On time dependent MHD nanofluid dynamics due to enlarging sheet with bioconvection and two thermal boundary conditions

Abstract

The current study pertains to heat and mass transportation of magnetic fluid flow having dilute diffusion of nanoparticles and motile microorganisms over a permeable stretched sheet to examine the influence of thermal radiation and activation energy. Similarity functions are utilized to convert the highly mixed non-linear partial differential equations into higher-order non-linear ordinary differential equations. Five coupled equations are derived to be resolved numerically by employing a computing function Bvp4c, built-in Matlab. Two sets of thermal boundaries prescribed surface temperature (PSF) and prescribed heat flux (PHF) are considered. Basic physical quantities, temperature distribution, concentration, velocity field, and motile micro-organism profiles are observed as influenced by emerging parameters. The microorganisms distribution undergoes decreasing behavior against growing values of bio-convection Lewis number and Peclet number. These results are highly useful in the application of heat-transmitting devices and microbial fuel cells. It is seen that decreasing trend is observed in velocity profile when parameters Nr and Nc are uplifted. Also, the motility of the nanofluid decreases when the Lb parameter is raised. On the other hand, an increase in Peclet number Pe showed a rising trend in motility profile. Additionally, the implications of Brownian motion, Rayleigh number, Bioconvection Lewis number thermophoresis parameter, Peclet number, and buoyancy ratio parameter are discussed. Moreover, the obtained outcomes are validated as compared to the existing ones as limiting cases. Representative findings for microorganism concentration, skin friction coefficient, temperature gradient, local Sherwood number and density number of motile microorganisms, velocity field, temperature, the volumetric concentration of nanoparticles, are discussed in tabulated and graphical form.