A steady MHD boundary layer fow of Powell–Eyring dusty nanofuid over a stretching
surface with heat fux condition is studied numerically. It is assumed that the fuid is
incompressible and the impacts of thermophoresis and Brownian motion are taken
into regard. In addition, the Powell–Eyring terms are considered in the momentum
boundary layer and thermal boundary layer. The dust particles are seen as to be having
the same size and conform to the nanoparticles in a spherical shape. We obtain a sys‑
tem of ordinary diferential equations that are suitable for analyzed numerically using
the fourth-order Runge–Kutta method via software algebraic MATLAB by applying
appropriate transformations to the system of the governing partial diferential equa‑
tions in our problem. There is perfect compatibility between the bygone and current
results when comparing our numerical solutions with the available data for values of
the selected parameters. This confrms the validity of the method used here and thus
the validity of the results. The infuence of some parameters on the boundary layer
profles (the velocity and temperature for the particle phase and fuid phase, and nano‑
particle concentration) is discussed. The results of this study display that the profles of
the velocity for particle and fuid phases increase with increasing Powell–Eyring fuid
parameter, but reduce with height in magnetic feld values. Mass concentration of the
dust particles decreases the temperature of both the particle and fuid phases. The
results also indicate the concentration of nanoparticle contraction as Schmidt number
increases