Bioconvection has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies. The improved design of such systems requires continuous refinements in biomathematical modeling in conjunction with laboratory and field testing. Motivated by exploring deeper the near-wall transport phenomena involved in bio-inspired fuel cells, in the present paper, we examine analytically and numerically the combined free-forced convective steady boundary layer flow from a solid vertical flat plate embedded in a Darcian porous medium containing gyrotactic microorganisms. Gyrotaxis is one of the many taxes exhibited in biological microscale transport, and other examples include magneto-taxis, photo-taxis, chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field, light, chemical concentration or gravity, respectively). The bioconvection fuel cell also contains diffusing oxygen species which mimics the cathodic behavior in a proton exchange membrane (PEM) system. The vertical wall is maintained at iso-solutal (constant oxygen volume fraction and motile microorganism density) and iso-thermal conditions. Wall values of these quantities are sustained at higher values than the ambient temperature and concentration of oxygen and biological microorganism species. Similarity transformations are applied to render the governing partial differential equations for mass, momentum, energy, oxygen species and microorganism species density into a system of ordinary differential equations. The emerging eight order nonlinear coupled, ordinary differential boundary value problem features several important dimensionless control parameters, namely Lewis number (Le), buoyancy ratio parameter i.e. ratio of oxygen species buoyancy force to thermal buoyancy force (Nr), bioconvection Rayleigh number (Rb), bioconvection Lewis number (Lb), bioconvection Péclet number (Pe) and the mixed convection parameter ([Formula: see text] spanning the entire range of free and forced convection. The transformed nonlinear system of equations with boundary conditions is solved numerically by a finite difference method with central differencing, tridiagonal matrix manipulation and an iterative procedure. Computations are validated with the symbolic Maple 14.0 software. The influence of buoyancy and bioconvection parameters on the dimensionless temperature, velocity, oxygen concentration and motile microorganism density distribution, Nusselt, Sherwood and gradient of motile microorganism density are studied. The work clearly shows the benefit of utilizing biological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems. In particular, the deployment of gyrotactic microorganisms is shown to stimulate improved transport characteristics in heat and momentum at the fuel cell wall.

中文翻译：

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多孔介质燃料电池内近壁传输中具有氧扩散的回旋自由强制生物对流的生物数学模型

生物对流已显示出对环境友好、可持续的“绿色”燃料电池技术的巨大希望。此类系统的改进设计需要结合实验室和现场测试不断改进生物数学建模。通过深入探索仿生燃料电池中涉及的近壁传输现象，在本文中，我们分析和数值研究了来自嵌入达西多孔介质中的固体垂直平板的组合自由强迫对流稳定边界层流含有回旋微生物。Gyrotaxis 是生物微尺度运输中表现出的众多税种之一，其他例子包括趋磁性、趋光性、趋化性和地趋性（反映微生物对磁场、光、化学浓度或重力，分别）。生物对流燃料电池还包含模拟质子交换膜 (PEM) 系统中的阴极行为的扩散氧物质。垂直壁保持在等溶质（恒定的氧气体积分数和活动微生物密度）和等温条件下。这些量的壁值维持在高于环境温度和氧气和生物微生物物种浓度的值。应用相似变换将质量、动量、能量、氧种类和微生物种类密度的控制偏微分方程转化为常微分方程组。新兴的八阶非线性耦合，研究了氧浓度和活动微生物密度分布、Nusselt、Sherwood和活动微生物密度梯度。这项工作清楚地表明了在燃料电池设计中利用生物有机体的好处，并提出了一个用于模拟此类系统的逻辑生物数学建模框架。特别是，回旋微生物的部署显示出刺激改进的燃料电池壁处的热量和动量传输特性。