Abstract
The increasing need of the modern era of technology for better ways to increase the heat transfer performance of thermal systems has made nanoliquids much more critical than they have been for the previous two decades. With such demand in mind, the Carreau-Yasuda nanofluid in the presence of motile microorganisms and thermal radiation along with Robin's boundary conditions has been scrutinized. The controlling PDEs are cracked into ordinary differentials through suitable similarity transformation. The transformed ODEs are solved numerically utilizing bvp4c built-in MATLAB computational software. The graphical results of the main parameters against the velocity profile, temperature profile, and solutal field of nanoparticles and motile microorganisms' concentration are illustrated through graphs. Furthermore, the consequence of the involved parameters on the heat transfer rate is also deliberated and offered through table values. This study analyzed that velocity is a declining function of magnetic parameter and buoyancy ratio parameter. Besides, the additional amount of thermal radiation improves the heat transport rate. The concentration field is an escalating function of the thermophoresis parameter. Furthermore, microorganisms' profile is boosted up by enlarging the magnitudes of microorganism's Biot number.