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 EngineeringHeat 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  =   − 