<p>Heat transfer in a flow comprised of two Hiemenz stagnation point flows on a hot rigid plate is investigated. One of the Hiemenz stagnation point flows of strain rate <i>a</i> is aligned along the <i>x</i>-axis which intersects the flow of strain rate <i>b</i> at an angle <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_869_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation> with the <i>x</i>-axis. Heat transfer in the vicinity of stagnation point on the hot rigid plate in the case when there is a flow far away from the plate is studied. The velocity fields are transformed along the principal axes and the application of similarity transformation to the Navier Stokes equations and temperature equation reduce to three ordinary differential equations containing the parameters <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_869_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="66" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma (= b/a)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>σ</mi> <mo stretchy="false">(</mo> <mo>=</mo> <mi>b</mi> <mo stretchy="false">/</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> (the strain rate ratio), <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_869_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation> (oblique intersection angle) and <i>Pr</i> (Prandtl number). The far field behavior of heat transfer is obtained analytically. Large <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_869_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-asymptotic behavior for <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_869_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi = 0^{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϕ</mi> <mo>=</mo> <msup> <mn>0</mn> <mn>0</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_869_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi = 90^{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϕ</mi> <mo>=</mo> <msup> <mn>90</mn> <mn>0</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> has been investigated. The numerical solution of temperature equation in the principal co-ordinate system for <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_869_Article_IEq7.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">\(-1\le \sigma \le 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>1</mn> <mo>≤</mo> <mi>σ</mi> <mo>≤</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, various Prandtl number and obliquely-intersecting angles are obtained. Wall shear stress parameter and variation of temperature are shown in figures and discussed.</p>

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Heat Transfer in Three Dimensional Obliquely-intersecting Hiemenz flows over a Rigid Plate

  • Priyajit Mondal,
  • T. R. Mahapatra

摘要

Heat transfer in a flow comprised of two Hiemenz stagnation point flows on a hot rigid plate is investigated. One of the Hiemenz stagnation point flows of strain rate a is aligned along the x-axis which intersects the flow of strain rate b at an angle \(\phi \) ϕ with the x-axis. Heat transfer in the vicinity of stagnation point on the hot rigid plate in the case when there is a flow far away from the plate is studied. The velocity fields are transformed along the principal axes and the application of similarity transformation to the Navier Stokes equations and temperature equation reduce to three ordinary differential equations containing the parameters \(\sigma (= b/a)\) σ ( = b / a ) (the strain rate ratio), \(\phi \) ϕ (oblique intersection angle) and Pr (Prandtl number). The far field behavior of heat transfer is obtained analytically. Large \(\sigma \) σ -asymptotic behavior for \(\phi = 0^{0}\) ϕ = 0 0 and \(\phi = 90^{0}\) ϕ = 90 0 has been investigated. The numerical solution of temperature equation in the principal co-ordinate system for \(-1\le \sigma \le 2\) - 1 σ 2 , various Prandtl number and obliquely-intersecting angles are obtained. Wall shear stress parameter and variation of temperature are shown in figures and discussed.