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Questions and Answers
Which region of the turbulent boundary layer represents a very small portion?
What percentage of the turbulent boundary layer does the buffer layer represent?
What is used as a substitute for TW wall temperature in practical problems?
What happens if the plate is long enough in terms of the laminar portion?
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Where does transition typically occur in the turbulent boundary layer?
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What is used to evaluate fluid properties in calculations unless otherwise noted?
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Which region of the turbulent boundary layer represents approximately 85%?
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What range does transition typically occur within?
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Which equation is solved for the constant wall heat flux problem?
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What is assumed about the fluid in the analysis of boundary layer flow?
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In the force balance on the elemental control volume, which direction are viscous-shear forces assumed to be negligible?
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What does the momentum flux in the x direction represent for the control volume?
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What assumption is made regarding the depth in the z-direction within the control volume?
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In fluid dynamics, why is it not convenient to work with elements of mass?
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Which assumption is made about pressure variations in relation to the plate direction?
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Why are viscous-shear forces assumed to be negligible in the y direction for boundary layer analysis?
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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.
