Fractional order transient free-convection flow in a channel: application of the optimal homotopy asymptotic method

In this study, a new physical model has been created to look into the behaviour of transient incompressible unsteady flow between two infinite parallel plates exposed to high temperatures. The model takes into consideration thermal radiation flux, chemical reaction, and mass diffusion at the boundaries. To handle non -integer behaviour, the model incorporates the Caputo notion of time fractional derivative. To solve this complex physical fractional order fluid model, a novel optimal homotopy asymptotic method and semi -analytical methodology is extended and utilized successfully. This method provides a third -order highly approximate solution, offering valuable insights into the behaviour within the system. The study comprehensively examines the effects of varied flow characteristics and fractional order on the dynamics of the system. The results are visually presented through graphs, offering a clear understanding of the system's response under different conditions. The effectiveness and ease of use of the optimal homotopy asymptotic method make it a valuable tool for solving boundary value fractional order problems encountered in scientific fields. The developed physical model and its fractional extension contribute significantly to the understanding of unsteady flow phenomena with thermal and chemical effects, advancing knowledge in this area of research.