Abstract The current study investigates the magnetized thermal time‐dependent fluid movement over a permeable vertical for energy and mass transportation. The impact of a chemical reaction and the applied magnetic field is also investigated. The flow characteristics are altered to PDEs via similarity transformation in dimensionless form and then numerically computed by the RK4 method. For the confirmation bvph2s also applied. The influence of embedded factors is depicted in the flow phenomena. It is depicted that the heat and concentration are increased with the increasing magnitude of the thermal factor. The effect of a heat source on the flow rate is measured and increasing behavior is observed. Moreover, the error approximation for the involved factors is also displayed in terms of graphs. It is observed that as the thermal radiation factor rises in the presence of magnetic Prandtl number, the heat distribution significantly improves. Additionally, greater temperatures coincide with bigger magnetic Prandtl number. Increases in magnetic field strength improve temperature curve because of the presence of a radiation impact on the flow of fluids. The innovative part of this investigation is to analyze the unsteady magnetized chemical reaction flow over a permeable vertical surface enclosing the influence of thermal radiation and induced magnetic field. For validation, the current study is validated with the published study.
Khan et al. (2025) studied this question.