Transient thermal convective and radiative diffusion–reaction of magneto‐metallic Brinkman‐type nanofluid flow with isothermal and ramped temperature impacts

Abstract Fluid‐containing nanoparticle research is well‐known for its heat transmission properties due to real‐world applications in various thermal systems. This demonstration shows how time‐dependent magneto‐hydrodynamic (MHD) Brinkman‐type nanofluid can flow through a vertical oscillating absorbent plate immersed in a porous environment. The governing dimensional partial differential system of equations is translated into a non‐dimensional partial differential system with applicable scaling variables. The transient equations governing nanofluid flow's momentum, thermal and mass are solved using the finite semi‐discretization difference line method. The obtained outcomes are validated by comparing them with previous works. Graphical resolutions for momentum, heat, and mass distribution fields are presented to examine essential physical terms with the isothermal and ramped temperature impacts. It was found that magnifying the Brinkman parameter and magnetic parameter brings in a decrement in fluid velocity. In contrast, reversal deportment is exposed with an enlargement of permeability parameters and thermal and solute buoyancy effects. Reynold's number has shown a declining impact in the fluid velocity, but time progress unveiled a contrary tendency. The sprouting radiation parameter deepens the fluid temperature, whereas the rising heat absorption parameter curtails the fluid temperature. The fluid concentration deflates for growing Schmidt number and chemical reactive agent. The wall friction increased with the porosity parameter but has shown a reverse trend with magnetic and Brinkman parameters. Increasing the Prandtl number and heat‐consumption parameter helps to raise the temperature gradient. The concentration gradient lessened on augmentation of chemical reaction and Schmidt number.