AUTHOR=Ali Qasim , Amir Muhammad , Raza Ali , Khan Umair , Eldin Sayed M. , Alotaibi Abeer M. , Elattar Samia , Abed Ahmed M. 

TITLE=Thermal investigation into the Oldroyd-B hybrid nanofluid with the slip and Newtonian heating effect: Atangana–Baleanu fractional simulation

JOURNAL=Frontiers in Materials

VOLUME=10

YEAR=2023

URL=https://www.frontiersin.org/journals/materials/articles/10.3389/fmats.2023.1114665

DOI=10.3389/fmats.2023.1114665

ISSN=2296-8016

ABSTRACT=<p>The significance of thermal conductivity, convection, and heat transportation of hybrid nanofluids (HNFs) based on different nanoparticles has enhanced an integral part in numerous industrial and natural processes. In this article, a fractionalized Oldroyd-B HNF along with other significant effects, such as Newtonian heating, constant concentration, and the wall slip condition on temperature close to an infinitely vertical flat plate, is examined. Aluminum oxide (Al<sub>2</sub>O<sub>3</sub>) and ferro-ferric oxide (Fe<sub>3</sub>O<sub>4</sub>) are the supposed nanoparticles, and water (H<sub>2</sub>O) and sodium alginate (C<sub>6</sub>H<sub>9</sub>NaO<sub>7</sub>) serve as the base fluids. For generalized memory effects, an innovative fractional model is developed based on the recently proposed Atangana–Baleanu time-fractional (AB) derivative through generalized Fourier and Fick’s law. This Laplace transform technique is used to solve the fractional governing equations of dimensionless temperature, velocity, and concentration profiles. The physical effects of diverse flow parameters are discussed and exhibited graphically by Mathcad software. We have considered <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>0.15</mml:mn><mml:mo>≤</mml:mo><mml:mi>α</mml:mi><mml:mo>≤</mml:mo><mml:mn>0.85</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>≤</mml:mo><mml:mi mathvariant="italic">Pr</mml:mi><mml:mo>⁡</mml:mo><mml:mo>≤</mml:mo><mml:mn>9</mml:mn><mml:mo>,</mml:mo><mml:mn>5</mml:mn><mml:mo>≤</mml:mo><mml:mi>G</mml:mi><mml:mi>r</mml:mi><mml:mo>≤</mml:mo><mml:mn>20</mml:mn><mml:mo>,</mml:mo><mml:mn>0.2</mml:mn><mml:mo>≤</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>≤</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mn>3.5</mml:mn><mml:mo>≤</mml:mo><mml:mi>G</mml:mi><mml:mi>m</mml:mi><mml:mo>≤</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>0.1</mml:mn><mml:mo>≤</mml:mo></mml:mrow></mml:math></inline-formula> Sc <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>≤</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula id="inf4"><mml:math id="m4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mn>0.3</mml:mn><mml:mo>≤</mml:mo><mml:mi>λ</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>λ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>≤</mml:mo><mml:mn>1.7</mml:mn><mml:mo>.</mml:mo></mml:mrow></mml:math></inline-formula> Moreover, for validation of our present results, some limiting models, such as classical Maxwell and Newtonian fluid models, are recovered from the fractional Oldroyd-B fluid model. Furthermore, comparing the results between Oldroyd-B, Maxwell, and viscous fluid models for both classical and fractional cases, Stehfest and Tzou numerical methods are also employed to secure the validity of our solutions. Moreover, it is visualized that for a short time, temperature and momentum profiles are decayed for larger values of <inline-formula id="inf5"><mml:math id="m5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula>, and this effect is reversed for a long time. Furthermore, the energy and velocity profiles are higher for water-based HNFs than those for the sodium alginate-based HNF.</p>