The behavior of a laminar boundary layer can be substantially influenced by either adding or removing...

 

Transcribed Image Text:

The behavior of a laminar boundary layer can be substantially influenced by either adding or removing fluid at the solid surface by injection or suction processes. Consider the steady flow of a constant-property fluid parallel to a porous flat plate with constant and uniform free-stream velocity U and temperature T., such that the fluid is sucked uniformly at a velocity v, by the plate. Assume that the quantity of fluid removed from the stream is so small that only those fluid particles in the immediate neighborhood of the plate are sucked away, and the no-slip condition as well as the expression T = μ(aulay), for the shear stress at the plate's surface is retained with suction present. Also let the plate be isothermal at temperature T a. Assuming that the flow in the boundary layer is laminar and two-dimensional, show that the corresponding boundary-layer equations yield solutions for the velocity components and v in the x- and y-directions, respectively, and the temperature distribution T which is inde- pendent of x for large x. b. Using the exact solution for u = u(y), develop an expression for the local friction coefficient for large x. c. Using the exact solution for T = T(y) develop an expression for local heat transfer coefficient for large x. The behavior of a laminar boundary layer can be substantially influenced by either adding or removing fluid at the solid surface by injection or suction processes. Consider the steady flow of a constant-property fluid parallel to a porous flat plate with constant and uniform free-stream velocity U and temperature T., such that the fluid is sucked uniformly at a velocity v, by the plate. Assume that the quantity of fluid removed from the stream is so small that only those fluid particles in the immediate neighborhood of the plate are sucked away, and the no-slip condition as well as the expression T = μ(aulay), for the shear stress at the plate's surface is retained with suction present. Also let the plate be isothermal at temperature T a. Assuming that the flow in the boundary layer is laminar and two-dimensional, show that the corresponding boundary-layer equations yield solutions for the velocity components and v in the x- and y-directions, respectively, and the temperature distribution T which is inde- pendent of x for large x. b. Using the exact solution for u = u(y), develop an expression for the local friction coefficient for large x. c. Using the exact solution for T = T(y) develop an expression for local heat transfer coefficient for large x.

Answer rating: 100% (QA)

a Assuming that the flow in the boundary layer is laminar and twodimensional show that the corresponding boundarylayer equations yield solutions for the velocity components u and v in the x and ydirec... View the full answer