In this article, a Riga plate is exhibited with an electric magnetization actuator consisting of permanent magnets and electrodes assembled alternatively. This exhibition produces electromagnetic hydrodynamic phenomena over a fluid flow. A new study model is formed with the Sutterby nanofluid flow through the Riga plate, which is crucial to the structure of several industrial and entering advancements, including thermal nuclear reactors, flow metres and nuclear reactor design. This article addresses the entropy analysis of Sutterby nanofluid flow over the Riga plate. The Cattaneo–Christov heat and mass flux were used to examine the behaviour of heat and mass relaxation time. The bioconvective motile microorganisms and nanoparticles are taken into consideration. The system of equations for the current flow problems is converted from a highly non-linear partial system to an ordinary system through an appropriate transformation. The effect of the obtained variables on velocity, temperature, concentration and motile microorganism distributions are elaborated through the plots in detail. Further, the velocity distribution is enhanced for a greater Deborah number value and it is reduced for a higher Reynolds number for the two cases of pseudoplastic and dilatant flows. Microorganism distribution decreases with the increased magnitude of Peclet number, Bioconvection Lewis number and microorganism concentration difference number. Two types of graphical outputs are presented for the Sutterby fluid parameter (β = −2.5, β = 2.5). Finally, the validation of the present model is achieved with the previously available literature.

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.