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External Flow: The Flat Plate in Parallel Flow. Chapter 7 Section 7.1 through 7.3. Overall Reynolds number: Critical Reynolds number for smooth surface:. Boundary Layer. Physical Features. For rough surface, the flow may be turbulent throughout. Thermal Boundary Layer.
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External Flow:The Flat Plate in Parallel Flow Chapter 7 Section 7.1 through 7.3
Overall Reynolds number: • Critical Reynolds number for smooth surface: Boundary Layer Physical Features • For rough surface, the flow may be turbulent throughout .
Thermal Boundary Layer • Surface conditions are commonly idealized as being of uniform • temperature or uniform heat flux . Equivalent surface and free stream temperatures for and uniform (or ) for Physical Features (cont.) • Thermal boundary layer development may be delayed by an unheated starting length:
Let the dimensionless x-velocity component, f = • and dimensionless temperature, • are functions of a dimensionless similarity parameter: Similarity Solution for Laminar Boundary Layer Similarity Solution • The x-momentum and energy equations (PDE) can be • transformed into ordinary differential equations (ODE):
Similarity Solution (cont.) • Numerical solutions to these ODE equations yield the following results for • local boundary layer parameters:
Similarity Solution (cont.) • How would you characterize relative laminar velocity and thermal boundary layer • growth for a gas? An oil? A liquid metal? • How do the local shear stress and convection coefficient vary with distance from • the leading edge? • Average Boundary Layer Parameters: • The values of the fluid properties are • determined at the film temperature:
Turbulent Boundary Layer Turbulent Flow • Boundary Layer Equations (for laminar flow) is invalid • Experiments have to be conducted • Local friction coefficient by measuring velocity gradient at wall • Local heat convection coefficients found by measuring temperature gradient at wall • Experimental determination of overall average heat convection coefficient:
Correlations of Experimental Data Turbulent Flow • Local coefficients for Turbulent • boundary layer on flat plate:
Experimental Data for Average Coefficients Turbulent Flow
Substituting expressions for the local coefficients and assuming Correlations of Experimental Data Turbulent Flow • Average heat convection coefficient: • Similarly, average friction • coefficientcan be found as: • For fully turbulent boundary layer:
Sketch the variation of hx versus for two conditions: What effect does an USL have on the local convection coefficient? Unheated Starting Length (USL) and/or Uniform Heat Flux Special Cases For both uniform surface temperature (UST) and uniform surface heat flux (USF), the effect of the USL on the local Nusselt number may be represented as follows:
Special Cases (cont.) • For UST, the local heat flux and total heat transfer rate: • For USHF, the local surface • temperature can be found as: • Evaluate fluid properties • at the film temperature:
Problem: Orientation of Heated Surface Problem 7.21: Preferred orientation (corresponding to lower heat loss) and the corresponding heat rate for a surface with adjoining smooth and roughened sections.
Problem: Conveyor Belt Problem 7.24: Convection cooling of steel plates on a conveyor by air in parallel flow.
