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 (c), dependent on the Prandtl number , of the heat transfer coefficient was identified, with solutions for the corresponding steady problem possible only for < (c). The unsteady problem considered here shows that these steady states are attained at large times when < (c). For > (c), 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 and and asymptotically for large and both large and small .