+#u'lin( #! !luid !l#w and %eat tans!e 
+#nducti#n
+#nvecti#n
Radiati#n
Int#ducti#n
Heat tans!e is t%e stud& #! t%e*al ene(& %eat !l#ws
Heat alwa&s !l#ws !#* %#t t# c#ld
a*'les ae u)i3uit#us %eat !l#ws in t%e )#d&
%#*e %eatin(/c##lin( s&ste*s
e!i(eat#s #vens #t%e a''liances
aut#*#)iles '#we 'lants t%e sun etc.
 
$#des #! Heat Tans!e 
+#nducti#n - di!!usi#n #! %eat due t# te*'eatue (adient
+#nvecti#n - w%en %eat is caied awa& )& *#vin( !luid
Radiati#n - e*issi#n #! ene(& )& elect#*a(netic waves
3c#nvecti#n
3c#nducti#n
3adiati#n
T&'ical 6esi(n 7#)le*s
T# dete*ine #veall %eat tans!e c#e!!icient - e.(. !# a ca adiat# 
%i(%est # l#west te*'eatue in a s&ste* - e.(. in a (as tu)ine
te*'eatue disti)uti#n elated t# t%e*al stess - e.(. in t%e walls #! a
s'aceca!t
 
Heat Tans!e and Fluid Fl#w
;s a !luid *#ves it caies %eat wit% it -- t%is is called c#nvecti#n
T%us %eat tans!e can )e ti(%tl& c#u'led t# t%e !luid !l#w s#luti#n
;dditi#nall& T%e ate #! %eat tans!e is a st#n( !uncti#n #! !luid vel#cit&
 
+#nducti#n Heat Tans!e 
+#nducti#n is t%e tans!e #! %eat )& *#lecula inteacti#n
In a (as *#lecula vel#cit& de'ends #n te*'eatue %#t ene(etic *#lecules c#llide wit% nei(%)#s inceasin( t%ei s'eed
 
F#uie=s >aw
%eat !lu is '#'#ti#nal t# te*'eatue (adient
w%ee k  ? t%e*al c#nductivit&
in (eneal k = k(x,y,z,T,…)
    
   
  ∂ ∂
+ ∂ ∂
 A
Q
dx
dT 
1

units !# q 
GenealiAed Heat 6i!!usi#n 3uati#n
I! we 'e!#* a %eat )alance #n a s*all v#lu*e #! *ateialB
B we (et
qT k  t 
T%eat c#nducti#n
in
C#unda& +#nditi#ns
Heat tans!e )#unda& c#nditi#ns (eneall& c#*e in t%ee t&'es
T ? ,00D 
 irich!et condition
c#e!!icient
 #o$in condition
T )#d&
+#nducti#n a*'le
+#*'ute t%e %eat tans!e t%#u(% t%e wall #! a %#*e
s%in(les
?0.15 @/*2-D 
;lt%#u(% sli(%t &
 )id(in( e!!ect
 
