HEAT TRANSFER CHAPTER 9 Free Convection 们au Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER CHAPTER 9 Free Convection
Natural Convection Where we’ ve been. Up to now, have considered forced convection that is an external driving force causes the flow. Where we’ re going: Consider the case where fluid movement is by buoyancy effects caused by temperature differential Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 2 Natural Convection Where we’ve been …… • Up to now, have considered forced convection, that is an external driving force causes the flow. Where we’re going: • Consider the case where fluid movement is by buoyancy effects caused by temperature differential
When natural convection is important Weather events such as a thunderstorm Glider planes · Radiator heaters Hot air balloon Heat transfer with pipes and electrical lines Heat flow through and on outside of a double pane window Just sitting there Oceanic and atmospheric motions Coffee cup example Small velocity Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 3 When natural convection is important • Weather events such as a thunderstorm • • Glider planes • Radiator heaters • Hot air balloon • Heat transfer with pipes and electrical lines • Heat flow through and on outside of a double pane window • Just sitting there • Oceanic and atmospheric motions • Coffee cup example …. Small velocity
Natural Convection KEY POINTS THIS LECTURE New terms Volumetric thermalexpansion coefficient Grashofnumber Rayleigh number Buoyancy is the driving force Stable versus unstable conditions Nusselt number relationship for laminar free convection on vertical surface Boundary layer impacts: laminar= turbulent Text book sections:$9.1-9.5 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 4 Natural Convection KEY POINTS THIS LECTURE • New terms – Volumetric thermal expansion coefficient – Grashof number – Rayleigh number • Buoyancy is the driving force – Stable versus unstable conditions • Nusselt number relationship for laminar free convection on vertical surface • Boundary layer impacts: laminar turbulent • Text book sections: §9.1 – 9.5
Buoyancy is the driving force Buoyancy is due to combination of Differences in fluid densit Body force proportional to density Body forces gravity, also Coriolis force in atmosphere and oceans Convection flow is driven by buoyancy in unstable conditions plr) P P 少0 o fluid motion may be (no constraining surface)or along a surface Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 5 Buoyancy is the driving force • Buoyancy is due to combination of – Differences in fluid density – Body force proportional to density – Body forces gravity, also Coriolis force in atmosphere and oceans • Convection flow is driven by buoyancy in unstable conditions • Fluid motion may be (no constraining surface) or along a surface
Buoyancy is the driving force( Cont d) Free boundary layer flows p7 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 = −
Governing Equations(Contd) Define B, the volumetric thermal expansion coefficient B pa7丿p For an ideal gas:P、RT RT Thus: B For liquids and non-ideal gases, see appendix a In general 1△, B p△Tp1-7 p≈pB(T-7 Density gradient is due to the temperature gradient Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 9 Governing Equations (Cont’d) • Define , the volumetric thermal expansion coefficient. • In general, T Thus RT RT P P T P 1 : For an ideal gas : 1 = = = = − For liquids and non-ideal gases, see appendix A T T −T − = − − 1 1 ( ) − T −T Density gradient is due to the temperature gradient
Governing Equations(cont'd Now, we can see buoyancy effects replace pressure gradient in the momentum equation 8(T-1)+ ax a The buoyancy effects are confined to the momentum equation, so the mass and energy equations are the same 0 Ox dy aT a aT v/au OX Strongly coupled and must be solved simultaneously Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 10 Governing Equations (cont’d) • Now, we can see buoyancy effects replace pressure gradient in the momentum equation • The buoyancy effects are confined to the momentum equation, so the mass and energy equations are the same. 2 2 ( ) y u g T T v y u v x u u = − + + = 0 + y v x u 2 2 2 + = + y u y c T y T v x T u p Strongly coupled and must be solved simultaneously
