Chapter_6_Part_A__Notes

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
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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 Why does increase in the flow direction? ( ) 0.99 uy u →= 0 s y u y τ µ = = Manifested by a surface shear stress that provides a drag force, . s D F s D ss A F dA = How does vary in the flow direction? Why? s
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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. ( ) 0.99 s t s TT y δ →= A region between the surface and the free stream whose thickness increases in the flow direction. t 0 s fy T qk y = ′′ =− Why does increase in the flow direction? t Manifested by a surface heat flux and a convection heat transfer coefficient h . s q 0 / s kT y h = −∂ ∂ If is constant, how do and h vary in the flow direction? () s s q
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Local and Average Coefficients Local and Average Coefficients Distinction between Local and Average Heat Transfer Coefficients Local Heat Flux and Coefficient : () s qh TT ′′ =− Average Heat Flux and Coefficient for a Uniform Surface Temperature : ss ATT s s A qq d A = s s s A T T hdA 1 s s A s h hdA A = •Fo r a flat plate in parallel flow : 1 L o hh d x L =
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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 . ( ) , , p ck 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 : ,, uv uu v v yx y x ∂∂ ± ± Thermal Boundary Layer : TT ±
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Boundary Layer Equations (cont.) Boundary Layer Equations (cont.) Conservation of Mass : 0 uv xy ∂∂ += 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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Chapter_6_Part_A__Notes - Introduction to Convection...

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