The development of forced convection heat transfer near a forward stagnation point with Newtonian heating

A mathematical model for the unsteady forced convection boundary-layer flow near a forward stagnation point is considered when there is Newtonian heating on the surface whereby the heat transfer is proportional to the local surface temperature. In a previous paper (Salleh et al. J Eng Math 69:101–110, 2011), a critical value γc, dependent on the Prandtl number σ, of the heat transfer coefficient γ was identified, with solutions for the corresponding steady problem possible only for γ < γc. The unsteady problem considered here shows that these steady states are attained at large times when γ < γc. For γ > γc, the solution still continues to large time, now growing exponentially with time. This rate of growth is determined by an eigenvalue problem which we solve numerically for general values of γ and σ and asymptotically for large γ and both large and small σ.