HEAT TRANSFER Final review 们au Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER Final Review
Final review session 50 TED HAS BEEN BASED ON YOUR S0METIMES THERES A TRAINING YOU FOR WORK, ID SAY HE S FINE LINE BE TWEEN THE PAST SIX MONTHS. EI PLAYING THE WORLDS E CRIMINALLY ABUSIVE ONGEST PRACTICAL BEHAVIOR AND FUN JOKE ON YOU Copyright 9 2003 Uni ted Feature Syndicate, Inc Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 2 Final Review Session
Viscous flow The Navier-Stokes Equations Nonlinear, second order, partial differential equations au auau au a-u auau +l+y-+ +pgx+u at a a-y ay ay +ng1+1 at a ay az ax ay az a21a21 +g:+p O au ay a 0 ox ay a Couette flow. Poiseuille flow Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 3 Viscous Flow • The Navier-Stokes Equations Nonlinear, second order, partial differential equations. • Couette Flow, Poiseuille Flow. + + + + = − + + + + + + + = − + + + + + + + = − + + + 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 z w y w x w g z p z w w y w v x w u t w z v y v x v g y p z v w y v v x v u t v z u y u x u g x p z u w y u v x u u t u z y x = 0 + + z w y v x u
Convection Basic heat transfer equation q=h As(TS-Too)h= average heat transfer coefficient Primary issue is in getting convective heat transfer coefficient h ∫ hda. or, for unit width:h=r∫h A L 0 h relates to the conduction into the fluid at the y 0 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 4 Convection • Basic heat transfer equation • Primary issue is in getting convective heat transfer coefficient, h • h relates to the conduction into the fluid at the wall q = h A (T −T ) s s h = average heat transfer coefficient = = L A s s h dx L h dA h A h s 0 1 or,for unit width: 1 ( ) = − = T T y T k h s y f x 0 -
Convection Heat Transfer Correlations Key is to fully understand the type of problem and then make sure you apply the appropriate convective heat transfer coefficient correlation External flow For laminar flow over flat plate dP 0 ao 2 X nu 0.332Re . 2D- Nur k 0.66 4Rel2 pr X For mixed laminar and turbulent flow over flat plate h hamdx +hurd 0 uL 0037Re4871/P3 0.6<Pr<60 5×10·<Rer<10 Xc=5×105 Fq.7.41 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 5 Convection Heat Transfer Correlations • Key is to fully understand the type of problem and then make sure you apply the appropriate convective heat transfer coefficient correlation External Flow For laminar flow over flat plate For mixed laminar and turbulent flow over flat plate = 0 dx dP T ,U Ts y 3 1 2 1 = 0.332Rex Pr k h x Nu x x 3 1 2 1 = 0.664Rex Pr k h x Nu x x = + L xc turb xc x hlamdx h dx L h 1 0 ( ) Eq. 7.41 5 10 Re 10 Re 5 10 0.6 Pr 60 0.037 Re 871 Pr 5 x,c 5 8 4 5 1 3 L = = − L NuL
External Convection Flow For flow over cylinder Overall Average nusselt number hD NuD k CRe 2P+13/P)4 Pr Table 7.2 has constants C and m as f(Re For flow over sphere hD Nu D =2+(04Re k D+0.068D少104/4) μ For falling liquid drop Nun=2+0. re pr Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 6 External Convection Flow For flow over cylinder Overall Average Nusselt number Table 7.2 has constants C and m as f(Re) For flow over sphere For falling liquid drop 1 4 1 3 Pr Pr Re Pr = = s m D D C k hD Nu 1 4 1 2 2 3 0.4 2 (0.4 Re 0.06 Re )Pr = = + + s D D D k hD Nu 1 2 1 3 2 0.6 Re Pr NuD = + D
Convection with Internal flow Main difference is the constrained boundary layer Inviscid flow region Boundary layer region (r,x) ,6 Hydrodynamic entrance region fully developed region x fd.力 Different entry length for laminar and turbulent flow Compare external and internal flow Externalflow: Reference temperature: Too is constant Internalflow. Reference temperature: Tm will change if heat transfer is occurring Tm increases if heating occurs(Is> Tm) Tm decreases if cooling occurs(Is< Im) Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 7 Convection with Internal Flow • Main difference is the constrained boundary layer • Different entry length for laminar and turbulent flow • Compare external and internal flow: – External flow: Reference temperature: T is constant – Internal flow: Reference temperature: Tm will change if heat transfer is occurring! • Tm increases if heating occurs (Ts > Tm ) • Tm decreases if cooling occurs (Ts < Tm ) ro
Internal Flow(Cont'd For constant heat flux: T(x) conv.x +T .x n c X fd, thermal For constant wall temperature if ts Ti ift> t T Sections 8.4 and 8.5 contain correlation equations for Nusselt number cony A、h△T LM Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 8 Internal Flow (Cont’d) • For constant heat flux: • For constant wall temperature • Sections 8.4 and 8.5 contain correlation equations for Nusselt number T (x) s Tm (x) fd thermal x , T x Tm Ts T x Tm Ts T x Ts Ti if Ts Ti if qconv = As h TLM in p conv m x T m c q T x , + =
Free(Natural) Convection \TE) P a>0 <0 <0 dx Unstable Stable, Bulk fluid motion No fluid motion Grashofnumber in natural convection is analogous to the reynolds number in forced convection G2=8B(7,-Tm)3 Buoyancy forces Viscous forces Natural Natural Rel convection can Re 2 convection be neglected L dominates Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 9 Free (Natural) Convection • Grashof numberin natural convection is analogous to the Reynolds number in forced convection Unstable, Bulk fluid motion Stable, No fluid motion ( ) Viscousforces Buoyancy forces 2 3 = − = g T T L Gr s L 1 Re2 L GrL 1 Re2 L GrL Natural convection dominates Natural convection can be neglected
Free(Natural) Convection Rayleigh number: For relative magnitude of buoyancy and viscous forces Ra=GrPr For vertical surface transition to turbulence at Rax= 109 Review the basic equations for different potential cases, such as vertical plates, vertical cylinders, horizontal plates (heated and cooled) For horizontal plates, discuss the equations 9.30 9.32.(P513) Please refer to problem 9.34 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 10 Free (Natural) Convection Rayleigh number: For relative magnitude of buoyancy and viscous forces • Review the basic equations for different potential cases, such as vertical plates, vertical cylinders, horizontal plates (heated and cooled) • For horizontal plates, discuss the equations 9.30- 9.32. (P513) • Please refer to problem 9.34. = Pr Rax Grx For vertical surface, transition to turbulence at Rax 109
