Published 2023-10-01
“…The benchmark results thoroughly validate the graphics process unit (GPU) based in-house compute unified device architecture (
CUDA) C/C++ code. Numeral simulations were performed for a variety of dimensionless variables, including the Rayleigh number, (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>a</mi></mrow></semantics></math></inline-formula> = <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>10</mn><mn>4</mn></msup><mo>,</mo><msup><mn>10</mn><mn>5</mn></msup><mo>,</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></semantics></math></inline-formula>), the Darcy number, (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mi>a</mi></mrow></semantics></math></inline-formula> = <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>,</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo>,</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></semantics></math></inline-formula>), the Soret number, (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>r</mi></mrow></semantics></math></inline-formula> = <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.0</mn><mo>,</mo><mn>0.1</mn><mo>,</mo><mn>0.2</mn></mrow></semantics></math></inline-formula>), the Dufour number, (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>f</mi></msub></semantics></math></inline-formula> = <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.0</mn><mo>,</mo><mn>0.1</mn><mo>,</mo><mn>0.2</mn></mrow></semantics></math></inline-formula>), the buoyancy ratio, (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>2</mn><mo>≤</mo><mi>B</mi><mi>r</mi><mo>≤</mo><mn>2</mn></mrow></semantics></math></inline-formula>), the Lewis number, (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>e</mi></mrow></semantics></math></inline-formula> = <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn></mrow></semantics></math></inline-formula>), the volume fraction, (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>ϕ</mi><mo>≤</mo><mn>0.04</mn></mrow></semantics></math></inline-formula>), and the porosity, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> = (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.2</mn><mo>−</mo><mn>0.8</mn></mrow></semantics></math></inline-formula>), and the Prandtl number, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>r</mi></mrow></semantics></math></inline-formula> = <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>6.2</mn></mrow></semantics></math></inline-formula> (water) is fixed to represent the base fluid. …”
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