This study investigates the effects of melting phenomena and non-linear thermal radiation in Cross nanofluid bioconvection flow with motile microorganisms with a convective boundary over a cylinder. Brownian motion and thermophoresis diffusion are also taken into account in this mathematical model. A governing partial differential equation is used to represent the given flow phenomena. The proper dimensionless transformation is then employed to convert the PDE controlling system into an ordinary one. Bvp4c numerically solves redesigned ODE problems using a shooting strategy in the computational tool MATLAB. Figures versus velocity, temperature distribution, nanoparticle concentration, and microbe concentration profiles are used to analyze and expound on the notably involved aspects thoroughly. It has been demonstrated that increasing the estimates of a mixed convection parameter can enhance velocity. By increasing the Prandtl number, the temperature and concentration of nanoparticles decrease. A high Peclet value lowers the microorganism's profile.

本研究调查了熔化现象和非线性热辐射对跨纳米流体生物对流流动的影响，其中运动微生物在圆柱上具有对流边界。在这个数学模型中也考虑了布朗运动和热泳扩散。控制偏微分方程用于表示给定的流动现象。然后采用适当的无量纲变换将 PDE 控制系统转换为普通系统。Bvp4c 使用计算工具 MATLAB 中的射击策略对重新设计的 ODE 问题进行数值求解。数字与速度、温度分布、纳米颗粒浓度和微生物浓度分布图用于对显着涉及的方面进行彻底的分析和阐述。已经证明，增加混合对流参数的估计值可以提高速度。通过增加普朗特数，纳米颗粒的温度和浓度降低。高 Peclet 值会降低微生物的分布。