Numerical framework for unsteady bioconvection flow of third-grade nanofluid over a porous Riga surface with convective Nield approach

The ultra-high significances of thermal radiation, magnetic field and activation energy in thermal enhancement processes allow significant applications in chemical and mechanical engineering, modern technology and various thermal engineering eras. The improvement in energy resources and production became one of the major challenges for researchers and scientists for sustained development in industrial growths. Beside this, the bioconvection assessment in nanomaterials conveys prestigious applications in biotechnology like bio-sensors, enzymes, petroleum industry, bio-fuels and many more. In view of such renewable applications, present exploration discloses unsteady two-dimensional flow of third-grade nanomaterial accommodating gyrotactic microorganisms induced by unsteady stretched Riga sheet in porous medium. The formulated flow problem is further scrutinized by utilizing the chemical reaction, activation energy, thermal radiation and magnetic aspects. The convective Nield constraints are further subjected in the current investigation. Apposite transformations are used to condense the nonlinear developed problem into dimensionless ordinary form. The numerical solution of such similar flow problem is presented via shooting technique. The detailed graphical illustrations of the dimensionless temperature, nanoparticles concentration, velocity and motile microorganisms for physical significance of diverse relevant parameters are deliberated. Furthermore, numerical data of local Sherwood, Nusselt and motile density numbers is designated in tabular form. Study accentuated that velocity increases for higher modified Hartmann and material constants, while the effects of buoyancy ratio and bioconvected Rayleigh numbers are rather opposite. The temperature, microorganism and concentration distributions were enhanced for unsteady parameter. It is also acknowledged that the concentration distribution is enhanced for activating the energy number. Moreover, the microorganism distribution enhances for concentration difference and magneto-porous constants, while bioconvected Lewis and Peclet numbers show conflicting trend.