The Convection Boundary layers Thermal Boundary Layer (Contd) Free stream (x) Therma T boundary layer Heat flux Heat flux analogous to shear stress in velocity boundary layer Heat flux proportional to the temperature gradient at the surface AND since uy=0)=0, energy transfer to/from fluid occurs by conduction only! fluid thermal q-h or wall temperature gradient conductivity 0 Since thermal boundary layer gets larger along direction, the temperature gradient changes with X, and therefore Heat Transfer Su Yongkang School of Mechanical EngineeringHeat Transfer Su Yongkang School of Mechanical Engineering # 11 The Convection Boundary Layers Thermal Boundary Layer (Cont’d) Heat Flux • Heat flux analogous to shear stress in velocity boundary layer • Heat flux proportional to the temperature gradient at the surface, AND since u(y=0) =0, energy transfer to/from fluid occurs by conduction only! • Since thermal boundary layer gets larger along x direction, the temperature gradient changes with x, and therefore Ts T fluid thermal conductivity wall temperature gradient ____________________ =0    = − y s f y T q k