Significance of magnetic field and activation energy on the features of stratified mixed radiative-convective couple-stress nanofluid flows with motile microorganisms

The current non-homogeneous nanofluid flow model is carried out to scrutinize the performance of the generalized Fourier's and Fick's laws on the MHD bioconvective aspects of couple-stress nanofluid flows through a convectively heated stretching sheet in the presence of activation energy and multiple stratified boundary conditions. Herein, both the concentrations of solid nanoparticles and motile microorganisms are incorporated explicitly into the nonlinear differential expressions describing the present non-Newtonian nanofluid flow model. Besides, the combined thermal influence of the Cattaneo-Christov heat flux and thermal radiation are also discussed. From a practical point of view, the couple-stress nanofluids are useful for examining different types of thermophysical and rheological features, since this kind of enhanced fluids can clarify realistically the dynamical behavior of various liquids, like the human blood and some polymeric suspensions. For reducing the mathematical complexity of the present physical problem, several effective similarity transformations are introduced formally to simplify the resulting partial differential equations (PDEs) into a nonlinear coupled structure of ordinary differential equations (ODEs). Moreover, the transformed dimensionless self-similarity equations are then numerically solved using the built-in shooting technique with the aid of the bvp4c solver MATLAB package. Furthermore, The obtained results are authenticated with an outstanding agreement. In this respect, the engineering quantities of interest are computed extensively with a higher level of accuracy and then summarized tabularly. To illustrate the impacts of the embedded physical parameters on the profiles of velocity, temperature, nanoparticles concentration, and microorganisms concentration, various illustrations are done successfully along with detailed elucidations. As the main findings, it is found that the temperature distribution and the microorganisms concentration profile can be enhanced with the higher values of the bioconvection Rayleigh number. Similarly, it is revealed that the nanoparticles concentration sketch and the microorganisms concentration profile can be boosted up for the higher magnitudes of the buoyancy ratio parameter.