Numerical analysis of Casson-micropolar nanofluid flow over a porous stretching sheet with thermal radiation and chemical reactions

Abstract This study presents a comprehensive analysis of Casson-micropolar nanofluid flow over a porous stretching sheet, addressing a critical gap in non-Newtonian fluid dynamics where previous studies have treated yield stress and microrotation effects in isolation. While Casson fluids (modeling yield stress) and micropolar fluids (modeling particle rotation) have been extensively studied separately, their combined behavior in nanofluids remains largely unexplored despite being essential for applications like targeted drug delivery (where blood’s yield stress coexists with cellular rotation) and industrial slurry transport. Our novel hybrid model unifies these effects with thermal radiation and chemical reactions, solved using an optimized fourth-order Runge–Kutta method. Key findings reveal a 32% increase in velocity gradients under strong yield stress ( $$\beta = 0.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.5</mml:mn> </mml:mrow> </mml:math> ), a 12% temperature enhancement from radiation ( $$R = 0.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.5</mml:mn> </mml:mrow> </mml:math> ), and a 40% concentration reduction due to chemical reactions ( $$K = 1.0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>K</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1.0</mml:mn> </mml:mrow> </mml:math> ). The work’s primary innovation lies in introducing the dominance ratio $$\frac{d}{\beta }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mi>d</mml:mi> <mml:mi>β</mml:mi> </mml:mfrac> </mml:math> that predicts whether microrotation ( $$\frac{d}{\beta }&gt; 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mfrac> <mml:mi>d</mml:mi> <mml:mi>β</mml:mi> </mml:mfrac> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> ) or yield stress ( $$\frac{d}{\beta } &lt; 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mfrac> <mml:mi>d</mml:mi> <mml:mi>β</mml:mi> </mml:mfrac> <mml:mo>&lt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> ) controls flow behavior—a crucial distinction absent in prior literature. These results provide actionable guidelines for biomedical engineering (optimal $$d = 0.2-0.4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.2</mml:mn> <mml:mo>-</mml:mo> <mml:mn>0.4</mml:mn> </mml:mrow> </mml:math> for drug delivery) and industrial processes ( $$\lambda = 0.4-0.6$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.4</mml:mn> <mml:mo>-</mml:mo> <mml:mn>0.6</mml:mn> </mml:mrow> </mml:math> for oil recovery), bridging the gap between theoretical models and real-world applications.