Formula Sheet: Introduction to Heat Transfer | Heat Transfer - Mechanical Engineering PDF Download

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In tro duction to Heat T ransfer F orm ula Sheet
Conduction
• F ourier’s La w of Conduction : Heat transfer rate through a material.
q =-kA
dT
dx
(Units: W )
whereq is heat transfer rate, k is thermal conductivit y (Wm
-1
K ), A is cross-sectional
area (m
2
),
dT
dx
is temp erature gradien t (Km
-1
).
• Steady-State Conduction (Plane W all) :
q =
kA(T
1
-T
2
)
L
where L is w all thic kness (m ), T
1
,T
2
are surf ace temp eratures (K ).
• Thermal Resistance (Conduction) :
R
cond
=
L
kA
(Units: KW
-1
)
• Cylindrical Conduction (Radial) :
q =
2pkL(T
1
-T
2
)
ln(r
2
/r
1
)
where r
1
,r
2
are inner and outer radii (m ), L is length (m ).
• Thermal Resistance (Cylindrical) :
R
cyl
=
ln(r
2
/r
1
)
2pkL
Con v ection
• Newton’s La w of Co oling : Con v ectiv e heat transfer rate.
q = hA(T
s
-T
8
) (Units: W )
where h is con v ectiv e heat transfer co e?icien t ( Wm
-2
K ), T
s
is surface temp erature
(K ), T
8
is fluid temp erature ( K ).
• Thermal Resistance (Con v ection) :
R
con v
=
1
hA
(Units: KW
-1
)
• Nusselt Num b er : Dimensionless heat transfer co e?icien t.
Nu=
hL
c
k
f
where L
c
is c haracteristic length (m ), k
f
is fluid thermal conductivit y ( Wm
-1
K ).
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Page 2


In tro duction to Heat T ransfer F orm ula Sheet
Conduction
• F ourier’s La w of Conduction : Heat transfer rate through a material.
q =-kA
dT
dx
(Units: W )
whereq is heat transfer rate, k is thermal conductivit y (Wm
-1
K ), A is cross-sectional
area (m
2
),
dT
dx
is temp erature gradien t (Km
-1
).
• Steady-State Conduction (Plane W all) :
q =
kA(T
1
-T
2
)
L
where L is w all thic kness (m ), T
1
,T
2
are surf ace temp eratures (K ).
• Thermal Resistance (Conduction) :
R
cond
=
L
kA
(Units: KW
-1
)
• Cylindrical Conduction (Radial) :
q =
2pkL(T
1
-T
2
)
ln(r
2
/r
1
)
where r
1
,r
2
are inner and outer radii (m ), L is length (m ).
• Thermal Resistance (Cylindrical) :
R
cyl
=
ln(r
2
/r
1
)
2pkL
Con v ection
• Newton’s La w of Co oling : Con v ectiv e heat transfer rate.
q = hA(T
s
-T
8
) (Units: W )
where h is con v ectiv e heat transfer co e?icien t ( Wm
-2
K ), T
s
is surface temp erature
(K ), T
8
is fluid temp erature ( K ).
• Thermal Resistance (Con v ection) :
R
con v
=
1
hA
(Units: KW
-1
)
• Nusselt Num b er : Dimensionless heat transfer co e?icien t.
Nu=
hL
c
k
f
where L
c
is c haracteristic length (m ), k
f
is fluid thermal conductivit y ( Wm
-1
K ).
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• Reynolds Num b er : Flo w regime indicator.
Re=
?vL
c
µ
=
vL
c
?
where ? is fluid densit y ( kgm
-3
), v is v elo cit y (ms
-1
), µ is dynamic viscosit y (Pas ),
? is kinematic viscosit y (m
2
s
-1
).
• Prandtl Num b er : Ratio of momen tum to thermal diffusivit y .
Pr =
?
a
=
µc
p
k
f
where a is thermal diffusivit y ( m
2
s
-1
), c
p
is sp ecific heat ( Jkg
-1
K ).
Radiation
• Stefan-Boltzmann La w : Radiativ e heat transfer from a surface.
q = ?sAT
4
s
(Units: W )
where ? is emissivit y (0 to 1), s =5.67×10
-8
W/m
2
K
4
is Stefan-Boltzmann constan t,
T
s
is surface temp e rature (K ).
• Net Radiation Bet w een T w o Surfaces :
q
1-2
=
sA
1
(T
4
1
-T
4
2
)
1-?
1
?
1
+
1
F
1-2
+
1-?
2
?
2
·
A
1
A
2
where F
1-2
is view factor (0 to 1), ?
1
,?
2
are emissivities, A
1
,A
2
are surface areas (m
2
).
• Thermal Resistance (Radiation) :
R
rad
=
1
h
r
A
, h
r
= ?s(T
s
+T
8
)(T
2
s
+T
2
8
)
where h
r
is radiation heat transfer co e?icien t ( Wm
-2
K ).
Com bined Heat T ransfer
• Ov erall Heat T ransfer Co e?icien t ( U ) : F or comp osite w alls or heat exc hangers.
q = UA?T,
1
U
=
?
R
total
where U is o v erall heat transfer co e?icien t ( Wm
-2
K ), R
total
includes conduction,
con v ection, and radiation resistances.
• Comp osite W all (Series) :
q =
?T
?
R
cond
+R
con v
• Critical Radius of Insulation (Cylindrical) :
r
cr
=
k
h
(Units: m )
where k is insulation conductivit y , h is con v ectiv e co e?icien t.
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