This paper theoretically investigates the conjugate effects of viscous dissipation and non-uniform heat source/ sink on the double-diffusive boundary layer flow of a viscoelastic nanofluid over a stretching sheet. In this model, where binary nanofluid is used, the Brownian motion, thermophoresis and cross-diffusion are classified as the main mechanisms which are responsible for the enhancement of the convection features of the nanofluid. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of group theory transformations. Computations are made by the hp-Galerkin finite element method (FEM). The hp-FEM needs a smaller number of nodes and consequently, less computational time and less memory to achieve the same or even better accuracy than h-FEM. A detailed evaluation of the effects of the governing physical parameters on the velocity, temperature, solutal and nanoparticle concentration via graphical plots is conducted for two different cases, namely prescribed surface temperature (PST) and prescribed heat flux (PHF). The reduced Sherwood number (in PST-case) is observed to be increased with the effects of nanofluid and the modified Dufour parameter, whereas the contrary behaviour is computed for the surface solutal concentration in PHF-case. Heat transfer is increasing function of viscoelastic parameter and decreasing function of Brownian motion, thermophoresis, space and time dependent heat source/sink parameter and Eckert number. Mass transfer is increasing function of Eckert number, space and time dependent heat source/sink parameter and decreasing function of viscoelastic parameter.