Please Answer: Develop the similarity forms of the boundary layer momentum and e
ID: 1862590 • Letter: P
Question
Please Answer:
Develop the similarity forms of the boundary layer momentum and energy equations for uniform flow past an inclined wall (U infinity (x) = cxm) as shown in the following sketch: The exponent in the free-stream velocity m is related to the wedge total angle by m = beta /(2 pi - beta). For the momentum equation in the boundary layer, using the Bernoulli's equation in the free stream, we obtain an estimate for the pressure gradient as 1 / rho dP infinity / dx = - U infinity dU infinity / dx, where U infinity (x) = Cxm. Thus, the momentum boundary layer effectively becomes Apply the similarity transformation eta = y / x Rex1/2 and psi = (U infinity vx)1/2 f(eta) and show that the above momentum equation simplifies to the following similarity equation (know as the Falkner-Skan equation, which is a generalization of the Blasius equation 2f''' + (m + 1) ff" + 2m[1 - (f')2] = 0 Apply the same transformation to the energy equation and show that the corresponding similarity equation now becomes 2theta" + Pr(m + 1) ftheta' = 0 where theta = T - T0 / Tinfinity - T0. Establish whether the angle of inclination has any effect on the boundary condition to be used in conjunction with the equation above.Explanation / Answer
Look here http://www.dur.ac.uk/suzanne.fielding/teaching/BLT/sec4b.pdf