Boundary-layer Flow and Transition Process Quiz

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Questions and Answers

Which region of the turbulent boundary layer represents a very small portion?

Buffer layer

Transition layer

Turbulent layer

Viscous (or laminar) sublayer (correct)

What percentage of the turbulent boundary layer does the buffer layer represent?

~15% (correct)

~85%

~50%

~30%

What is used as a substitute for TW wall temperature in practical problems?

Fluid properties

Nusselt number

Constant wall heat flux (q″) (correct)

Film temperature (Tf)

What happens if the plate is long enough in terms of the laminar portion?

The laminar portion can be neglected Signup and view all the answers

Where does transition typically occur in the turbulent boundary layer?

At Rex = 5x10^5 Signup and view all the answers

What is used to evaluate fluid properties in calculations unless otherwise noted?

(Tw + T∞)/2 Signup and view all the answers

Which region of the turbulent boundary layer represents approximately 85%?

~85% - turbulent layer Signup and view all the answers

What range does transition typically occur within?

[2x10^5, 3x10^6] Signup and view all the answers

Which equation is solved for the constant wall heat flux problem?

Continuity, momentum, and energy equations Signup and view all the answers

What is assumed about the fluid in the analysis of boundary layer flow?

It is incompressible and the flow is steady Signup and view all the answers

In the force balance on the elemental control volume, which direction are viscous-shear forces assumed to be negligible?

Y direction Signup and view all the answers

What does the momentum flux in the x direction represent for the control volume?

Mass flow through a side and x component of velocity Signup and view all the answers

What assumption is made regarding the depth in the z-direction within the control volume?

Unit depth Signup and view all the answers

In fluid dynamics, why is it not convenient to work with elements of mass?

Dealing with elemental control volumes is simpler Signup and view all the answers

Which assumption is made about pressure variations in relation to the plate direction?

Pressure remains constant in all directions Signup and view all the answers

Why are viscous-shear forces assumed to be negligible in the y direction for boundary layer analysis?

To simplify calculations Signup and view all the answers

Study Notes

Boundary Layer Flow

The boundary layer flow on a flat plate can be divided into two regimes: laminar and turbulent flow.
Initially, the boundary-layer development is laminar, but at some critical distance from the leading edge, the flow becomes turbulent due to small disturbances in the flow.
The transition from laminar to turbulent flow occurs when the Reynolds number, a dimensionless grouping of terms, is used as a criterion.

Laminar Velocity Profile

The laminar velocity profile on a flat plate can be pictured as a random churning action with chunks of fluid moving to and fro in all directions.
The equation of motion for the boundary layer can be derived by making a force-and-momentum balance on an elemental control volume.

Assumptions

To simplify the analysis, assumptions are made:
- The fluid is incompressible and the flow is steady.
- There are no pressure variations in the direction perpendicular to the plate.
- The viscosity is constant.
- Viscous-shear forces in the y direction are negligible.

Momentum Flux and Force Balance

The momentum flux in the x direction is the product of the mass flow through a particular side of the control volume and the x component of velocity at that point.
The mass entering the left face of the element per unit time is calculated by applying Newton's second law of motion.

Prandtl Number and Heat Transfer

The Prandtl number is a dimensionless group that represents the ratio of the transport coefficient for viscous momentum transport to the transport coefficient for heat conduction.
When the Prandtl number is large, the ability of the fluid to transport momentum is greater than that to transport thermal energy.
For Pr = 1, the equation of energy is similar to the equation of motion, and the dimensionless velocity profile solution is the same as the dimensionless temperature profile solution.

Turbulent Flow over a Flat Plate

As the boundary layer thickens, turbulence appears, characterized by a sudden rapid increase in the thickness of the boundary layer.
The turbulent boundary layer is divided into three regions: the viscous (or laminar) sublayer, the buffer layer, and the turbulent layer.
For purposes of calculation, transition is assumed to occur at Rex= 5x10^5.

Procedure for Calculations

Identify the flow geometry (flow over flat plate, cylinder, or sphere, or flow through pipe).
Evaluate fluid properties at film temperature Tf = (Tw + T∞)/2 unless otherwise noted.
Calculate Reynolds number and determine whether the flow is laminar or turbulent.

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Description

Test your knowledge on boundary-layer flow development, transition from laminar to turbulent flow, and turbulent-flow characteristics on a flat plate. Explore different flow regimes and velocity profiles in this quiz.