Influence of thermal radiation and magnetic field on convective transfer within an inclined square enclosure filled with Cu-water nanofluid

Abstract

Abstract The present work investigates the effects of thermal radiation and magnetic field on the laminar convective transfer process on copper-based nanofluid within an inclined square enclosure. The studied configuration is a rigid-walled cavity subjected to a horizontal temperature gradient where the left wall is maintained at a hot temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> and subjected to a magnetic field <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> <mml:mo>.</mml:mo> </mml:math> In contrast, the right wall is kept at a cold temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> <mml:mo>.</mml:mo> </mml:math> The horizontal walls are adiabatic. The dimensionless governing equations are solved using the finite difference method and the UPWIND scheme to solve the convective terms. Formulated using the stream function, vorticity, and temperature. Effects on mean Nusselt numbers are investigated at different Rayleigh numbers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mn>4</mml:mn> </mml:msup> <mml:mo>,</mml:mo> <mml:mspace width="-0.10em"/> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mn>5</mml:mn> </mml:msup> <mml:mo>,</mml:mo> <mml:mspace width="-0.10em"/> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mn>6</mml:mn> </mml:msup> </mml:mrow> </mml:mfenced> <mml:mo>,</mml:mo> </mml:math> Hartmann numbers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:mi>H</mml:mi> <mml:mi>A</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>t</mml:mi> <mml:mi>o</mml:mi> <mml:mspace width="0.25em"/> <mml:mn>100</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mo>,</mml:mo> </mml:math> tilt angles <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>6</mml:mn> <mml:mo>,</mml:mo> <mml:mspace width="0.25em"/> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> <mml:mi>d</mml:mi> <mml:mspace width="0.25em"/> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfenced> <mml:mo>,</mml:mo> </mml:math> nanofluid volume fractions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>%</mml:mo> <mml:mspace width="-0.10em"/> <mml:mo>≤</mml:mo> <mml:mspace width="-0.10em"/> <mml:mi>φ</mml:mi> <mml:mspace width="-0.10em"/> <mml:mo>≤</mml:mo> <mml:mspace width="-0.10em"/> <mml:mn>6</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:mfenced> </mml:math> and different radiation parameters ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>R</mml:mi> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mspace width="-0.10em"/> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mspace width="-0.10em"/> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mspace width="-0.10em"/> <mml:mn>3</mml:mn> </mml:math> ). The findings show that the HTR increased 3.6 times by augmenting the Ra from 10 4 to 10 6 . Also, increasing the Ha number from 0 to 100 causes an 83.16% reduction in the HTR. Considering the radiation mode of heat transfer causes an increase in HTR. The average Nusselt values increase by 59.72% for the concentration of 6% while increasing the radiation parameter from 0 to 3. On the other hand, an increase in volume fraction leads to a deterioration in mean Nusselt numbers (Nu mean ).