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The present article describes the fully developed natural convective flow on a conducting viscous fluid towards a vertical parallel porous plates channel. Furthermore, the velocity slip and temperature jump conditions are implemented on both the vertical walls of the channel. Besides, the effects of the applied magnetic field along with thermal radiation are also considered. We employ the entropy generation method (EGM) to discuss the thermodynamic optimization. To model the flow equations, the Cartesian coordinates system is used. Closed-form solutions of the resulting coupled differential equations describing the flow behavior are obtained for velocity and temperature distribution. The obtained exact form solution is also validated to examine the accuracy by two different numerical approaches namely, Keller- box and shooting method, and found in good agreement. A comprehensive analysis of the influence of velocity slip and temperature jump condition in the presence of the magnetic field, thermal radiation and suction or injection parameters on the velocity field, volumetric flow rate, temperature distribution, skin friction coefficients, and the rate of entropy generation was carried out. The obtained results reveal that by taking the specific value of the velocity slip and temperature jump conditions, change in the magnetic and suction or injection parameter affects the fluid velocity at the solid–fluid interface.