Question

Consider airflow over a flat plate of length L=1m under conditions for which transition occurs at xc=0.5mx_{c}=0.5 \mathrm{m} based on the critical Reynolds number, Rex,c=5×105R 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, hlam(x)=Clamx0.5 and htutb=Cturbx0.2h_{\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, Clam=8.845W/m3/2K,Cturb=49.75W/m1.8KC_{\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, hˉlam(x)\bar{h}_{\operatorname{lam}}(x), as a function of distance from the leading edge, x, for the laminar region, 0xxc0 \leq x \leq x_{c}.

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

(d) On the same coordinates, plot the local and average convection coefficients, hxh_{x} and hˉx\bar{h}_{x}, respectively, as a function of x for 0xL0 \leq x \leq L.

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