Study on flow past an accelerated parabolic steep plate with existence of thermal radiation on incompressible nanofluid

The study examines the hall current effect and the MHD effect with the inclusion of thermal radiation in an unstable viscous convection flow with heat and mass transfer, it is an infinite uncompressible nanofluid past with a parabolic accelerated vertical plate in a variable temperature and also in uniform mass diffusion. The non-Newtonian nanofluid has been used as an incompressible fluid for the investigation. Titanium dioxide \({\mathrm{TiO}}_{2}\) has been taken and dissolved with water and mixed with non-Newtonian fluid. The provision of a homogenous magnetic field is perpendicular to the flow direction. The adimensional governance expressions have been derived by employing the Laplace transform approach. Analytical solutions have been found for the velocity field and temperature concentration dispensations. The outcomes for several emergent criteria are reviewed, including the Prandtl number \(\left({\mathrm{Pr}}\right),\) Grashof number \(({\mathrm{Gr}})\) and modified Grashof number \({(\mathrm{Gm}})\), Schmidt number \(({\mathrm{Sc}})\), and Hall parameter \((m)\). Graphs have been used to demonstrate how problems are measured with many parameters affecting the velocity, temperature, and concentration fields.