Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
3.4 Specification of a laminar boundary layer profile as an inflow condition is often used in incompressible flow simulations. Let us consider the Blasius profile, which is a similarity solution for the steady laminar boundary layer on a flat plate. Fig. 3.25 Flat-plate laminar boundary layer 1. Assume two-dimensional, steady flow with no imposed pressure gradient as shown in Fig. 3.25. Show that the Navier-Stokes equations inside the bound- ary layer can be reduced to ди ди u +v. =V- əx Əy 8²u dy2¹ Әр U Əy = 0, and ди Əx + Əv dy

3.4 Specification of a laminar boundary layer profile as an inflow condition is often used in incompressible flow simulations. Let us consider the Blasius profile, which is a similarity solution for the steady laminar boundary layer on a flat plate. Fig. 3.25 Flat-plate laminar boundary layer 1. Assume two-dimensional, steady flow with no imposed pressure gradient as shown in Fig. 3.25. Show that the Navier-Stokes equations inside the bound- ary layer can be reduced to ди ди u +v. =V- əx Əy 8²u dy2¹ Әр U Əy = 0, and ди Əx + Əv dy

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...
See similar textbooks
icon
Related questions
Question
2) 3.4 Specification of a laminar boundary layer profile as an inflow condition is often used in incompressible flow simulations. Let us consider the Blasius profile, which is a similarity solution for the steady laminar boundary layer on a flat plate. u(x, y) Fig. 3.25 Flat-plate laminar boundary layer 1. Assume two-dimensional, steady flow with no imposed pressure gradient as shown in Fig. 3.25. Show that the Navier-Stokes equations inside the bound- ary layer can be reduced to ди ди 8²u U +v =V Əx Əy მy2 U ap მ = 0, and ди Əx Əv dy
Transcribed Image Text:2) 3.4 Specification of a laminar boundary layer profile as an inflow condition is often used in incompressible flow simulations. Let us consider the Blasius profile, which is a similarity solution for the steady laminar boundary layer on a flat plate. u(x, y) Fig. 3.25 Flat-plate laminar boundary layer 1. Assume two-dimensional, steady flow with no imposed pressure gradient as shown in Fig. 3.25. Show that the Navier-Stokes equations inside the bound- ary layer can be reduced to ди ди 8²u U +v =V Əx Əy მy2 U ap მ = 0, and ди Əx Əv dy
მ 2. Consider the streamfunction (with u = transform from (x, y) to (x, n), where n = √ux/Ux Using the above and a streamfunction in the form = √xUf(n), show that the governing equations can be reduced to ff" +2f"" = 0 with boundary conditions of f(0) = f'(0) = 0 and lim, f(n) = 1. This equation is referred to as the Blasius equation and its solution is known as the Blasius profile. and v= 3. Solve the Blasius equation numerically. Note that this is a boundary-value prob- lem. y == Rex. u Plot as a function of 1,√e a as a function of n, C, as a function of Re, C as a function U₂ U₂ of Re, as a function of Re,, as a function of Re,, where, Re X du is the skin friction coefficient, T = μ| dy y=0 coefficient of the plate, is the momentum thickness. -L(₁-7) y=01 U₂ = and a coordinate UL. number, Re, =is Reynolds number based on plate length, L is the plate length, C, = V Ux is local wall shear stress, Cp = dy is the displacement thickness, 0 = is local Reynolds Tdx PUL -L-(1-7) U₂ Jx=0 Tw ŽPUZ is the drag dy
Transcribed Image Text:მ 2. Consider the streamfunction (with u = transform from (x, y) to (x, n), where n = √ux/Ux Using the above and a streamfunction in the form = √xUf(n), show that the governing equations can be reduced to ff" +2f"" = 0 with boundary conditions of f(0) = f'(0) = 0 and lim, f(n) = 1. This equation is referred to as the Blasius equation and its solution is known as the Blasius profile. and v= 3. Solve the Blasius equation numerically. Note that this is a boundary-value prob- lem. y == Rex. u Plot as a function of 1,√e a as a function of n, C, as a function of Re, C as a function U₂ U₂ of Re, as a function of Re,, as a function of Re,, where, Re X du is the skin friction coefficient, T = μ| dy y=0 coefficient of the plate, is the momentum thickness. -L(₁-7) y=01 U₂ = and a coordinate UL. number, Re, =is Reynolds number based on plate length, L is the plate length, C, = V Ux is local wall shear stress, Cp = dy is the displacement thickness, 0 = is local Reynolds Tdx PUL -L-(1-7) U₂ Jx=0 Tw ŽPUZ is the drag dy
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Compressible Flow
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi…
Principles of Heat Transfer (Activate Learning wi…
Mechanical Engineering
ISBN:
9781305387102
Author:
Kreith, Frank; Manglik, Raj M.
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS