Cattaneo-Christov and Darcy-Forchheimer heat flux on Reiner-Philippoff fluid with Velocity and Thermal Slip Boundary Condition under heat Sink/Source

Reiner–Philippoff (RP) fluid flow above a heated sheet concluded the model of Cattaneo–Christov heat flux for Darcy-Forchheimer is implemented in this work. The influences of thermal radiation, heat source/sink, velocity, and thermal slip boundary conditions are also deliberated. The transformations are used to convert obtained partial differential equations into a set of ordinary differential equations, and they are solved numerically using the shooting method (RK-4) solver with the help of the computational software MATLAB. The dimensionless temperature and velocity numbers are further developed. More engineering curiosity of local Nusselt and Skin frictions are tabulated, depicted, and interpreted. The study presents graphical and tabular illustrations depicting flow parameters, velocity profiles, and temperature profiles. Key conclusions drawn include, When the inertia coefficient \({F}_{r}\) $F_r$ increases, the velocity field \(f^{\prime}(\eta )\) $f^{\prime }(\eta )$ decreases. Analytical calculations are performed for the flow of a Reiner-Philippoff fluid over a shrinking sheet, considering influences such as thermal radiation, velocity slip, and temperature fluctuations. Increased heat absorption correlates with higher Nusselt numbers, whereas temperature generation lowers wall temperatures. The skin friction magnitude gradually increases in the order of dilatant, viscous, and pseudo-plastic fluids, respectively.