Introduction to Convection:Introduction to Convection:Flow and Thermal ConsiderationsFlow and Thermal ConsiderationsChapter Six and Appendix EChapter Six and Appendix ESections 6.1 to 6.9 and E.1 to E.3Sections 6.1 to 6.9 and E.1 to E.3
Boundary Layer FeaturesBoundary Layers: Physical Features•Velocity Boundary Layer –A consequence of viscous effectsassociated with relative motionbetween a fluid and a surface.–A region of the flow characterized byshear stresses and velocity gradients.–A region between the surfaceand the free stream whosethicknessincreases in the flow direction.δ–Why does increase in the flow direction? δ()0.99u yuδ∞→=0syuyτµ=∂=∂–Manifested by a surface shearstressthat provides a drag force, .sτDFsDssAFdAτ=∫–How does vary in the flowdirection? Why?sτ
Boundary Layer Features (cont.)•Thermal Boundary Layer–A consequence of heat transfer between the surface and fluid.–A region of the flow characterizedby temperature gradients and heatfluxes.()0.99stsTTyTTδ∞−→=−–A region between the surface andthe free stream whose thicknessincreases in the flow direction.tδ0sfyTqky=∂′′= −∂–Why does increase in theflow direction?tδ–Manifested by a surface heatfluxand a convection heattransfer coefficient h.sq′′0/fyskTyhTT=∞−∂∂≡−–If is constant, how do and hvary in the flow direction? ()sTT∞−sq′′
Local and Average CoefficientsDistinction betweenLocal andAverage Heat Transfer Coefficients•Local Heat Flux and Coefficient:()sqh TT∞′′=−•Average Heat Flux and Coefficient for a Uniform Surface Temperature:()ssqhATT∞=−ssAqq dA′′=∫()sssATThdA∞=−∫1ssAshhdAA=∫•For a flat plate in parallel flow:1LohhdxL=∫
Boundary Layer EquationsThe Boundary Layer Equations•Consider concurrent velocity and thermal boundary layer development for steady, two-dimensional, incompressible flowwith constant fluid propertiesand negligible body forces.(),,pckµ•Apply conservation of mass, Newton’s 2ndLaw of Motionand conservation of energyto a differential control volume and invoke the boundary layer approximations.Velocity Boundary Layer:,,uvuuvvyxyx∂∂∂∂∂∂∂∂±±Thermal Boundary Layer:TTyx∂∂∂∂±
Boundary Layer Equations (cont.)•Conservation of Mass:0uvxy∂∂+=∂∂In the context of flow through a differential control volume, what is the physicalsignificance of the foregoing terms, if each is multiplied by the mass density of the fluid?