Flow and heat transfer characteristics of the boundary layers over a stretching surface with a uniform-shear free stream

In this work, the momentum and thermal boundary layers over a continuously stretching surface with a uniform-shear free stream were investigated. Based on the boundary layer assumptions, the similarity equations were obtained, which were solved numerically. Theoretical analysis was conducted for certain special conditions. The solution domain for the momentum boundary layer was theoretically estimated and compared with the numerical results. It is found that the interaction of uniform-shear free stream and the wall stretching velocity greatly affects the fluid motion and heat transfer characteristics. Dual solutions exist for the stretching parameter γ > γc = −0.596985. There is one solution for γ = γc and no solution for γ < γc. The effects of the Prandtl number, Pr, the temperature power index, m, and the wall stretching parameter, γ, on the heat transfer behaviors were analyzed and discussed. A general exact analytical solution of thermal boundary layers was derived for non-stretching wall condition with γ = 0 and arbitrary values of Pr and γ. Analytical solutions were also given for image and m = 0 with arbitrary values of Pr and m. Interesting observations were found for negative wall stretching parameter, negative temperature power index, and the lower solution branch.