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External Flow: The Flat Plate in Parallel Flow

External Flow: The Flat Plate in Parallel Flow. To determine the conditions, compute and compare with the critical Reynolds number for transition to turbulence,. Physical Features. As with all external flows , the boundary layers develop freely without constraint.

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External Flow: The Flat Plate in Parallel Flow

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  1. External Flow:The Flat Plate in Parallel Flow

  2. To determine the conditions, compute • and compare with thecritical Reynolds numberfor transition to turbulence, Physical Features • As with allexternal flows, the boundary layers develop freely without constraint. • Boundary layer conditions may be entirely laminar, laminar and turbulent, • or entirely turbulent.

  3. Value of depends on free stream turbulence and surface roughness. • Nominally, • If boundary layer istrippedat the leading edge • and theflow is turbulent throughout. • Surface thermal conditionsare commonly idealized as being ofuniform • temperature or uniform heat flux . Equivalent surface and free stream temperatures for and uniform (or ) for . Is it possible for a surface to be concurrently characterized by uniform temperature and uniform heat flux? • Thermal boundary layer development may be delayed by anunheated • starting length.

  4. Based on premise that the dimensionless x-velocity component, , • and temperature, , can be represented exclusively in • terms of adimensionless similarity parameter and Similarity Solution for Laminar, Constant-Property Flow over an Isothermal Plate • Similarity permits transformation of the partial differential equations associated • with the transfer of x-momentum and thermal energy to ordinary differential • equations of the form

  5. Subject to prescribed boundary conditions, numerical solutions to the momentum • and energy equations yield the following results for importantlocal boundary layer • parameters:

  6. 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 effect of variable properties may be considered by evaluating all properties • at thefilm temperature.

  7. Empirical Correlations Substituting expressions for the local coefficients andassuming » » Turbulent Flow • Local Parameters: How do variations of the local shear stress and convection coefficient with distance from the leading edge for turbulent flow differ from those for laminar flow? • Average Parameters:

  8. Sketch the variation of hx versus for two conditions: What effect does an USL have on the local convection coefficient? Special Cases: Unheated Starting Length (USL) and/or Uniform Heat Flux For both uniform surface temperature (UST) and uniform surface heat flux (USF), the effect of the USL on thelocalNusselt number may be represented as follows:

  9. UST: • USF: • Treatment of Non-Constant Property Effects: Evaluate properties at thefilm temperature.

  10. Problem 7.21: Preferred orientation (corresponding to lower heat loss) and the corresponding heat rate for a surface with adjoining smooth and roughened sections.

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