Entropy optimized magnetohydrodynamics Darcy-Forchheimer second order velocity slip flow of nanomaterials between two stretchable disks

Here magnetohydrodynamics Darcy-Forchheimer second order velocity slip flow of nanomaterials is discussed between two stretchable surfaces of rotating disks, where the both disks are rotating with altered angular frequencies and rates. Flow in permeable medium is designated by implementing Darcy-Forchheimer relation. The energy expression is discussed and modeled subject to various effects like dissipation, Ohmic heating (Joule heating), and heat source/sink. Two different types of nanoparticles, i.e. graphene oxide (GO) and titanium dioxide (TiO2), are utilized and H2O as a base fluid. Total entropy rate which depends on five different types of irreversibilities (i.e., heat, mass fluid friction, Ohmic heating and Darcy-Forchheimer or porosity) is calculated via thermodynamics law (second). Furthermore, binary chemical reaction is accounted for the analysis of mass with activation energy. Numerical solutions are found out with the help of shooting method. Behaviors of flow variables on the skin friction coefficients, velocity field, Nusselt numbers, temperature distribution, entropy generation, concentration, and Bejan number are plotted graphically and discussed. The results are compared with previous literature and found good agreement with them. Our obtained results illustrate that the entropy rate is more subject to rising Brinkman number.