Effects of Heat Source/Sink and Fractional Time‐Derivatives on Transient Natural Convection Flow in a Vertical Channel Under Dynamic and Static Slip Conditions

ABSTRACT The study of the joint effects of dynamic and static slip conditions, fractional time‐derivative, and heat source/sink on the temporal natural convection flow in an upright channel with adiabatic and isothermal boundary conditions has been established. The Laplace transforms of Caputo–Fabrizio and Atangana–Baleanu in the Caputo sense and the method of undetermined coefficients are used to solve the governing equations. All the time‐dependent solutions are presented in a semi‐analytical form by converting the solutions from the Laplace domain into the time domain using the Riemann sum approximation. The effects of the governing parameters on temperature, velocity, and skin friction are presented graphically and numerically using MATLAB. Notably, the relaxation time parameters supported fluid movement, whereas the fractional‐order parameters slowed heat transfer and reduced fluid flow. It is evident that dynamic slip slows the fluid's movement, whereas static slip enhances convective flow. In addition, the heat source produced higher temperature, velocity, and skin friction than the heat sink. Similarly, the Caputo–Fabrizio model produced higher temperature, velocity, and skin friction than the Atangana–Baleanu model.