6a - Introduction to Convection: Introduction to...

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Unformatted text preview: Introduction to Convection: Introduction to Convection: Flow and Thermal Considerations Flow and Thermal Considerations Chapter Six and Appendix E Chapter Six and Appendix E Sections 6.1 to 6.9 and E.1 to E.3 Sections 6.1 to 6.9 and E.1 to E.3 Boundary Layer Features Boundary Layer Features Boundary Layers: Physical Features • Velocity Boundary Layer – A consequence of viscous effects associated with relative motion between a fluid and a surface. – A region of the flow characterized by shear stresses and velocity gradients. – A region between the surface and the free stream whose thickness increases in the flow direction. δ ( 29 0.99 u y u δ ∞ → = – Why does increase in the flow direction? δ – Manifested by a surface shear stress that provides a drag force, . s τ D F s y u y τ μ = ∂ = ∂ s D s s A F dA τ = ∫ – How does vary in the flow direction? Why? s τ Boundary Layer Features (cont.) Boundary Layer Features (cont.) • Thermal Boundary Layer – A consequence of heat transfer between the surface and fluid. – A region of the flow characterized by temperature gradients and heat fluxes. – A region between the surface and the free stream whose thickness increases in the flow direction. t δ – Why does increase in the flow direction? t δ – Manifested by a surface heat flux and a convection heat transfer coefficient h . s q ′′ ( 29 0.99 s t s T T y T T δ ∞- → =- s f y T q k y = ∂ ′′ = - ∂ / f y s k T y h T T = ∞- ∂ ∂ ≡- – If is constant, how do and h vary in the flow direction? ( 29 s T T ∞- s q ′′ Local and Average Coefficients Local and Average Coefficients Distinction between Local and Average Heat Transfer Coefficients • Local Heat Flux and Coefficient : ( 29 s q h T T ∞ ′′ =- • Average Heat Flux and Coefficient for a Uniform Surface Temperature : ( 29 s s q hA T T ∞ =- s s A q q dA ′′ = ∫ ( 29 s s s A T T hdA ∞ =- ∫ 1 s s A s h hdA A = ∫ • For a flat plate in parallel flow : 1 L o h hdx L = ∫ Boundary Layer Equations Boundary Layer Equations The Boundary Layer Equations • Consider concurrent velocity and thermal boundary layer development for steady, two-dimensional, incompressible flow with constant fluid properties and negligible body forces . ( 29 , , p c k μ • Apply conservation of mass , Newton’s 2 nd Law of Motion and conservation of energy to a differential control volume and invoke the boundary layer approximations . Velocity Boundary Layer : , , u v u u v v y x y x ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ? ? Thermal Boundary Layer : T T y x ∂ ∂ ∂ ∂ ? Boundary Layer Equations (cont.) Boundary Layer Equations (cont.) • Conservation of Mass : u v x y ∂ ∂ + = ∂ ∂ In the context of flow through a differential control volume, what is the physical significance of the foregoing terms, if each is multiplied by the mass density of the fluid?...
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This note was uploaded on 10/13/2010 for the course MECH 414 taught by Professor Ghia during the Winter '06 term at University of Cincinnati.

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6a - Introduction to Convection: Introduction to...

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