Brownian motion’s impact on MHDCuO-Al2O3/H2O hybrid nanofluid flow and heat transfer through annular duct

The present numerical work is to explore the effect of variable electrically conductivity on magneto-hydrodynamic, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>MHD</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> hybrid nanofluid flow through annular sector duct, for both <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> 1 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> thermally fully developed conditions. The nanofluid consists of basefluid water and aluminum oxide, (i.e. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>A</mml:mi> <mml:msub> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> / <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mi>O</mml:mi> </mml:mrow> </mml:math> nanofluid). The addition of copper oxide, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>CuO</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> nanoparticles in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>A</mml:mi> <mml:msub> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> / <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mi>O</mml:mi> </mml:mrow> </mml:math> nanofluid, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:math> , is known as hybrid nanofluid. Koo–Kleinstreuer–Li ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>KKL</mml:mi> </mml:mrow> </mml:math> ) model correlations are used to examine the effective dynamics viscosity and thermal conductivity of the resulting hybrid nanofluid. In this way, the Brownian motion’s impact of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>CuO</mml:mi> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>A</mml:mi> <mml:msub> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> nanoparticles are also accounted. The finite volume based method, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>FVBM</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and strongly implicit procedure, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>SIP</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> are adopted for the discretization and the numerical solution of the governing non-linear problem respectively. For this purpose, the well known technique ’the semi implicit method for pressure linked equations, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>SIMPLE</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> revised’ is utilized. Accordingly <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>SIMPLER</mml:mi> </mml:mrow> </mml:math> , the continuity equation is transformed into Poisson equation in term of the pressure by replacing the cross section velocity components’ discretized form. During the work, it has been observed that the velocity contours and isotherms against pertinent parameters, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> , have inversely and directly impacts respectively, for different values of apex angle, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> </jats: