We estimate the blow-up time for the reaction diffusion equation u t = Δu+λf(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here λ>λ*, where λ* is the 'extremal' (critical) value for λ, such that there exists an 'extremal' weak but not a classical steady-state solution at λ = λ* with ||w(λ)||∞ → infin; as 0<λ → λ*-. Estimates of the blow-up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s) = es, for λ - λ* ≪1, regarding the form of the solution during blow-up and an asymptotic estimate of blow-up time is obtained. Finally, some numerical results are also presented.