A computational numerical algorithm for thermal characterization of fractional unsteady free convection flow in an open cavity

A significant problem to study is how the fractional operators and physical structures may be interrelated and interconnected. The current model study reports the fractional time-dependent viscous, electric conductive fluid between two permeable infinitely large walls. The flow is driven by the mutual actions of imposed thermal buoyancy, pressure gradient, and transverse magnetic field of uniform strength. The suction and injection of the fluid take place at the right and left walls respectively. Transformations are used to convert the physical model into equivalent fractional partial differential equations (FPDEs). The finite difference computational code based on three difference fractional operators is developed to seek the behavior of modeled problem. The analysis of the model and code endorsement is provided through set of graphical plots and tabular form. It is noted that an increment into the Hartmann and Reynolds number causes a dropped pattern of the velocity while the drop is more substantial for the smaller choices of fractional parameters. Higher choices of heat source, thermal radiation, Ecker, pressure gradient and magnetic parameters cause an enhanced behavior of the thermal profile. The smaller values caused a slight increment on the thermal layer as higher choices of the fractional parameters. However, the patterns of the thermal and velocity layers are found clearer while using the ABC and CF fractional operators compared with the CC idea of fractional derivative.