Entropy analysis in Darcy-Forchheimer flow of nanofluids with thermal radiation: A comparative numerical study

Heat transfer in the transportation of nanoparticles has a significant impact on raising the efficiency of various devices in industrial and technological fields. Here we investigated heat transfer and entropy generation rate for Darcy-Forchheimer stagnation point fluid flow toward a stretched surface in the presence of two types of nanofluids (Al 2 O 3 +water) and (Al 2 O 3 +kerosene oil). In the modeling of energy expression, we utilized the impact of radiative heat flux, internal heat generation, and viscous dissipation. Slip and thermal stratification effects are also present. By employing appropriate transformations, a nonlinear partial differential system can be converted into an ordinary differential system. For solutions computations, a numerical scheme ND-Solve, along with shooting techniques, is implemented. The outcomes of variables that have an impact on temperature and velocity are analyzed. Entropy rate and Bejan number for the considered model are discussed. A physical description of entropy generation against various sundry variables is presented. From the results, it is observed that with greater values of both inverse Darcy number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> <mml:msup> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> ) and slip parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) velocity field shows decreasing trend and temperature field intensifies for higher radiation parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>R</mml:mi> <mml:msup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> ) and heat generation parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>δ</mml:mi> </mml:mrow> <mml:mo>^</mml:mo> </mml:mover> </mml:mrow> </mml:math> ). Entropy rate rises for all flow parameters of both nanofluids while Bejan number decreases for inverse Darcy number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> <mml:msup> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> ) and Eckert number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Ec</mml:mi> </mml:mrow> </mml:math> ). Heat transfer rate boosted for radiation parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>R</mml:mi> <mml:msup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> ) and surface drag reduces for convection parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ).

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