The centrifugal spinning method is a recently invented technique to extrude polymer melts/solutions into ultra-fine nanofibres. Here, we present a superior integrated string-based mathematical model, to quantify the nanofibre fabrication performance in the centrifugal spinning process. Our model enables us to analyse the critical flow parameters covering an extensive range, by incorporating the angular momentum equations, the Giesekus viscoelastic constitutive model, the air-to-fibre drag effects and the energy equation into the string model equations. Using the model, we can analyse the dynamic behaviour of polymer melt/solution jets through the dimensionless flow parameters, namely, the Rossby (
$Rb$
), Reynolds (
$Re$
), Weissenberg (
$Wi$
), Weber (
$We$
), Froude (
$Fr$
), air Péclet (
$Pe^*$
) and air Reynolds (
$Re^*$
) numbers as well as the viscosity ratio (
$\delta _s$
), corresponding to rotational, inertial, viscous, viscoelastic, surface tension, gravitational, air thermal diffusivity, aerodynamic and viscosity ratio effects. We find that the nonlinear rheology remarkably affects the fibre trajectory, radius and normal stresses. Increasing
$Wi$
leads to a thicker fibre, whereas increasing
$\delta _s$
shows an opposite trend. In addition, by increasing
$Wi$
, the fibre curvature is enhanced, causing the fibre to spiral closer to the rotation centre.