This paper investigates the combined effects of wall permeability in the second law analysis of buoyancy -driven unsteady channel flow of water -based nanofluids confined between two vertical channels with convective cooling. Specifically, the study aims to: formulate a mathematical model of nanofluid flow for the case of a vertical channel with wall permeability; determine the effects of various parameters on velocity and temperature; and analyze the influence of different parameters and wall permeability on the second law of thermodynamics. Using a semi -discretization finite difference method combined with a Runge -Kutta-Fehlberg integration scheme implemented in MATLAB, the nonlinear governing partial differential equations were transformed into a system of initial value ordinary differential equations and solved numerically. The numerical results showing the effects of variations in thermophysical parameters on velocity and temperature profiles were presented graphically and discussed.