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convective heat transfer
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dimensional analysis forced convection in a closed conduit # of variables; 7 # of dimensions; 5 # of ranks; 4 # of independent dimensionless groups; 3
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natural convection # of variables; 9 # of dimensions; 5 # of ranks; 5 # of independent dimensionless groups; 4
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Laminar boundary layer
No matter how turbulent the flow is far from the surface Negligible viscous effect outside the boundary layer
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Blasius’ similarity transformation
Boundary conditions Blasius’ similarity transformation
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Ux becomes nearly U along the boundary layer
Boundary layer thickness Friction coeff. Shear force Local Reynolds number
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laminar boundary layer; Blasius
for Pr=1
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effect of Pr; Pohlhausen
fluid properties are evaluated at the film temperature ; laminar boundary layer over a flat plate (von Karman)
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energy and momentum transfer analogy
Reynolds analogy ; for Pr=1 coefficient of skin friction Colburn analogy ; 0.5<Pr<50, no form drag Colburn j-factor
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turbulent flow Prandtl analogy von Karman analogy
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convective heat transfer correlations
natural convection; vertical plates, vertical cylinders, horizontal plates, horizontal cylinders, spheres, rectangular enclosures forced convection for internal flow; laminar flow, turbulent flow forced convection for external flow; flow parallel to plane surfaces, cylinders in crossflow, single spheres, tube banks in crossflow, special considerations; whether to evaluate fluid properties at bulk or film temperature what significant length is used what is the allowable Pr, Re range for a given set of data
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natural convection; vertical plates
12.5cm high Ts=65C Tinf=15C
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forced convection for internal flow
laminar flow; Graetz solution
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Sieder and Tate
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turbulent flow; Dittus and Boelter
n=0.4 if the fluid is being heated, n=3 if the fluid is being cooled all fluid properties are evaluated at the arithmetic-mean bulk temperature Re>104 0.7<Pr<100 L/D>60 Colburn; Sieder and Tate ;
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forced convection for external flow
flow parallel to plane surfaces laminar; turbulent; (Colburn analogy) (von Karman)
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cylinders in crossflow
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