity’s maximum by 21.43%. Increasing a fusion temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> </mml:math> shifts the phase change zone towards the inserted heated crescent. The angular rotation parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ω</mml:mi> </mml:math> for an inner crescent is changing the heat/mass transport and nanofluid movements within a circular cylinder. The phase change zone is affected by the variations of an amplitude parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>A</mml:mi> </mml:math> at higher values of the frequency <mml:math x

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