Gold nanoparticles (AuNPs) are increasingly being widely used in several biomedical applications for their compatibility of synthesis and less toxicity. The mixture of gold and titanium oxide nanoparticles is suspended in water to make a new class of nanofluid, which is called a hybrid nanofluid. The problem of direct current (DC)/alternating current (AC) magnetohydrodynamic (MHD) micropump of the hybrid nanofluid through a porous medium in the gap between vertical coaxial microtubes with heat transfer has been discussed. The mathematical model is established and then solved with the help of the Laplace transform. The inversion of the transformed functions is calculated numerically. The velocity, the flowrate, the pressure, and the heat transfer are discussed graphically. The higher concentration of the mixture of particles enhances the stream so that the required pressure is small. Moreover, it is found that the variation of the Nusselt number is noticeable by increasing the concentrations of nanoparticles, but this variation vanishes near the outer tube.