Consider the conditions of Example 6.4. A laminar boundary layer can be tripped to a turbulent condition at \(x=x_{r}\) by roughening the surface of the plate at \(x_{r}\). Calculate the minimum and maximum possible average convection coefficients for the plate. At which temperature, \(T=300 \mathrm{~K}\) or \(T=350 \mathrm{~K}\), do each of the extreme values of \(\bar{h}\) occur? What are the corresponding values of \(x_{r}\) ?

Data From Example 6.4:-

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Water flows at a velocity u = 1 m/s over a flat plate of length L = 0.6 m. Consider two cases, one for which the water temperature is approximately 300 K and the other for an approximate water temperature of 350 K. In the laminar and turbulent regions, experimental measurements show that the local convection coefficients are well described by -0.5 ham (x)=Cam05 hub (x) = Curb-x-0.2 where x has units of m. At 300 K, while at 350 K, Clam,300 = 395 W/m 15 K Curb,300 = 2330 W/m1.8. K 1.8 Clam,350 477 W/mK Curb,350 3600 W/m. K As is evident, the constant C depends on the nature of the flow as well as the water tem- perature because of the thermal dependence of various properties of the fluid. Determine the average convection coefficient, h, over the entire plate for the two water temperatures.