Abstract & Overview
Abstract The addition of gyrotactic microbes in the nanoparticles is essential to embellish the thermal efficiency of many systems such as microbial fuel cells, bacteria-powered micro-mixers, micro-volumes like microfluidics devices, enzyme biosensor, and chip-shaped microdevices like bio-microsystems. This analysis investigates the second law analysis in the bioconvection flow of a Carreau nanoliquid through a convectively stretching surface. The heat transports characteristics encountered with Cattaneo–Christove heat flux and thermal radiation. The Buongiorno model is used for nanoliquid, which comprises the Brownian motion and thermophoretic. The appropriate transformation is invoked to change the system of the partial differential equation into ordinary differential equations. Afterward, these equations are classified analytically with the help of the homotopy analysis method. The influence of numerous physical variables is interpreted and elaborated via graphs. The tabular result shows the numerical consequences of different physical flow parameters. It is examined that a more significant Weissenber number We {\rm{We}} results in deprecation in the velocity field. It is appraised that the temperature profile reduces to augment the value of thermal relaxation time. Justification of the current work has existed through previous publishing results. The utilization of Carreau nanoparticles in the shear rate-dependent viscous fluid is of significant importance due to their potential to improve heat and mass transmission.