2. Consider supersonic flow at a free-stream Mach number 2 over a flat plate airfoil at zero angle of attack, modeled as

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2 Consider Supersonic Flow At A Free Stream Mach Number 2 Over A Flat Plate Airfoil At Zero Angle Of Attack Modeled As 1 (25.06 KiB) Viewed 28 times

2 Consider Supersonic Flow At A Free Stream Mach Number 2 Over A Flat Plate Airfoil At Zero Angle Of Attack Modeled As 2 (25.06 KiB) Viewed 28 times

2 Consider Supersonic Flow At A Free Stream Mach Number 2 Over A Flat Plate Airfoil At Zero Angle Of Attack Modeled As 3 (48.17 KiB) Viewed 28 times

2. Consider supersonic flow at a free-stream Mach number 2 over a flat plate airfoil at zero angle of attack, modeled as a laminar boundary layer. The flight altitude is 10 km, at which the air temperature is 223 K, the kinematic viscosity is 3.525 x 10-5m²/s. Assume that the temperature recovery factor is given by the square root of the Prandtl number, and neglect effects due to variation of fluid properties within the flow. For Prandtl numbers 1 and 0.7, determine: (a) the adiabatic wall temperature (hint: use the recovery factor), and (b) whether heat is being transferred to or from the plate, if the plate surface tem- perature is 390 K. (Note: you need not calculate the rate of heat transfer.)
3. In Question 2 above we assumed adiabatic boundary condtions for the temperature field: i.e., we prescribed the temperature gradient (zero) at the wall and then calculated what the wall temperature (T) would need to be. Another common application is that of an isothermal wall, where we instead prescribe the wall temperature (T) and try to determine the temperature gradient and hence heat flux at the wall. Note that the stagnation temperature equation is still given by U ƏTo ƏTo ər dy +v k 8²To pCp dy² (a) If the Prandtl number (Pr=uCp/k) is unity, comment on any similarities or resemblances between this equation and the momentum equation that governs the incompressible laminar boundary layer on a flat plate. Write that equation down from the discussion of Blasius theory in the class notes. (b) Define the non-dimensional quantity To-Tu To,00-Tw Show that this quantity satisfies the same boundary conditions as u/U at y = 0 and y = 00.