Unsteady Finite Amplitude Magneto-Convection of Oldroyd-B Nanofluids with Internal Heat Source

This work presents a numerical and an analytical review of analysis of the convective phenomenon in a non-Newtonian nanofluid layer with the applied vertical magnetic field and having an internal heating source. Buongiorno model is used to examine the convective instability considering
 the impacts of thermophoresis, Brownian diffusion, and viscoelasticity of the nanofluid. The effect of significant parameters concerning stability is visualized through graphs and further interpreted. For the non-linear study, the fundamental PDEs are converted into non-linear simultaneous
 autonomous ODEs. The solutions are computed by taking the help of the software Mathematica. Nusselt number and Sherwood number are graphed for numerous parametric situations to offer a clear outlook of heat and mass transfer rate. The magnetic field parameter stabilizes the system and diminishes
 heat and mass transfer. Elevating the internal heat parameter promotes heat and mass transfer significantly. Viscoelasticity of the fluid affects prominently since non-Newtonian fluid yields lower heat and mass transfer coefficients than Newtonian fluid due to advancement of the convection.