The magnetohydrodynamic flow of Silver (Ag) based carbon nanotubes (SWCNTs and MWCNTs) nanofluid between two stretchable rotating disks is presented in this article. The magnetic field is functioned in the tangential direction. The modeled equations are attempted with the homotopy analysis approach. The convergence of the applied approach is shown through figures and tables. The performance of influential factors on velocity (radial, axial and tangential), thermal, and concentration profiles for both CNTs are portrayed through figures. Also, the performance of influential parameters on physical quantities of interests for both CNTs is numerically examined through tables. The velocities along the radial, axial, and tangential directions are intensified with nanoparticles volume fraction CNTs nanoparticles, Reynolds number, and magnetic parameter. The heightening volume fraction of CNTs nanoparticles, thermophoresis, and Brownian motion parameters increased the thermal profile. The concentration profile is escalated with the thermophoresis parameter and Lewis number.