Bioconvective Flow Characteristics of NEPCM–Water Nanofluid over an Inclined Cylinder in Porous Medium: An Extended Darcy Model Approach

Bioconvection phenomena play a pivotal role in diverse applications, including the synthesis of biological polymers and advancements in renewable energy technologies. This study develops a comprehensive mathematical model to examine the effects of key parameters, such as the Lewis number (Lb), Peclet number (Pe), volume fraction ( φ ), and angle of inclination ( α ) , on the flow and heat transfer characteristics of a nanofluid over an inclined cylinder embedded in a non-Darcy porous medium. The investigated nanofluid comprises nano-encapsulated phase-change materials (NEPCMs) dispersed in water, offering enhanced thermal performance. The governing non-linear partial differential equations are transformed into dimensionless ordinary differential equations using similarity transformations and solved numerically via the Network Simulation Method (NSM) and an implicit Runge–Kutta method implemented through the bvp4c routine in MATLAB R2021a. Validation against the existing literature confirms the accuracy and reliability of the numerical approach, with strong convergence observed. Quantitative analysis reveals that an increase in the Peclet number reduces the shear stress at the cylinder wall by up to 18% while simultaneously enhancing heat transfer by approximately 12%. Similarly, the angle of inclination ( α ) significantly boosts heat transmission rates. Additionally, higher Peclet and Lewis numbers, along with greater nanoparticle volume fractions, amplify the density gradient of microorganisms, intensifying the bioconvection process by nearly 15%. These findings underscore the critical interplay between bioconvection and transport phenomena, providing a framework for optimizing bioconvection-driven heat and mass transfer systems. The insights from this investigation hold substantial implications for industrial processes and renewable energy technologies, paving the way for improved efficiency in applications such as thermal energy storage and advanced cooling systems.