THEORETICAL ANALYSIS OF ACTIVATION ENERGY OF DARCY–FORCHHEIMER FRACTIONAL BIOCONVECTION FLOW OF NANOFLUID DUE TO A ROTATING DISK WITH ENTROPY GENERATION

This paper examines the theoretical Darcy–Forchheimer bioconvective flow of a nanoliquid due to a porous disk. The convective condition, heat radiation and heat generation are all used to represent the energy equation. The energy of Arrhenius activation addresses numerous aspects, including heat and mass transitions. Entropy generation under bioconvection is described. Using Buongiorno’s model, the properties of the nanoliquid are discussed considering Brownian movement with the thermophoresis force effect. The highly nonlinear equation of the current model has been altered through a suitable alteration. The transform equations are further handled through the Bvp4c technique. The consequences of significant parameters on Bejan number, entropy generation, velocity, temperature field, microbe field and concentration are graphically represented. Evidently, axial and azimuthal velocity lessening is confirmed considering the inertia coefficient and porosity effect. A Biot number and Brownian movement tend to an escalation in thermal analysis, while the temperature diffusion variable, chemical reaction and Schmidt number cause a depreciation in the concentration distribution. Moreover, microorganism for the Bioconvection Lewis number and Peclet number is reduced. The present study is also applicable in the bioengineering process and in different industrial processes. Fractal-fractional order derivative operators are widely regarded as extremely complex mathematical tools that can be used to obtain real solutions in a wide range of engineering and physics scenarios. Fractal-fractional derivatives allow us to simultaneously study fractional order and fractal dimension.