influences of gyrotactic microorganisms and nonlinear mixed bio-convection on hybrid nanofluid flow over an inclined extending plate with porous effects

This study investigates nonlinear mixed convective hybrid nanofluid flow over a spongy, inclined stretching surface. there are numerous applications of nonlinear convection, and it is especially pivotal in predicting weather patterns accurately and optimizing heat transfer for efficient electronic and industrial cooling systems. the flow is also influenced by the porous behavior of the plate and the presence of the microorganisms. the main emphasis is given to analyzing the influence of thermal and mass grashof numbers for their nonlinear nature upon the flow system. the equations that administered the flow system are converted to dimensionless notations by using suitable variables. the homotopy analysis approach has been used for the solution of modeled equations. it has been perceived in this work that fluid velocity declines with the upsurge in inertial factor, permeability parameter, volume fraction, and magnetic factor. thermal profiles upsurge with growth in brownian, thermophoresis factors, eckert number, and weaken with prandtl number. concentration of fluid increases with progression in the thermophoresis factor and drops with greater values of schmidt number and brownian factor. density number has declined with growth in peclet, bioconvective lewis numbers, and inclination angle. over the range  the heat transfer rate jumps from 1.8057 to 2.1332 in case of , from 1.8057 to 2.1968 in case of  and it jumps from 1.8057 2.3177 in case of  that shows maximum heat transfer rate in case of variations in eckert number.