The resent development of research in the field of nano technology introduced hybrid nanofluids which are advanced classes of fluids with augmented thermal properties and it gives better results comparing to regular nanofluid. The aim of the present work is to study the significant effects of variable viscosity and viscous dissipation on a porous stretching sheet in the presence of hybrid nanofluid and radiative heating. In this model, two types of nanoparticles, namely copper (Cu) and alumina oxide (Al 2 O 3), are suspended in the base fluid H 2 O to form a hybrid nanoliquid. The novelty of this study is to introduce variable viscosity along with natural convection in the momentum equation and viscous dissipation in the energy equation. Mathematical modeling is employed in this study, whereby partial differential equations for the fluid flow are constructed and transformed to a set of ordinary differential equations, and hence resolved computationally by Runge-Kutta-Fehlberg method along with shooting scheme. The most important results for relevant parameters concerning the flow heat measure, surface drag, and heat transfer coefficients are thoroughly examined and presented graphically for both Cu-Al 2 O 3 /water hybrid nanofluids. There is an increase in hybrid