Chapter_6_Part_A__Notes - Introduction to Convection Introduction Flow and Thermal Considerations Chapter Six and Appendix E Sections 6.1 to 6.9 and E.1

Chapter_6_Part_A__Notes - Introduction to Convection...

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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 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 Why does increase in the flow direction? δ ( ) 0.99 u y u δ = 0 s y u y τ µ = = Manifested by a surface shear stress that provides a drag force, . s τ D F s D s s A F dA τ = How does vary in the flow direction? Why? s τ
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. ( ) 0.99 s t s T T y T T δ = A region between the surface and the free stream whose thickness increases in the flow direction. t δ 0 s f y T q k y = ′′ = − Why does increase in the flow direction? t δ Manifested by a surface heat flux and a convection heat transfer coefficient h . s q ′′ 0 / f y s k T y h T T = If is constant, how do and h vary in the flow direction? ( ) s T T s q ′′
Local and Average Coefficients Distinction between Local and Average Heat Transfer Coefficients Local Heat Flux and Coefficient : ( ) s q h T T ′′ = Average Heat Flux and Coefficient for a Uniform Surface Temperature : ( ) s s q hA T T = s s A q q dA ′′ = ( ) 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 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 . ( ) , , 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.) Conservation of Mass : 0 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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