For the situation described in Example 6.4, the boundary layer can be tripped into a turbulent state by applying roughness to the surface of the flat plate at a particular x-location. Hence the location where transition occurs, x_c, can be moved upstream relative to the transition location associated with the smooth plate of the example. Calculate and plot the average convection coefficient over the entire plate for roughness applied over the range 0 ≤ x_r ≤ L. What values of xr provide the minimum and maximum values of h? Assume the water temperature is 300 K.

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 ham(x) = ClamX-0.5 turb(x) = Cturb-X where x has units of m. At 300 K, while at 350 K, Clam,300 = 395 W/m ¹-5. K Clam,350 = 477 W/m¹.5. K Cturb.300 = 2330 W/m¹.8. K Cturb,350 = 3600 W/m¹.8. K