MHD mixed convection of hybrid nanofluid in a wavy porous cavity employing local thermal non-equilibrium condition

Abstract The current study treats the magnetic field impacts on the mixed convection flow within an undulating cavity filled by hybrid nanofluids and porous media. The local thermal non-equilibrium condition below the implications of heat generation and thermal radiation is conducted. The corrugated vertical walls of an involved cavity have $${T}_{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> and the plane walls are adiabatic. The heated part is put in the bottom wall and the left-top walls have lid velocities. The controlling dimensionless equations are numerically solved by the finite volume method through the SIMPLE technique. The varied parameters are scaled as a partial heat length ( B : 0.2 to 0.8), heat generation/absorption coefficient ( Q : − 2 to 2), thermal radiation parameter ( R d : 0–5), Hartmann number ( Ha : 0–50), the porosity parameter ( ε : 0.4–0.9), inter-phase heat transfer coefficient ( H * : 0–5000), the volume fraction of a hybrid nanofluid ( ϕ : 0–0.1), modified conductivity ratio ( k r : 0.01–100), Darcy parameter $$\left(Da: 1{0}^{-1}\,\mathrm{ to }\,1{0}^{-5}\right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mi>D</mml:mi> <mml:mi>a</mml:mi> <mml:mo>:</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:mi>to</mml:mi> <mml:mspace/> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mfenced> </mml:math> , and the position of a heat source ( D : 0.3–0.7). The major findings reveal that the length and position of the heater are effective in improving the nanofluid movements and heat transfer within a wavy cavity. The isotherms of a solid part are significantly altered by the variations on $$Q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Q</mml:mi> </mml:math> , $${R}_{d}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:math> , $${H}^{*}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> </mml:math> and $${k}_{r}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:math> . Increasing the heat generation/absorption coefficient and thermal radiation parameter is improving the isotherms of a solid phase. Expanding in the porous parameter $$\varepsilon$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ε</mml:mi> </mml:math> enhances the heat transfer of the fluid/solid phases.

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