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(2) Two sides of a metal strip are exposed to horizontal, uniform flow at their leading edges, and independent boundary layers develop, as shown below. The fluid is the same on both sides. The strip contains a heating element that maintains the strip temperature at a uniform 1200 K. The flows are isolated and never interact with each other. The fluid properties are listed below the diagram. Flow 1 T. 8(x) -81,7(x) A U60.1 71 111 x 3 As x = 100 m U20,2 TO Flow 2 82(x) – 82,7(x) Fluid properties Flow properties Metal properties a = 75 x 10-6 m/s 0.9,1 = 50 m/s T'metal = 1200 K v = 75 x 10-6 m/s U 0,2 = 20 m/s l= 3 mm k = 0.05 W/( mK) To = 300 K L = 100 m w = 1 m (into page) (a) The diagram indicates that at both the top and bottom surfaces, the hydrodynamic boundary layer thickness 8(x) is of the same order of magnitude as thermal boundary layer thickness &f(x). That is, 8(x) ~87(x). Write a mathematical relation showing why this must be true for this scenario. (b) If the fluid is Newtonian, will the viscous shear stress at x = 0.1 m be greater at surface 1 or surface 2? Provide brief mathematical justification. (c) At any specific x position along the metal strip, will the local heat transfer coefficient be: (1) greater at surface 1, (2) greater at surface 2, (3) not enough information is provided to know. Write 1, 2, or 3 and provide brief mathematical justification. (d) Determine the total heat transferred from the metal strip over the length x = 0 to x = xc.1, where xe,1 is the x position where the transition to turbulence occurs for the top flow (Flow 1).