Theoretical study on bio-convection of micropolar fluid with an exploration of Cattaneo-Christov heat flux theory

This research explores the heat transfer rate for micropolar fluid in a channel flow. In spite of formal Fourier's law, the Cattaneo-Christov heat flux design is implemented in energy system. Using appropriate dimensionless parameters, the guiding coupled partial differential equations that represent the fluid flow are modified into ordinary differential equations. By executing Runge-Kutta integration procedure and the shooting method, the numerical results are achieved. The impacts of thermal relaxation time and bio-convection flow of micropolar fluid are examined in this assessment. Graphical analyses are used to assess the effects of physical factors for the momentum, micro-rotation, concentration, density of micro-organisms and temperature gradient. The skin friction values, motile density number, heat and mass transfer rate are the fascinating physical quantities whose numerical data are computed and validated against different parametric values. The variational iteration method (VIM) and Adomian decomposition method are the analytical modules which have been incorporated here for solving the nonlinear systems for showing better approximity. It is found from the study that larger the thermal relaxation time values, the more likely they are to increase heat transfer, hence lowering the fluid temperature. Moreover, both Fourier and Cattaneo-Christov heat conduction module exhibit qualitatively similar influence on embedded parameters also the temperature profile diminishes for larger values of Peh. The culminations evidently disclose that the bio-convection Peclet number and the motile microbes parameter enhance the density of motile micro-organisms. From a computational perspective, the VIM is more effective, practical and ease of use. The numerical and analytical results are compared well with the existing articles. The optimum parameter level for maximum heat transfer is considered to be A3B4C1D2E3. Taguchi approach was successfully used to determine the optimum design parameters for maximum heat transfer is 1.724012 for the parameters A-5:B-5:C-0.5:D-0.5:E-0.7.