#### Question

Consider airflow over a flat plate of length L=1m under conditions for which transition occurs at $x_{c}=0.5 \mathrm{m}$ based on the critical Reynolds number, $R e_{x, c}=5 \times 10^{5}$.

(a) Evaluating the thermophysical properties of air at 350 K, determine the air velocity.

(b) In the laminar and turbulent regions, the local convection coefficients are, respectively, $h_{\operatorname{lam}}(x)=C_{\operatorname{lam}} x^{-0.5} \text { and } h_{\mathrm{tutb}}=C_{\mathrm{turb}} x^{-0.2}$ where, at T=350 K, $C_{\mathrm{lam}}=8.845 \mathrm{W} / \mathrm{m}^{3 / 2} \cdot \mathrm{K}, C_{\mathrm{turb}}=49.75 \mathrm{W} / \mathrm{m}^{1.8} \cdot \mathrm{K}$, and x has units of m. Develop an expression for the average convection coefficient, $\bar{h}_{\operatorname{lam}}(x)$, as a function of distance from the leading edge, x, for the laminar region, $0 \leq x \leq x_{c}$.

(c) Develop an expression for the average convection coefficient, $\bar{h}_{\mathrm{turb}}(x)$, as a function of distance from the leading edge, x, for the turbulent region, $x_{c} \leq x \leq L$.

(d) On the same coordinates, plot the local and average convection coefficients, $h_{x}$ and $\bar{h}_{x}$, respectively, as a function of x for $0 \leq x \leq L$.