It is obvious that due to its higher viscosity, non-Newtonian fluid show better heat transport than the Newtonian fluid. Moreover, shear flow helps us to make our surrounding environment friendly. With this view point, an attempt has been taken in this paper to explore the two-dimensional flow of low electrically conducting Eyring–Prandtl fluid and heat transfer over a moving porous plate subject to suction/blowing with externally applied magnetic field. The flow is maintained due to the incoming shear away from the plate so that boundary layer type of flow is formed over the plate. This makes the problem new, not yet been addressed by any researcher. Similarity transformations are applied to obtain self-similar structure of the leading equations. However, similar solutions of the problem are attained for a specific power-law velocity (index, \(n=1/3\) ) of the moving plate. The equations are solved numerically and compared with different flow quantities having different grid sizes. The data are plotted graphically to represent velocity, velocity gradient and temperature for different parametric values. The influences of suction/blowing parameter, fluid material parameters, Prandtl number and magnetic parameter on velocity, temperature and velocity gradient are shown and explained at length with physical explanations as far as practicable. The velocity decreases with increasing values of magnetic parameter due to the appearance of Lorenz force. However, temperature increases. So, the boundary layer flow can be controlled using a suitable magnetic field. It is found that fluid velocity rises with the growing suction/blowing parameter and fluid material parameter \(\alpha \) but the temperature is found to diminish resulting in the reduction of heat transfer in fluid. The analysis reveals that blowing destabilises the flow, while the suction stabilises the boundary layer flow. This study explores the boundary layer flow structure of a fluid with low electrical conductivity along with heat transfer in the presence of suction/blowing, externally applied magnetic field and shear flow.
