Stability of the flow due to a heated stretching sheet

The stability of the flow induced by a linearly stretched, flat sheet with a temperature gradient between the sheet and the free stream is investigated via a complementary numerical and large Reynolds number lower-branch asymptotic analysis. This analysis involves the derivation of new basic flow solutions which extend the exact analytical solutions of Crane, by coupling the energy and momentum equations with a temperature-dependent viscosity. In the most extreme case considered, the Reynolds number at which instabilities are observed is approximately halved compared to the isothermal case, thereby justifying its consideration as a physically meaningful flow variable of interest with potential implications for industrial extrusion processes.