+#nvecti#n is *#ve*ent #! %eat wit% a !luid
.(. w%en c#ld ai swee's 'ast a wa* )#d& it daws awa& wa* ai
nea t%e )#d& and e'laces it wit% c#ld ai 
#!ten we want t# n#w t%e %eat tans!e c#e!!icient h net 'a(e
!l#w #ve a
T )#d&
avea(e %eat tans!e c#e!!icient @/*2-D=h
3
Heat Tans!e +#e!!icient
h is n#t a c#nstant )ut h = h( T)
T%ee t&'es #! c#nvecti#n  Natual c#nvecti#n
!luid *#ves due t# )u#&anc&
F#ced c#nvecti#n
!l#w is induced )& etenal *eans
C#ilin( c#nvecti#n
 )#d& is %#t en#u(% t# )#il li3uid
,
>##in( in *#e detail...
ust as t%ee is a visc#us )#unda& la&e in t%e vel#cit& disti)uti#n
t%ee is als# a t%e*al )#unda& la&e 
δ  t δ 
 Nusselt Nu*)e 
3uate t%e %eat c#nducted !#* t%e wall t# t%e sa*e %eat tans!e in
c#nvective te*s
T%en eaan(e t# (et
∞−= ∂ ∂
ne(& 3uati#n
GenealiAe t%e %eat c#nducti#n e3uati#n t# include e!!ect #! !luid
*#ti#n
;ssu*es inc#*'essi)le !luid n# s%ea %eatin( c#nstant '#'eties
ne(li(i)le c%an(es in inetic and '#tential ene(&
+an n#w s#lve !# te*'eatue disti)uti#n in )#unda& la&e 
T%en calculate h usin( F#uie=s law
qT k T  t 
+#elati#ns !# Heat Tans!e +#e!!icient
;s an altenative can use c#elati#ns t# #)tain h
.(. %eat tans!e !#* a !lat 'late in la*ina !l#w
w%ee t%e 7andtl nu*)e is de!ined as
T&'ical values ae 7 ? 0.01 !# li3uid *etals
7 ? 0.< !# *#st (ases
,,,.05.0 7 Re,,2.0 Nu  x x  =
α 
+#nvecti#n a*'les
6evel#'in( !l#w in a 'i'e c#nstant wall te*'eatue
∞ T  'T 
∞ T  'T 
∞ T  'T 
%eat !lu !#* wall
 Natual c#nvecti#n !#* a %eated vetical 'late
u
T
Tw
(avit&
;s t%e !luid is wa*ed )& t%e 'late
its densit& deceases and a )u#&ant
!#ce aises w%ic% induces !l#w in
t%e vetical diecti#n. T%e !#ce is
e3ual t#
∞∞   ρ T 
(#vens natual c#nvecti#n is t%e
Ra&lei(% nu*)e
Radiati#n Heat Tans!e 
T%e*al adiati#n is e*issi#n #! ene(& as elect#*a(netic waves
Intensit& de'ends #n )#d& te*'eatue and su!ace c%aacteistics
I*'#tant *#de #! %eat tans!e at %i(% te*'eatues
+an als# )e i*'#tant in natual c#nvecti#n '#)le*s
a*'les t#aste (ill )#ile 
!ie'lace
suns%ine
τ  ρ α    ++=1
τ3 tans*itted
; )lac )#d& is a *#del #! a 'e!ect adiat# 
a)s#)s all ene(& t%at eac%es it e!lects n#t%in(
t%ee!#e α ? 1 ρ ? τ ? 0
T%e ene(& e*itted )& a )lac )#d& is t%e t%e#etical *ai*u*
T%is is te!an-C#ltA*ann law σ is t%e te!an-C#ltA*ann c#nstant
5.::9<e-8 @/*2-D 4
Real C#dies
Real )#dies will e*it less adiati#n t%an a )lac )#d&
a*'le adiati#n !#* a s*all )#d& t# its su#undin(s  )#t% t%e )#d& and its su#undin(s e*it t%e*al adiati#n
t%e net %eat tans!e will )e !#* t%e %#tte t# t%e c#lde 
4T q   εσ =
-   44
∞ T 
∞ q
@%en is adiati#n i*'#tant
Radiati#n ec%an(e is si(ni!icant in %i(% te*'eatue '#)le*s e.(.
c#*)usti#n
Radiati#n '#'eties can )e st#n( !uncti#ns #! c%e*ical c#*'#siti#n
es'eciall& +"2 H2"
Radiati#n %eat ec%an(e is di!!icult s#lve ece't !# si*'le
 
Heat Tans!e u**a&
Heat tans!e is t%e stud& #! t%e*al ene(& %eat !l#ws c#nducti#n
c#nvecti#n
adiati#n
T%e !luid !l#w and %eat tans!e '#)le*s can )e ti(%tl& c#u'led t%#u(% t%e c#nvecti#n te* in t%e ene(& e3uati#n
w%en '#'eties ρ µ ae de'endent #n te*'eatue
@%ile anal&tical s#luti#ns eist !# s#*e si*'le '#)le*s we *ust
el& #n c#*'utati#nal *et%#ds t# s#lve *#st industiall& elevant
a''licati#ns +an I (# )ac t#
slee' n#w