<p>The current study explores the behavior of Brinkman-type magnetized dusty-fluid flow in a horizontal penetrable microchannel system for case (i) under transient pressure gradient, which varies inversely with the distance between the channels or is directly proportional to the squeezing ratio of the channels, and case (ii) under uniform injection and suction applied at the lower and upper channel, respectively. The study highlights the versatility and effectiveness of using dusty fluids in microchannel systems with magnetic effects which offer several industrial applications that capitalize on the unique properties of dusty fluids, ultimately enhancing process efficiency and product quality. The governing Darcy–Brinkman equations are transformed into dimensionless form, utilizing the similarity technique. Further, we have established an analytical perturbation approach which enabled us to derive the expressions up to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2024_13869_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$O(\epsilon ^2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>ϵ</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2024_13869_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\epsilon $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation> as an amplitude, characterizing the motion of mobile oscillatory upper plate. Furthermore, the effects of chemical reaction, thermal radiation, heat source, magnetic field, the Darcy and the Brinkman parameter, the Schmidt number and the Prandtl number on dusty-fluid flow are discussed graphically using MATLAB ode15s solver. Additionally, the shear stress and the rate of heat and mass transfer are evaluated at both channels. We found that the shear stress is decreased at the lower channel with increase in injection (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2024_13869_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$ \delta _{{\text{i}}} $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>δ</mi> <mtext>i</mtext> </msub> </math></EquationSource> </InlineEquation>) while it is enhanced at the upper channel with increase in suction (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2024_13869_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$ \delta _{{\text{s}}} $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>δ</mi> <mtext>s</mtext> </msub> </math></EquationSource> </InlineEquation>). Also, the velocity profile of both the Brinkman-type fluid and the dust particle rises with increase in pressure gradient and squeezing parameter (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2024_13869_Article_IEq5.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="87" /> </InlineMediaObject> <EquationSource Format="TEX">$0\le \alpha \le 0.5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>α</mi> <mo>≤</mo> <mn>0.5</mn> </mrow> </math></EquationSource> </InlineEquation>). The present work is also validated with existing works for limiting cases and is found to be in good accord.</p>

Influence of injection/suction and transient pressure gradient on the Brinkman-type dusty magnetized fluid flow through a horizontal microchannel system

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发表日期：

2025年1月3日

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Shabiha Naz,
Tamizharasi R

摘要

The current study explores the behavior of Brinkman-type magnetized dusty-fluid flow in a horizontal penetrable microchannel system for case (i) under transient pressure gradient, which varies inversely with the distance between the channels or is directly proportional to the squeezing ratio of the channels, and case (ii) under uniform injection and suction applied at the lower and upper channel, respectively. The study highlights the versatility and effectiveness of using dusty fluids in microchannel systems with magnetic effects which offer several industrial applications that capitalize on the unique properties of dusty fluids, ultimately enhancing process efficiency and product quality. The governing Darcy–Brinkman equations are transformed into dimensionless form, utilizing the similarity technique. Further, we have established an analytical perturbation approach which enabled us to derive the expressions up to $O(\epsilon ^2)$ $O (ϵ^{2})$ with $\epsilon $ $ϵ$ as an amplitude, characterizing the motion of mobile oscillatory upper plate. Furthermore, the effects of chemical reaction, thermal radiation, heat source, magnetic field, the Darcy and the Brinkman parameter, the Schmidt number and the Prandtl number on dusty-fluid flow are discussed graphically using MATLAB ode15s solver. Additionally, the shear stress and the rate of heat and mass transfer are evaluated at both channels. We found that the shear stress is decreased at the lower channel with increase in injection ( $ \delta _{{\text{i}}} $ $δ_{i}$ ) while it is enhanced at the upper channel with increase in suction ( $ \delta _{{\text{s}}} $ $δ_{s}$ ). Also, the velocity profile of both the Brinkman-type fluid and the dust particle rises with increase in pressure gradient and squeezing parameter ( $0\le \alpha \le 0.5$ $0 \leq α \leq 0.5$ ). The present work is also validated with existing works for limiting cases and is found to be in good accord.