Computational Role in Thermal Engineering and Chemical Analytics During the Rotating Disk of Generalized Williamson Viscosity and Thermal Conductivity

ABSTRACT Thermal conductivity, temperature gradient, and diffusivities dependent viscosities based on two‐model approaches are used in this work to examine the nature of shear‐thinning materials in the presence of microorganisms. The consideration of such rheological material is further significantly affected by vertical rotating disk and gravitational acceleration. The variable nature of the viscosity introduces a set of complex mathematical equations that are very useful for prediction in terms of many industrial processes and technological advancement. The mathematical formulations are based on the conservation laws, including temperature, momentum, concentration, and mass. The leading equations are presented in the form of partial differential equations (PDEs) and then converted the same to a set of second‐order differential equations (DEs) that depend on a single local, similar independent variable. A modified version of the built‐in command is implemented by using MATLAB to analyze the importance of the entire work. Every leading and novel factor introduces very interesting and productive results. These parameters are determined very effectively while plotting their role via material speed, concentration, temperature, thermal and mass flow rates, and surface‐oriented resistive forces. The rotation velocity and gravity initiated complex dynamical types of results, which include higher thermal conductivity and diffusivities, respectively, for larger material parameters. Both the bio convection Schmidth and Peclet numbers reduced the speed of microorganisms during the typical swirling motion of Williamson fluid. The tangential and azimuthal components’ velocities of the materials are declining functions of the Richardson number. An opposite trend is observed in the flow velocity along the direction of radiation. The radial component of skin friction is found in higher order with the variation in the Richardson number, and oppositely observed for the tangential component. The method validation test is performed by providing an excellent comparison with existing works.