Buoyancy is the driving force( Cont d) Free boundary layer flows p<p Plume T>7 1 Heated wire or hot pipe Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 6 Buoyancy is the driving force (Cont’d) • Free boundary layer flows Heated wire or hot pipe
A heated vertical plate We focus on free convection flows bounded by a surface The classic example is T>1 u(x, Extensive quiescent fluid g (b) Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 7 A heated vertical plate • We focus on free convection flows bounded by a surface. • The classic example is Ts T u(x,y) y g Ts T x v u Extensive, quiescent fluid
Governing Equations The difference between the two flows(forced flow and free flow)is that, in free convection,a major role is played by buoyancy forces Consider the x-momentum equation Ⅴ ery important auau 1 ap l-+ -g+v As we know, ap/ay=0, hence the x-pressure gradient in the boundary layer must equal that in the quiescent region outside the boundary layer aP -pog n,,O(△p1,,02n +y Buoyancy force△p=-p Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 8 Governing Equations • The difference between the two flows (forced flow and free flow) is that, in free convection, a major role is played by buoyancy forces. • Consider the x-momentum equation. • As we know, , hence the x-pressure gradient in the boundary layer must equal that in the quiescent region outside the boundary layer. X = −g Very important 2 2 g 1 y u x P y u v x u u − + = − + p / y = 0 - g x P = 2 2 g y u y u v x u u + = + Buoyancy force = −