Study of Motile Microorganisms and Variable Thermal Conductivity in a Binary Chemical Reactive Hyperbolic Tangent Fluid in a Porous Microchannel

This study examines the effects of variable thermal conductivity and binary chemical reactions on hyperbolic tangent fluid flow within a porous microchannel in the presence of bioconvection. The combined influences of magnetism, Joule heating, and viscous dissipation are considered. To facilitate analysis, the governing system of partial differential equations is transformed into a system of ordinary differential equations using appropriate dimensionless transformations. The numerical solutions are obtained using the Runge–Kutta–Fehlberg fourth–fifth‐order method in conjunction with the shooting technique. The impact of key governing parameters on velocity, temperature distribution, concentration, and motile microorganism density is analyzed in detail through graphical representations. The results indicate that the thermal field exhibits a dual behavior in response to variations in thermal conductivity and magnetic effects. A similar trend is observed in velocity profiles concerning the Weissenberg number. Furthermore, an increase in the Peclet number reduces the thickness of the actively moving microorganism layer, while a higher bioconvection Lewis number promotes the accumulation of motile microorganisms. The study also reveals that the chemical reaction rate diminishes with concentration levels, whereas an increase in activation energy enhances concentration. Additionally, the heat transfer rate improves with variable thermal conductivity at the microchannel walls, whereas the skin friction coefficient decreases with higher Weissenberg numbers. These findings have practical implications in various engineering and biomedical applications, such as microfluidic device design, biofuel production, drug delivery systems, and the control of microbial transport in porous media.