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• W4386880908 abstract "Abstract This paper investigates the pulse electromagnetic flow of a Jeffery fluid between parallel plate microchannels, where the pulse is considered as a relatively stable and common rectangular pulse. The Laplace transform and residue theorem are employed to derive the analytical solutions for the velocity and volumetric flow rate of the pulse electromagnetic flow. Graphical representations depict the effects of several important parameters, including the Hartmann number <?CDATA $Ha,$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi>H</mml:mi> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> </mml:math> pulse width <?CDATA $bar{a},$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mover accent=true> <mml:mi>a</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>,</mml:mo> </mml:math> relaxation time <?CDATA ${bar{lambda }}_{1}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mrow> <mml:mover accent=true> <mml:mi>λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> and retardation time <?CDATA ${bar{lambda }}_{2}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mrow> <mml:mover accent=true> <mml:mi>λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> on them. The study findings demonstrate that the Hartmann number <?CDATA $Ha$?> <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> plays a vital role in the investigation of pulse electromagnetic flow. During the first half-cycle of the pulse electric field, the magnitude of the velocity amplitude increases and then decreases with the Hartmann number <?CDATA $Ha.$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi>H</mml:mi> <mml:mi>a</mml:mi> <mml:mo>.</mml:mo> </mml:math> An interesting observation is that in the second half-cycle, larger Hartmann number <?CDATA $Ha$?> <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> values result in a decrease in velocity followed by a reverse increase. The profiles of velocity and volumetric flow rate exhibit oscillations over a relatively short period of time, then gradually reach a stable state with time and display periodic variation characteristics. Moreover, a larger pulse width <?CDATA $bar{a}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mover accent=true> <mml:mi>a</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> leads to a longer variation period and more stable profiles of velocity and volumetric flow rate. For smaller Hartmann numbers <?CDATA $Ha,$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi>H</mml:mi> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> </mml:math> the magnitude of the volumetric flow rate amplitude grows with the relaxation time <?CDATA ${bar{lambda }}_{1}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mrow> <mml:mover accent=true> <mml:mi>λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> and reduces with the retardation time <?CDATA ${bar{lambda }}_{2}.$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mrow> <mml:mover accent=true> <mml:mi>λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>.</mml:mo> </mml:math> However, as the Hartmann number <?CDATA $Ha$?> <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> increases, the influence of relaxation time <?CDATA ${bar{lambda }}_{1}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mrow> <mml:mover accent=true> <mml:mi>λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> and retardation time <?CDATA ${bar{lambda }}_{2}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mrow> <mml:mover accent=true> <mml:mi>λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> on the volumetric flow rate becomes significantly weakened, especially the retardation time <?CDATA ${bar{lambda }}_{2}.$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mrow> <mml:mover accent=true> <mml:mi>λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>.</mml:mo> </mml:math>" @default.
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• W4386880908 date "2023-09-29" @default.
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• W4386880908 title "Pulse electromagnetic flow of Jeffrey fluid in parallel plate microchannels" @default.
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