Thermo-bioconvective MHD Williamson nanofluid flow over an inclined stretching surface with radiation, chemical reaction, viscous dissipation and joule heating

The present study investigates an MHD Williamson nanofluid model incorporating thermal radiation, chemical reaction, viscous dissipation, Joule heating, slip effects, and microorganism-driven bioconvection over an inclined exponentially stretching surface. Similarity transformations are employed to transform the governing partial differential equations into a system of non-linear ordinary differential equations. These are solved numerically using the MATLAB bvp4c solver. The results show that the velocity decreases with increasing magnetic, Williamson, and suction parameters, whereas it increases with the Richardson number and viscous dissipation. The temperature increases with thermal radiation and viscous dissipation but decreases with Richardson number and suction parameter. The nanoparticle concentration increases with Lewis number and Prandtl number, while it decreases with heat capacity ratio parameter and suction parameter. The microorganism concentration decreases with increasing chemical reaction, bioconvective Lewis number, Peclet number, Schmidt number, Eckert number, heat capacity ratio parameter, and suction parameter, whereas it increases with the Lewis number. Quantitative analysis indicates that increasing the magnetic parameter reduces the Nusselt number by 10.52% and the Sherwood number by 31.07%, while increasing the motile microorganism density by 2.51%. Thermal radiation decreases the Nusselt number by 13.72% and the Sherwood number by 42.44%, accompanied by a 12.65% increase in the motile microorganism density. Furthermore, increasing the Williamson parameter decreases the Nusselt number by 4.76% and the Sherwood number by 14.00%, with a 0.41% increase in the motile microorganism density. Likewise, a higher Eckert number reduces the Nusselt number by 4.79% and the Sherwood number by 14.75%, while increasing the motile microorganism density by 4.34%. In addition, the chemical reaction parameter decreases the Nusselt number by 1.52% and the Sherwood number by 10.92%, together with a 3.02% increase in the motile microorganism density. Overall, the study provides insights into the coupled effects of electromagnetic forces, reactive transport, and bioconvection in non-Newtonian nanofluids, with potential applications in bio-thermal systems, microfluidics, and advanced heat transfer technologies.