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External Convection: Laminar Flat Plate

External Convection: Laminar Flat Plate. For a constant property, laminar flow a similarity solution exists for the flow field u ( y ). Major flow parameters:. local boundary layer thickness. local skin friction coefficient. average skin friction coefficient.

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External Convection: Laminar Flat Plate

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  1. External Convection: Laminar Flat Plate For a constant property, laminar flow a similarity solution exists for the flow field u(y) Major flow parameters: local boundary layer thickness local skin friction coefficient average skin friction coefficient

  2. External Convection: Laminar Flat Plate For a constant property, laminar flow a similarity solution exists for the flow field u(y) Major heat transfer parameters: local thermal boundary layer thickness uniform surface temperature, Ts local Nusselt number (Pr > 0.6) average Nusselt number uniform surface heat flux, q”s local Nusselt number (Pr > 0.6) average Nusselt number

  3. External Convection: Turbulent Flat Plate For turbulent flow, only empirical relations exist local skin friction coefficient uniform surface temperature, Ts uniform surface heat flux, q”s local Nusselt number (Pr > 0.6) Average parameters assuming xc for Rex,c = 5×105 average skin friction coefficient uniform surface temperature, Ts average Nusselt number For xc= 0 or L >> xc (Rex,L>> Rex,c) average skin friction coefficient uniform surface temperature, Ts average Nusselt number

  4. External Convection: Starting Length where • The effect of an unheated starting length (USL) can be represented on the local Nusselt number as: • Parameters a, b, C, & m depend on • thermal boundary condition: uniform surface temperature (UST) or uniform heat flux (UHF) • flow conditions: laminar or turbulent

  5. External Convection: Starting Length p = 1 (laminar throughout) p = 4 (turbulent throughout) numerical integration for laminar/turbulent flow • Uniform Surface Temperature (UST) • Uniform Heat Flux (UHF) • The Nusselt number (and heat transfer coefficient) are functions of the fluid properties (ν,ρ,α,cp,k) • the effect of variable properties may be considered by evaluating all properties at the film temperature • most accurate solutions often require iteration on the film properties

  6. External Convection: Cylinder in Cross Flow • As with flat plate flow, flow conditions determine heat transfer • Flow conditions depend on special features of boundary layer development, including onset at stagnation point, separation, and onset of turbulence • Stagnation point: location of zero velocity and maximum pressure • boundary layer development under a favorable pressure gradientacceleration of the free stream flow • There is a minimum in the pressure distribution p(x) and toward the rear of the cylinder, the pressure increases. • boundary layer development under an adverse pressure gradient

  7. External Convection: Cylinder in Cross Flow note: • Separationoccurs when the momentum of the free stream flow is insufficient to overcome the adverse pressure gradient • the velocity gradient reduces to zero • flow reversal occurs accompanied by a downstream wake • Location of separation depends on boundary layer transition

  8. External Convection: Cylinder in Cross Flow Afis the area projected perpendicular to free stream drag coefficient • Force (FD) imposed by the flow on the cylinder is composed of two phenomena • friction  boundary layer shear stress • form drag (pressure drag)  pressure differential due to wake

  9. External Convection: Cylinder in Cross Flow • Thermal considerations: uniform surface temperature, Ts • heat transfer a function of the angel of separation θ • empirical correlations are used to determine average Nusselt numbers • Hilpert correlation: Pr ≥ 0.6 • also suitable for non-circular cylinders • Churchill and Bernstein: ReDPr > 0.2

  10. External Convection: Sphere in Cross Flow evaluate fluid properties at T∞except for μs which is evaluated at Ts • Similar flow issues as cylinder in cross flow arise • Thermal considerations: uniform surface temperature, Ts • heat transfer again defined by empirical correlations • Whitaker correlation: • 0.71 < Pr < 380 • 3.5 < ReD < 7.6×104

  11. External Convection: Impinging Jet • Impinging jet consists of a high speed flow impacting a flat surface • generates large convection coefficients • The flow and heat transfer are affected by a number of factors • shape/size of jet, velocity of jet, distance from plate, … • Significant hydrodynamic features: • mixing and velocity profile development in the free jet • stagnation point and zone • velocity profile development in the wall jet

  12. External Convection: Impinging Jet • Local Nusselt number distribution: • Average Nusselt number based on empirical correlations for single nozzles and arrays of nozzles • function of Reynolds number, Pr, distance along wall (ror x), height of jet (H)

  13. External Convection: Impinging Jet valid for valid for • Martin correlation: uniform surface temperature, Ts • single round nozzle • Martin correlation: uniform surface temperature, Ts • single slot nozzle

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