External Flow: The Flat Plate in Parallel Flow Chapter 7 Section 7.1 through 7.3

Physical Features Boundary Layer Overall Reynolds number: Critical Reynolds number for smooth surface: For rough surface, the flow may be turbulent throughout.

Physical Features (cont.) Surface conditions are commonly idealized as being of uniform temperature or uniform heat flux. Thermal boundary layer development may be delayed by an unheated starting length: Equivalent surface and free stream temperatures for and uniform (or ) for Thermal Boundary Layer

Similarity Solution Similarity Solution for Laminar Boundary Layer Let the dimensionless x-velocity component, f = and dimensionless temperature, are functions of a dimensionless similarity parameter: 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 Flow Turbulent Boundary Layer 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:

Turbulent Flow Correlations of Experimental Data Local coefficients for Turbulent boundary layer on flat plate:

Turbulent Flow Experimental Data for Average Coefficients

Turbulent Flow Correlations of Experimental Data Average heat convection coefficient: Substituting expressions for the local coefficients and assuming Similarly, average friction coefficient can be found as: For fully turbulent boundary layer:

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 the local Nusselt number may be represented as follows: Laminar Laminar Turbulent TurbulentUSTUSFUSTUSF a3/43/49/109/10 b1/31/31/91/9 C m1/21/24/54/5 Sketch the variation of h x versus for two conditions: What effect does an USL have on the local convection coefficient?

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.

Orientation of Heated Surface (cont.)

Problem: Conveyor Belt Problem 7.24: Convection cooling of steel plates on a conveyor by air in parallel flow.

Problem: Conveyor Belt (cont.)