Solar thermal collectors distribute, capture, and transform the solar energy into a solar thermal concentration device. The present paper provides a mathematical model for analyzing the flow characteristics and transport of heat to solar collectors (SCs) from non-Newtonian nanofluids. The non-Newtonian power-law scheme is considered for the nanofluid through partial slip constraints at the boundary of a porous flat surface. The nanofluid is assumed to differ in viscosity and thermal conductivity linearly with temperature changes and the magnetic field is appliqued to the stream in the transverse direction. The method of similarity conversion is used to convert the governing structure of partial differential formulas into the system of ordinary differential ones. Using the Keller box procedure, the outcoming ordinary differential formulas along with partial slip constraints are numerically resolved. A discussion on the flowing and heat transport characteristics of nanofluid influenced by power law index, Joule heating parameter, MHD parameter and slip parameters are included from a physical point of view. Comparison of temperature profiles showed a marked temperature increase in the boundary layer due to Joule heating. The thickness of the motion boundary-layer is minimized and the transport of heat through boundary-layer is improved with the partial slip velocity and magnetic parameters rising. Finally, With an increase in the Eckert number, the distribution of temperature within boundary layer is increased.