This study examines the effects of thermal radiation and viscous dissipation on the transient free convective flow occurring over an oscillating, semi-infinite vertical plate, characterized by uniform mass diffusion and a surface temperature that varies. The governing equations, presented in non-dimensional form, are addressed through   a stable and convergent implicit finite-difference approach. The influence of different physical parameters, such as thermal radiation, Eckert number, Prandtl number, Schmidt number, thermal Grashof number, mass Grashof number, and phase angle, is illustrated via graphical representations of velocity, temperature and concentration. The results underscore the notable influence of the radiation parameter, viscous dissipation, and plate oscillation on the flow pattern.

radiation, viscous dissipation, oscillating plate, variable temperature, finite difference