Retracted: Functional shape effects of nanoparticles on nanofluid suspended in ethylene glycol through Mittage-Leffler approach

Abstract

Abstract It is fundamental fact that nanoparticles are strong function of their shapes and sizes; this is because nanoparticles certainly play an adhesive and a significant role in fluid phenomenon. This manuscript investigates the functionality and thermodynamics of different nanoparticles namely gold, alumina, silver and copper suspended in ethylene glycol considered as a base fluid. The problem of mixed convection is modeled by modern fractional derivative by invoking initial and boundary conditions. The analytic calculation of velocity field and temperature distribution is obtained by employing Laplace transforms then transformed into Fox- H function. The effects of critical physical characteristics (sizes and shapes) have been analyzed through velocity field and temperature distribution using different nanoparticles. Obviously, all nanoparticles are not made equal in terms of sizes and shapes; hence a remarkable comparison of different nanoparticles is analyzed for the interactions with their sizes and shapes on the velocity field and temperature distribution. Importantly, we seek to illustrate the shape and size impacts of nanoparticles namely platelet, blade, cylinder and brick on velocity field and temperature distribution. In short, our results suggest that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>E</mml:mi> <mml:mi>G</mml:mi> <mml:mo>−</mml:mo> <mml:mi>A</mml:mi> <mml:mi>u</mml:mi> </mml:math> moves more rapidly in comparison with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>E</mml:mi> <mml:mi>G</mml:mi> <mml:mo>−</mml:mo> <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:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mi>G</mml:mi> <mml:mo>−</mml:mo> <mml:mi>A</mml:mi> <mml:mi>g</mml:mi> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>E</mml:mi> <mml:mi>G</mml:mi> <mml:mo>−</mml:mo> <mml:mi>C</mml:mi> <mml:mi>u</mml:mi> </mml:math> at larger time while <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>E</mml:mi> <mml:mi>G</mml:mi> <mml:mo>−</mml:mo> <mml:mi>C</mml:mi> <mml:mi>u</mml:mi> </mml:math> moves faster in comparison with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>E</mml:mi> <mml:mi>G</mml:mi> <mml:mo>−</mml:mo> <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:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mi>G</mml:mi> <mml:mo>−</mml:mo> <mml:mi>A</mml:mi> <mml:mi>g</mml:mi> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>E</mml:mi> <mml:mi>G</mml:mi> <mml:mo>−</mml:mo> <mml:mi>A</mml:mi> <mml:mi>u</mml:mi> </mml:math> for smaller time. The identical similarities and differences have also been analyzed on the basis of shape and size impacts of nanoparticles.

Topics & Concepts