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2. Consider the streamfunction (with u = 3y and v = -) and a coordinate transform from (x, y) to (x, 7), where n= = Rex V √UX/U 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.

2. Consider the streamfunction (with u = 3y and v = -) and a coordinate transform from (x, y) to (x, 7), where n= = Rex V √UX/U 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.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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 Dv 2. Consider the streamfunction(with u = and v=- transform from (x, y) to (x, n), where n = y √ux/U% = Rex u(x, y) and a coordinate 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.
Transcribed Image Text: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 Dv 2. Consider the streamfunction(with u = and v=- transform from (x, y) to (x, n), where n = y √ux/U% = Rex u(x, y) and a coordinate 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.
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