This study investigates the exact solutions of laminar velocity and thermal boundary layers of \(\text{Al}_{2}{\text{O}}_{3} -\text{CNT}/\text{water}\) hybrid nanofluid flow over a permeable stretching sheet. The sheet with a nonlinear temperature distribution, placed through a porous medium under a vertical magnetic field, is considered as a general problem. The solutions of momentum and energy equations are derived for all the conditions under which there are analytical answers, based on comprehensive boundary conditions and Whittaker’s functions. The hybrid nanofluid flow performance is comprehensively investigated based on the velocity and temperature distributions as well as the non-dimensional quantities. In addition, the impact of 7 problem parameters, including the mass transfer factor, characteristic velocity and temperature nonlinearity of sheet, as well as the nanoparticles concentration, the magnetic field strength, the medium permeability and the base fluid Prandtl number are addressed. The results indicate that the sheet mass transfer parameter has the highest effect on the thermo-hydraulic performance of flow, competing with the influence of Prandtl number on the system heat transfer. Indeed, the wall suction significantly increases both the heat transfer rate and pressure loss, and the Prandtl number is an upward function of the former parameter. The boundary layer thickness varies from \(15\text{\%}\) to \(100\text{\%}\) if \({f}_{0}\) changes from \(-2\) to \(C\) . Additionally, when \({f}_{0}=-2\) , heat transfer performance is threefold greater than its value under \({f}_{0}=0\) . This performance also increases from 2 to 13 by the increase in the Prandtl number from 1 to 6.5 at \({f}_{0}=-2\) . Eventually, the range of wall mass transfer factor for which there are exact solutions relies on all the parameters existing in the momentum equation, which is also completely discussed.
