Gyrotactic Microorganisms modeling of free forced Convective Boundary Layer flow

Abstract

The study of microorganisms has attracted the focus of researchers for observing the emergence of microorganisms in bioconvection. Due to their intermixing traits and capacity in order to enhance mass transit, major applications of biological convection phenomena have been observed in numerous biotechnology and biological systems. Some exemplary applications exist in the biomedical fields (nanodrug administration and cancer treatment) and bio-microsystems (the use of enzyme biosensors in technology). Owing to their numerous industrial applications, including heat exchange in low-velocity environments, wind-exposed solar collectors, atmospheric boundary layer flows, and emergency cooling of nuclear reactors, combined (free and forced) or mixed convection problems with gyrotactic microorganisms have attracted considerable attention in recent years. This dissertation analyses the behaviour of gyrotactic microorganisms in free-forced convective flow over a variety of surface geometries (vertical plates, horizontal plates, cylinders, cones, and spheres). For physical consideration, significant quantities including the melting effect, isothermal and non-isothermal processes, internal heat generation, variable fluid characteristics, and dispersion effects are considered. The first objective of this study is to examine and establish the mathematical formulation for the considered problems. Different emerging laws of physics accustomed to model the partial differential equations system. Then, the second objective is to impose finite difference method, MAPLE algorithm, and MATLAB bvp4c scheme to solve a set of ordinary differential equations. To do numerical calculations, the controlling partial differential equations for energy, momentum, mass conservation, and mobile microorganism conservation balances were initially transformed by similarity transformations into a collection of interconnected nonlinear ordinary differential equations. The last objective is to analyze the effect of governing parameters on different flow fields (velocity, temperature, concentration and microorganism) and also on heat, mass and motile microorganism transfer rate profiles. Motivated by the exploration of the fuel cells with bio-inspired design use phenomenon involving near-wall transport, we first quantitatively and analytically examined the free-forced, steady boundary layer flow from a solid vertical flat plate that is immersed in a porous material with Darcian pores that is home to gyrotactic microorganisms. Subsequently, in our second problem, we analysed the mass, heat, and bioconvective flow, including moving microorganisms on a porous material-covered a vertical surface with varying porosity. Various fluid characteristics are presumptively porosity-dependent due to the varying porosity. The Darcy model was used to examine bioconvection through porous and impermeable surfaces in the case of uniform and varied permeability, and the consequences of heat generation were considered. Then, in third problem, the work on variable fluid characteristics was expanded to include nonNewtonian

fluids with melting influences harbouring gyrotactic microorganisms throughout a vertical plate that is immersed in an enriched non-Darcy porous media, where all flow profiles are observed for fluids that are dilatant, Newtonian, and pseudo-plastic. The fourth problem considered the dispersion effects and the impact on flow in a horizontal cone with mixed convection in a non-Darcy porous media. In order to address the phenomena of heat, mass, and motile microbe transport, several convective boundary conditions were used. This study incorporated the dispersion impact of gyrotactic microorganisms for applications in biology and the environment. The fifth study aims to determine whether an inclined, non-isothermal permeable cylinder containing a mixed, free, and forced convective flow with gyrotactic microorganisms has a stable or unstable solution. Few researches have been conducted on dual solutions for mixed convection with gyrotactic microorganisms, despite the fact that they have many engineering applications and have been studied extensively along a vertical cylinder. Finally, in the last problem, the consistent boundary layer flow of mixed convection approaching a solid sphere's bottom stagnation point with constant heat, mass, and motile microorganism flux containing gyrotactic microorganisms was analysed in the scenario of aiding and opposing flow, and dual solution phenomena were also observed with regard to a particular set of mixed convection characteristics. Throughout this study, the numerical solution acquired for the profiles of molecular motion, temperature, concentration, and density was plotted for various physical parameter choices. The numerical values representing the Nusselt, Sherwood, and motile microbe density have also been presented and analysed through tables. By contrasting the current study's findings with those of earlier studies, the research leads to a conclusion that upholds the validity of the computational algorithm results. Based on this thesis, we observed significant parametric effects on the flow boundaries. The results show that, in the forced convection regime, the influences of the physical parameters such as buoyancy parameters, Lewis parameter, bioconvection Lewis number, bioconvection Peclet number, dispersions parameter, Biot numbers are more prominent than in the pure free convection regime. Mixed convection parameter has a significant impact on heat mass and the pace at which motile microorganisms transfer when permeability is changeable with a porous surface especially for pseudo-plastic fluids. The temperature increases for the mixed-convection parameter and plunges for the melting parameter. On the other hand, the concentration slows for a high melting effect. Lewis parameter, bioconvection Lewis number, bioconvection Peclet number have pronounced effects on concentration and microorganism profiles. The results further demonstrate that flow through non-isothermal inclined cylinder where free convection is dominant could distinct flow profiles exist as dual solutions. Only vertical and inclined cylinders exhibit the dual solution phenomenon, and a study on a horizontal cylinder only shows a unique solution. Notably, at the lower stagnation flow of solid sphere dual solutions exist for opposing flows for a particular range of mixed convection parameters, where a stable solution is indicated by the first solution, and an unstable one by the second.