Combined Impact of Dynamic and Static Slips on Transient Natural Convection Flow in a Vertical Channel: Fractional Time‐Derivative

ABSTRACT The investigation of the unified approach of the dynamic and static slips with the Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo (ABC) fractional time‐derivative models through the Isothermal heating process has been done on the incompressible and viscous fluid of the transient natural convection flow in a vertical channel. The CF and ABC Laplace transform approaches are adopted in transforming the governing equations from the time purview to the Laplace purview. The transformed governing equations are solved, and semi‐analytical solutions are obtained through the inversion of the solutions from the Laplace domain to the time domain with a numerical Riemann sum approximation. The analysis of the governing parameters is presented with a graphical representation and in tabular form. Specifically, it is found that the CF and ABC temperature and velocity increase with the increment in time and relaxation time parameters. Vividly, it is perceived that the increment in the value of fractional order parameters led to the drop of heat and slowed down the flow of the fluid. It is confirmed that the position of the fluid raised pointedly near the hot and cold plates with the increment in static slips, while the fluid motion decreases with the increase in the value of the dynamic slip. It is noticeable that the values of the temperature, velocity, skin friction, and mass flux are higher in the case of the CF model than in the ABC model. Also, it is observed that the pooled impacts of the dynamic and static slips on the skin friction are higher near the hot plate than the cold plate. Similarly, it is observed that the mass flux is higher with the increment of time and Prandtl number in the case of static slips than the dynamic slip, and the collective of static and dynamic slips. Another significant observation is that the effects of the static slips on velocities are opposite to each other.