The current paper is concentrated on the MHD hybrid nanofluid-flow with heat-transfer on a moving/changing plate through porous media and thermal radiation. The great mixture Cu with Al2O3 nanoparticles along with H2O as the important base fluid is utilized for the analysis. Mathematical transformation decreases the convolution of important PDEs to a scheme of ODEs. This will be numerically solved with the help of function-bvp4c by making use of Software tool/MATLAB for multiple values with various significant parameters. This analysis is significant in identifying the crucial property thermal-behaviour of mixture Cu-Al2O3/H2O when the imperative physical parameters including magnetic_field(M), Heat_generation_parameter (β), velocity_slip_parameter(A), Thermal_radiation_parameter (R), Thermal_Slip_parameter(B), Porosity_parameter(P) and suction_parameter(S) are excellently entrenched. The findings are modern and unique with numerous practical uses in the contemporary industry. © 2023 Elsevier B.V., All rights reserved.