In this paper, we investigated the stagnation point flow of Maxwell viscoelasticity with incompressible based micropolar fluid over a Riga plate. The mathematical model has been constructed though micropolar fluid flows over Riga plate. The implement the boundary layer approximation, the system of partial differential equations is produced through momentum equation along with micro inertia theory. Nonlinear partial differential equations are become dimensionless nonlinear ordinary differential equations through suitable similarity transformations. This system is solved numerical scheme via BVP4C method. The effects of involving physical parameters like as dimensionless parameter, Modified Hartman number, Material parameter, Slip condition σ_s, Viscoelastic parameter δ_m and Soret coefficient S_T are highlighted through graphs and numerical results. The physical quantities like as Skin friction, local Nusselt number and local Sher-wood number are highlighted through tables. R is increasing with increasing dimensionless parameter, Material parameter K and Slip condition σ_s. R is decreasing with increasing behavior of Modified Hartman number Z and viscoelastic parameter δ_m.

This article investigates the phenomenon of gravity-driven flow of nanoliquid film along a vertical surface under the effects of nonlinear thermal radiations. The falling nanofluid film is subjected to a convectively heated surface along with slip condition. The flow and thermal properties are investigated considering four different nanoparticles namely Ag (silver), Cu (copper), \(\mathrm {TiO}_2\) (Titania) and \(\mathrm {Al}_2\mathrm{O}_3\) (alumina) with water as a acting base fluid. The physical model is presented in terms of nonlinear partial differential equations. These equations are reduced to a system of nonlinear ordinary differential equations through similarity transformations. The problem is solved numerically utilizing Bvp4c function in MATLAB. Multiple solutions are presented for unfavorable buoyancy or opposing flow (\(\sigma <0\)) and favorable buoyancy or assisting flow (\(\sigma >0\)). The impact of nanoparticle volume fraction is found to be useful in intensifying the temperature and dropping heat transfer rate because of dominant convection. It is worth mentioning that silver nanoparticles in the thin film of nanofluid lead to higher wall shear stress and heat transfer rate. The increasing nature of skin friction coefficient \((C_f)\) is examined in buoyancy assisting flow while in opposing buoyancy flow its behavior is noticed reduced for various values of solid fraction (\(\phi \)) of \(\mathrm {Ag}\) nanoparticles.