Combined Magnetic and Porosity Effects on Flow of Time-Dependent Tangent Hyperbolic Fluid with Nanoparticles and Motile Gyrotactic Microorganism Past A Wedge with Second-Order Slip

Abstract This research explores the time-dependent heat transport phenomena for the MHD flow of nanofluids containing motile microorganisms via porous matrix. The fluid flows through a porous stretched wedge with second-order slip and Nield boundary. Different physical and geometric parameters should be included to achieve more practicable effects. The developed equations are converted into a non - dimensional form through the use of appropriate similarity functions. The mathematical formulation is built for these transmuted equations using the built-in Matlab software bvp4c. Differences in physical quantities namely skin friction coefficient − f ″ ( 0 ) , local Nusselt number − θ ′ ( 0 ) , Sherwood number ϕ ′ ( 0 ) and microorganism organism density − χ ′ ( 0 ) have also been identified under the influences of emerging parameters. Bioconvection caused by microorganisms stabilized nanomaterials, resulting in effective thermal delivery. The findings showed good consistency as compared to the current literature. The higher mixed convection parameter contributes to the quantities of flow viscosity, temperature, and nanoparticle concentration in boundary conditions. The incremented slip parameter γ precedes the flow speed. The skin friction factor − f ″ ( 0 ) reduces against unsteadiness parameter A , Hartree pressure gradient β , velocity ratio parameter λ , bouancy ratio parameter N r but it develops progressively when the parameters M , W e , n , λ and bioconvection Rayleigh number N c are incremented. The elaborated discussion is also presented with graphical and tabular illustrations.