Effect of activation energy and nonlinear thermal radiation on flow, heat and mass transfer of magneto-bioconvective Eyring–Powell nanofluid due to a stretching sheet

This paper investigates the effects of activation energy and nonlinear thermal radiation on the flow, heat, and mass transfer of magneto-bioconvective Eyring–Powell nanofluid due to a stretching sheet. It analyzes the influences of magnetohydrodynamic forces, nonlinear thermal radiation, chemical reactions, and the activation energy of species within the Powell–Eyring nanofluid. Motile microorganisms are introduced alongside nanoparticles to prevent agglomeration and stabilize the suspension. The governing nonlinear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using similarity transformations and solved numerically with the RKF45 algorithm in MATLAB. Results indicate that increasing the Powell–Eyring fluid parameter and Grashof number enhances the velocity profile, while the Hartmann number and buoyancy ratio reduce it. Temperature distribution increases with higher thermal radiation, Hartmann, Eckert, Brownian motion, and thermophoresis parameters, but decreases with greater Grashof and Prandtl numbers. The nanoparticle concentration profile declines with increasing Lewis number, chemical reaction, and Brownian motion parameters but rises with thermophoresis and activation energy. The density of gyrotactic microorganisms decreases with higher bioconvection Lewis and Peclet number, concentration deference of motile microorganism parameter, while it increases with the Hartmann number. In table, we are observed that as the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>ε</mml:mi> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Gr</mml:mi> </mml:mrow> </mml:math> values are increases, then skin friction coefficient value are decreases. As the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Rb</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>δ</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Nr</mml:mi> </mml:mrow> </mml:math> values are increases, then skin friction coefficient value are increases. In table, we are observed that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Gr</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>w</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> values are increases, then local Nusslet number increases. As the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">Pr</mml:mi> </mml:mrow> </mml:math> , <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> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Nb</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Nt</mml:mi> </mml:mrow> </mml:math> values are increases, then local Nusslet number decreases. In table, we are observed that as the values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Le</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Nb</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Nt</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>ω</mml:mi> </mml:mrow> </mml:math> upsurges, then Sherwood number decreases. In table, we observed that as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> values increases, then Local density number decreases. As the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Lb</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">Ω</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Pe</mml:mi> </mml:mrow> </mml:math> increases, then Local density number increases. Main objective of the present study is observed from tables and the amount of heat transmission increases by increasing the values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll">