Air at 120 atm and 275 K flows with a freestream velocity of

Air at 1/20 atm and 275 K flows with a free-stream velocity of u_infinity = 700 m/s over a flat plate L = 1.2 m long. If the surface of the plate is to be maintained at 325 K, determine the amount of cooling needed per meter width of the plate.

Solution

Average temperature = (275+325)/2 = 300 K

At 300 K, air Kinemcatic viscosity neu = 1.807*10^-5 m^2/s

At 300 K, air Prandtl number Pr = 0.707

At 300K, air thermal conductivity k = 0.02624 W/m-K

Reynolds number Re = V*L/neu = 700*1.2/(1.807*10^-5) = 4.6485*10^7

Since Re > 5*10^5, flow is turbulent.

Nusselt number Nu = 0.037*(Re^0.8)*(Pr^0.33)

= 0.037*(4.6485*10^7)^0.8 *0.707^0.33

Nu = 44861

h = Nu*k/L

h = 44861*0.02624 / 1.2

h = 981 W/m^2-K

Heat transfer Q = hA*(Ts - Tf)

Q = 981*(1.2*1)*(325 - 275)

Q = 58857 W = 58.86 kW