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In this research work, the two-dimensional (2D), incompressible fluid flow has been taken into consideration. The flow is supposed to be steady and laminar. By considering the water-based nanoparticles of SWCNTs and MWCNTs in the presence of thermal radiation, the rate of heat transferring and entropy generation effects in a regenerative cooling system of a rocket engine are evaluated. The effects of the length and radius of the nanomaterials on the problem are also considered. Solutions for temperature, velocity profile, irreversibility (entropy generation) and the Bejan number are discussed graphically, and the effects of various significant factors are considered on these profiles. The modeled physical problems in current exploration are dependent upon governing laws which appear in terms of PDEs. These PDEs are reformed into a system of nonlinear ODEs. We used numerical scheme known as (RK-4) in combination with the shooting iteration technique to obtain the solutions to transformed fluid flow equations, because the resultant ODEs are extremely nonlinear and finding the exact solution is very difficult. It is investigated that the Eckert number, nanoparticles volume fraction and radiation parameter upsurge the thermal field as well as the irreversibility of the system. Furthermore, the dual behavior of nanoparticles volume fraction and viscosity parameter on velocity profile is observed. Bejan number shows increasing effects in response to nanoparticles volume fraction and radiation parameter, whereas a reverse impact of Bejan number is noticed for the rising values of Eckert number. [ABSTRACT FROM AUTHOR]