Here entropy optimized CNTs based flow of viscous liquid is addressed between two stretchable surfaces of disks. Both upper and lower disks stretch and rotate with different rates and angular frequencies. Carbon nanotubes (single and multi-walls) are considered as a nanoparticles and water as continuous phase liquid. Xue model is utilized in the mathematical modeling for the transport of nanoparticles. Energy expression is developed through first law of thermodynamics and discussed in the presence of viscous dissipation. Main attention is given to the modeling of entropy generation subject to CNTs nanoparticles. Total entropy rate is calculated. Average residual error is calculated through implementation of optimal homotopy analysis method. Flow parameters are graphically discussed for both single and multi-walls carbon nanotubes. Furthermore, engineering quantities like skin friction and Nusselt number are numerical calculated and discussed through Tables. From obtained outcomes it is examined that entropy rate boosts up versus larger Brinkman number and nanoparticles volume friction. No such attempt is yet done by the researchers on entropy optimized Darcy-Forchheimer CNTs based nanomaterial flow between two rotating disks. The obtained outcomes are compared with published literature and found good agreement. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.