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Flat Plate Flow

Flat Plate Flow. Ref: Incropera & DeWitt, Fundamentals of Heat and Mass Transfer, 3 rd ed. Nusselt Number Correlations. Remember from Ch. 6 that In general, (1) C, m, and n vary with geometry & flow type. They are usually determined experimentally, making (1) an empirical correlation.

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Flat Plate Flow

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  1. Flat Plate Flow Ref: Incropera & DeWitt, Fundamentals of Heat and Mass Transfer, 3rd ed.

  2. Nusselt Number Correlations • Remember from Ch. 6 that • In general, (1) • C, m, and n vary with geometry & flow type. • They are usually determined experimentally, making (1) an empirical correlation. • Evaluate properties at the film temperature (ave. boundary layer temp) unless otherwise noted.

  3. Convection Heat Transfer Measurements

  4. Example experiment to find h

  5. Laminar Flat Plate Flow • Assumptions: steady, incompressible, laminar, constant fluid properties, negligible viscous dissipation • dp/dx=0 • Simplified continuity equation:

  6. Simplified Momentum & Energy Equations • Momentum Equation: • Energy Equation • Momentum Equation is decoupled from Energy Equation (but not vice versa).

  7. Boundary Conditions • Velocity Boundary Conditions • Temperature Boundary Conditions

  8. Blasius Solution for laminar flow over a flat plate, constant plate surface temp • Solve using a similarity solution.

  9. Average Results • The results for Cf,x and Nux were local results. To find average results, we must integrate. Why is this true?

  10. Turbulent Flow • These results are determined experimentally. • These equations can be used if the boundary layer is “tripped” upstream. In other words, a flow disturbance upstream causes the flow to be turbulent everywhere over the plate.

  11. Mixed Boundary Layer Conditions, cont. If Rex reaches 500000, the flow will go turbulent. If the plate is long enough, the laminar portion can be neglected, and the flow can be treated as all turbulent. Otherwise, see the next slide….

  12. Mixed Boundary Layer Conditions, cont. • Integrate over the plate. • If Rex,c=5x105,

  13. Mixed Boundary Layer Conditions, cont. • For Cf, integrate in the same way. • To check what type of flow you have, calculate Re at the end of the plate. If it’s below Rex,c, use laminar equations. If it’s over Rex,c, use the mixed boundary layer calculations. For some complicated geometries, the fluid flow will have a high degree of turbulence in the freestream. In this case it may be turbulent over the entire plate. • What are some applications where this may be true?

  14. Unheated Starting Length If only part of the plate is heated, the thermal and velocity boundary layers will start growing at different positions. This will affect Nu.

  15. Unheated Starting Length • For laminar flow • For turbulent flow

  16. Uniform Heat Flux • If a plate has a uniform heat flux instead of a uniform surface temperature, use the following for laminar flow: • For turbulent flow:

  17. Method to Solve a Convection Problem • Determine the flow geometry. • Choose the reference temperature & evaluate fluid properties. • Calculate the Reynolds number. Determine if the flow is laminar or turbulent or a combination. This is very important!!! • See if a local or surface average coefficient is required. • Check the boundary condition – constant heat flux or constant surface temperature. • Pick the correct correlation. The most common problem in convection is choosing a correlation for the wrong geometry or Reynolds number.

  18. Example Air at 27ºC and 1 atm flows over a flat plate 1 m wide at a speed of 2 m/s. a) Calculate the boundary layer thickness 20 cm from the leading edge of the plate. b) If the plate temperature is 127ºC, calculate the average heat transfer rate over these first 20 cm.

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