Question

Consider a liquid metal Pr1\operatorname{Pr} \ll 1, with free stream conditions uu_{\infty} and TT_{\infty}, in parallel flow over an isothermal flat plate at TsT_{s}. Assuming that u=uu=u_{\infty} throughout the thermal boundary layer, write the corresponding form of the boundary layer energy equation. Applying appropriate initial (x=0) and boundary conditions, solve this equation for the boundary layer temperature field, T(x, y). Use the result to obtain an expression for the local Nusselt number NuxN u_{x}. Hint: This problem is analogous to one-dimensional heat transfer in a semi-infinite medium with a sudden change in surface temperature.

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