Transportation of Darcy–Forchheimer entropy optimized nonlinear flow toward a stretchable sheet with Ohmic heating and heat generation/absorption

Nanomaterials have achieved considerable prominence owing to their numerous applications such as thermal transport, heat exchangers, nuclear reactor cooling, paper production, microelectronics, thermal power plants, and architecture. Because of such thermal applications, the prime objective of the present analysis is to scrutinize the unsteady Darcy–Forchheimer flow of nanoliquid with Lorentz force. Stretching of the surface creates flow motion. Here three different types of nanoparticles, aluminum oxide ((Formula presented.)), copper ((Formula presented.)), and titanium dioxide ((Formula presented.)), are used. Furthermore, water ((Formula presented.)) is used as a base fluid. Heat expression is discussed through dissipation, radiation, heat generation, and Joule heating. Physical interpretation of entropy generation is discussed. The nonlinear partial system is reduced to a dimensionless ordinary system by appropriate dimensionless parameters. The resultant system is then solved by a numerical scheme (bvp4c technique). The influences of various involved parameters on entropy rate, velocity profile, and temperature are graphically examined. Drag force and thermal transport rate against flow variable are discussed. A larger Forchheimer number reduces velocity profile. A reverse trend is noted for temperature and velocity against volume fraction variable. An increment in magnetic variable augments entropy rate and temperature. An improvement in entropy analysis is noted for Reynold number. Thermal transport rate declines for a higher stretching variable. An enhancement in entropy rate and temperature is noticed for radiation variable. An amplification in drag force is observed through volume fraction. An augmentation in magnetic effect leads to decline the thermal transport rate. Comparative studies for different nanoparticles are done.