Comparative reaction dynamics in rotating nanofluid systems: Quartic and cubic kinetics under MHD influence

Abstract An electrically conducting Reiner–Rivlin nanoliquid flow is considered over a rough, infinitely spinning disk based on a von Kármán model. The flow incorporates partial slip conditions and a temperature jump at the disk surface. This investigation seeks to establish a more precise and practical framework for advanced thermal-fluid systems, with specific relevance to microscale heat management and electrohydrodynamic technologies. The novelty lies in addressing the comparative appraisal of quartic and cubic chemical reactions as these possess pivotal applications, including advanced cooling systems, corrosion and material processing, electromagnetic and MHD applications, and aerospace and turbomachinery. Additionally, Brownian motion and thermophoresis effects are included owing to nanoparticles. The 3-stage Lobatto IIIa method of MATLAB software is applied to compute the numerical solution of the present model. Results are demonstrated in the form of illustrations and tables. The velocity and temperature profiles display contrasting trends for the slip parameter. The fluid concentration decreases with the Reiner–Rivlin parameter and the Schmidt number. In addition, the heat flux rate is higher for a quartic chemical reaction than for a cubic chemical reaction. This study can be applied to microfluidic devices, rotary heat exchangers, and rotating machinery in aerospace and biomedical systems, where enhanced heat transfer, complex fluid behavior, and realistic boundary effects like slip, roughness, and magnetic fields are critical. A validation of the presented data is also a part of this study. To draw the graphs and for the tabulated values, the assumed ranges of the involved parameters are as follows: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:mtable displaystyle="true" columnalign="left"> <m:mtr> <m:mtd> <m:mn>2</m:mn> <m:mo>≤</m:mo> <m:mi>Pr</m:mi> <m:mo>≤</m:mo> <m:mn>20</m:mn> <m:mo>,</m:mo> <m:mspace width=".5em"/> <m:mn>0.1</m:mn> <m:mo>≤</m:mo> <m:mi>γ</m:mi> <m:mo>≤</m:mo> <m:mn>0.5</m:mn> <m:mo>,</m:mo> <m:mspace width=".5em"/> <m:mn>5</m:mn> <m:mo>≤</m:mo> <m:mi>M</m:mi> <m:mo>≤</m:mo> <m:mn>15</m:mn> <m:mo>,</m:mo> <m:mspace width=".5em"/> <m:mn>0.2</m:mn> <m:mo>≤</m:mo> <m:mi>α</m:mi> <m:mo>≤</m:mo> <m:mn>0.6</m:mn> <m:mo>,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd> <m:mn>4</m:mn> <m:mo>≤</m:mo> <m:msub> <m:mrow> <m:mi>N</m:mi> </m:mrow> <m:mrow> <m:mtext>b</m:mtext> </m:mrow> </m:msub> <m:mo>≤</m:mo> <m:mn>6</m:mn> <m:mo>,</m:mo> <m:mspace width=".5em"/> <m:mn>0.1</m:mn> <m:mo>≤</m:mo> <m:msub> <m:mrow> <m:mi>N</m:mi> </m:mrow> <m:mrow> <m:mtext>t</m:mtext> </m:mrow> </m:msub> <m:mo>≤</m:mo> <m:mn>0.3</m:mn> <m:mo>,</m:mo> <m:mspace width=".5em"/> <m:mn>0.3</m:mn> <m:mo>≤</m:mo> <m:mi>K</m:mi> <m:mo>≤</m:mo> <m:mn>0.4</m:mn> <m:mo>,</m:mo> <m:mspace width=".5em"/> <m:mn>2.5</m:mn> <m:mo>≤</m:mo> <m:mi>S</m:mi> <m:mi>c</m:mi> <m:mo>≤</m:mo> <m:mn>3.5</m:mn> <m:mo>.</m:mo> </m:mtd> </m:mtr> </m:mtable> </m:math> \begin{array}{c}2\le \Pr \le 20,\hspace{.5em}0.1\le \gamma \le 0.5,\hspace{.5em}5\le M\le 15,\hspace{.5em}0.2\le \alpha \le 0.6,\\ 4\le {N}_{\text{b}}\le 6,\hspace{.5em}0.1\le {N}_{\text{t}}\le 0.3,\hspace{.5em}0.3\le K\le 0.4,\hspace{.5em}2.5\le Sc\le 3.5.\end{array}