Question

. Compare the external flows of two different fluids over a flat plate held at a constant T,; air at a free-stream speed Ux-3 m and temperature Too-250 K to that of engine oil at a free-stream speed Un-3 ! ! and temperature T 400 K. For laminar flow over a flat plate, the velocity boundary layer thickness is given by δ- (In the absence of a known surface temperature, fluid properties are evaluated at the free-stream temperature.) (a) Determine the critical location, e, along the plate where each fluid transitions from laminar to turbulent (b) Determine an expression and plot the velocity boundary layer thickness δ over from 0 x Fe for both fluids. (c) Determine an expression and plot the thermal boundary layer thickness 5t over from 0 x 〈 xc for both fluids. (d) If the plate temperature is adjusted such that ΔT T- T was the same for both fluids, which fluid has the larger local Nusselt number Nu Explain your reasoning.

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Answer 1

Given data plate held at constant T_s air free - stream speed u_ infinity = 3 m/s temperature T_ infinity = 250 k engine oil speed u_ infinity = 3 m/s temperature T_ infinity = 400 k (a) For air p = p/RT = 1.0132 times 10^5/287 times 250 = 1.412 kg/m^3 mu = 1.906 times 10^- 5 kg/m^- 3 R_ex = p u_ infinity x/ mu critical distance R_px = 5 times 10^5 5 times 10^5 = 3 x_e (1.412)/1.906 times 10^- 5 X_e (air) = 5 times 1.906/3 times 1.412 X_e (air) = 225 m For oil: T_ infinity = 400 k, u_ infinity = 3 m/s, upsilon = 1.63 times 10^- 5 m^2/s R_ex = u ma x y c/3 X_e = 5 times 105 times 1.63 times 10^- 5/3 X_e = 2.77 m \r\n (b) for air: delta = 5 times 2.25/ squareroot 5 times 10^- 5 = 0.016 m = 16 times 10^- 3 m oil: delta = 5 times 2.77/ squareroot 5 times 10^5 = 0.0198 m = 19.5 times 10^- 3 m.