This article tries to explain how thermal diffusion and heat diffusion affect on the flow of magnetohydrodynamic (MHD) Powell-Erying nanofluids across a stretched surface filled with porous material when thermal and mass Biot numbers are present. Due to the nanoparticles and Powell-Erying fluid, thermophoresis and Brownian motion are brought into play. With right factors, the basic nonlinear equations of motion, energy, and concentration can be turned into formulas with no units. The The Runge-Kutta method is used in conjunction utilising the Shooting Technique to find the math answers. There are graphs that show how the combined factors affect speed, temperature, and the number of nanoparticles. The numbers of coefficient of skin friction, the area Nusselt numbers, and the Sherwood numbers are used to do calculations and studies