Biomathematical model for gyrotactic free-forced bioconvection with oxygen diffusion in near-wall transport within a porous medium fuel cell

Nima, NI; Ferdows, M; Beg, OA; Kuharat, S; Alzahrani, F

Abstract

Bioconvection has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies.
The improved design of such systems requires continuous refinements in biomathematical modelling in conjunction
with laboratory and field testing. Motivated by exploring deeper the near-wall transport phenomena involved in bioinspired fuel cells, in the present article, 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 many taxes exhibited in biological microscale transport, and other examples
include magneto-taxis, photo-taxis, chemotaxis and geo-taxis (reflecting the response of micro-organisms 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 membrane exchange (PEM) system. The vertical wall
is maintained at iso-solutal (constant oxygen volume fraction and motile micro-organism 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 micro-organism species. Similarity transformations are applied to render the
governing partial differential equations for mass, momentum, energy, oxygen species and micro-organism 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 spanning the entire range of free and forced convection. The transformed non-linear
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 modelling framework for simulating such
systems. In particular, the deployment of gyrotactic micro-organisms is shown to stimulate improved transport
characteristics in heat and momentum at the fuel cell wall.

Citation

Nima, N., Ferdows, M., Beg, O., Kuharat, S., & Alzahrani, F. (2020). Biomathematical model for gyrotactic free-forced bioconvection with oxygen diffusion in near-wall transport within a porous medium fuel cell. International Journal of Biomathematics, 13(4), 2050026. https://doi.org/10.1142/S1793524520500266

• Journal Article Type: Article
• Acceptance Date: Feb 23, 2020
• Online Publication Date: Apr 18, 2020
• Publication Date: Apr 18, 2020
• Deposit Date: Feb 24, 2020
• Publicly Available Date: Apr 18, 2021
• Journal: International Journal of Biomathematics
• Print ISSN: 1793-5245
• Electronic ISSN: 1793-7159
• Publisher: World Scientific Publishing
• Volume: 13
• Issue: 4
• Pages: 2050026
• DOI: https://doi.org/10.1142/S1793524520500266
• Publisher URL: https://doi.org/10.1142/S1793524520500266
• Related Public URLs: https://www-worldscientific-com.salford.idm.oclc.org/worldscinet/ijb