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Unformatted text preview: C HAPTER 7: E XTERNAL C ONVECTION In external convection, boundary layers will always form freely since there is no adjacent surface to restrict boundary layer development b there is always fluid outside the boundary layer where the velocity and temperature are constant External convection: Internal convection: δ u u ∞ u ∞ u max < u ∞ u ∞ Midline b Examples: Flow over flat plate (inclined or parallel), around cylinders/spheres/turbine blades, banks of tubes, etc. Goal of this chapter: to derive h for external convection geometries The typical form of the expression is: n m C &u Pr Re = Prandtl number (Pr) : ⋅ = k c p μ Pr • Dimensionless value based only on fluid properties (i.e. independent of flow conditions or geometry) • Normally found in tables Reynolds number (Re): = μ ρ VL Re • Relates fluid properties to the geometry of the object over (or through) which the fluid passes. • The characteristic length L is the length of a plate ( x ) or diameter ( D ) of a sphere, cylinder or duct (boundary layer development) Nusselt Number: = k hL &u • Relates the relative importance of convection versus conductive heat transfer from the vantage point of the fluid (i.e. k = k fluid ) • Or: relative contribution of advective heat transfer versus conductive heat transfer in determining h Relates convection (advection b fluid flow + conduction) to conduction ( b fluid properties) Defines thermal boundary layer Defines material properties of fluid Relates velocity and thermal boundary layers Relates flow and object geometry to the physical fluid properties ∝ C f b Defines velocity boundary layer n m C &u Pr Re = The terms C , m , and n are determined experimentally ( empirically ) using an electrical heater to maintain constant T s ( T s > T ∞ ) and measuring T s , T ∞ , and P = IV required to keep T s constant By energy balance: q elec = q conv IV= h L A s ( T sT ∞ ) Nu L = C Re L m Pr n Perform experiments over a range of different u ∞ , L ( Re ), and fluids ( Pr ) and plot log( Nu L /Pr n ) vs. log( Re L ) to find C (slope) and m,n values which give a linear relationship Log( Nu L ) Log( Nu L /Pr n ) Log( Re L ) Log( Re L ) Pr 1 Pr 2 Pr 3 IMPORTANT NOTE: All empirical correlations have significant errors (up to 25%) and constraints on their use (i.e. the range of conditions over which experimental data was linearly correlated with the given C, m, and n ) b Apply only over specific ranges of Re and/or Pr (or Pe = Re*Pr , where Pe = Peclet number = VL/ α ) b Apply only to local vs. average convection coefficients b Apply only when fluid properties ( k , c p , μ , ρ , Pr ) are evaluated at specific temperatures defined in the correlation definition; i.e....
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 Winter '10
 TODDHOARE
 Fluid Dynamics, Heat Transfer

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