  This paper presents the linear Global stability analysis of the
incompressible axisymmetric boundary layer on a circular cone. The base flow is
considered parallel to the axis of cone at the inlet. The angle of attack is
zero and hence the base flow is axisymmetric. The favorable pressure gradient
develops in the stream-wise direction due to cone angle. The Reynolds number is
calculated based on the cone radius (a) at the inlet and free-stream velocity
($U_{\infty}$). The base flow velocity profile is fully non-parallel and
non-similar. Linearized Navier-Stokes equations (LNS) are derived for the
disturbance flow quantities in the spherical coordinates. The LNS are
discretized using Chebyshev spectral collocation method. The discretized LNS
along with the homogeneous boundary conditions forms a general eigenvalues
problem. Arnoldi's iterative algorithm is used for the numerical solution of
the general eigenvalues problem. The Global temporal modes are computed for the
range of Reynolds number from 174 to 1046, semi-cone angles $2^o$, $4^o$, $6^o$
and azimuthal wave numbers from 0 to 5. It is found that the Global modes are
more stable at higher semi-cone angle $\alpha$, due to the development of
favorable pressure gradient. The effect of transverse curvature is reduced at
higher semi-cone angles ($\alpha$). The spatial structure of the eigenmodes
show that the flow is convectively unstable. The spatial growth rate ($A_x$)
increases with the increase in semi-cone angle ($\alpha$) from $2^o$ to $6^o$.
Thus, the effect of increase in semi-cone angle ($\alpha$) is to reduces the
temporal growth rate ($\omega_i$) and to increases the spatial growth rate
($A_x$) of the Global modes at a given Reynolds number.
