Assumptions : 1 .
Steady state
.
2 One dimensional
3
. Constant properties
Formula List 4
. No internal
energy production
5.
5 No heat loss
The following equations and data may be useful:
Radiation -
Boltzman's law
Fourier’s law: ↓
length of tube
Eguy"
&
Eblab :
ESTs" - Emission
𝑇1 − 𝑇2 Cylinder 2𝜋𝑘𝐿(𝑇1 − 𝑇2 )
Plain wall : 𝑄 = 𝑘𝐴 Tubes
i
𝑄= 𝑟
𝐿 ln (𝑟2 ) Q =
&E , A , CTs " -Ts) T is in Kelvin
[Thickness 1
Newton’s law of cooling:
Gainstivity
& :
absorb
𝑄 = ℎ𝐴(𝑇1 − 𝑇2 ) Q hAOTE : = hALTs -Tsat) Celticiency of
absorption
Thermal resistances:
𝐿 𝑟 1
𝑅= ln ( 2 ) 𝑅=
𝑟1 ℎ𝐴
𝑘𝐴 𝑅=
2𝜋𝑘𝐿
Dimensionless terms:
relative thickness
of the two 𝑐𝑝 𝜇 𝑣 momentum diffusivity
=> 𝜌𝑢 𝐿 &ℎ𝐿 significant length dimension that
is in the
boundary -
>
𝑃𝑟 = = 𝑅𝑒 = 𝑁𝑢 = direction of growth/thickness
layers in connection
𝑘 𝛼 Thermal diffusivity
- 𝜇 k ↳ Diameter of Cylinde
𝜇
where 𝑣 = 𝜌 and 𝛼 = 𝜌𝑐
𝑘 ↑ ratio of convection conduction b
x =
dynamic viscosity to
length of plate
𝑝
Colburn equation: heat traster system
I
Both and mass in the
𝑁𝑢 = 0.023 𝑅𝑒 0.8 𝑃𝑟 0.333
Range of application: 𝑅𝑒 > 10,000, 0.7 < 𝑃𝑟 < 160 , 𝐷𝐿 > 60 , smooth pipes
Calculate Nu
Dittus-Boelter equation: Use for
heating or
cooling applications
to find "h" 𝑁𝑢 = 0.023 𝑅𝑒 0.8 𝑃𝑟 𝑛
where 𝑛 =0.4 for heating, 0.3 for cooling.
Range of application: 𝑅𝑒 > 10,000, 0.7 < 𝑃𝑟 < 160 , 𝐷𝐿 > 60 , smooth pipes.
Sieder and Tate equation: Take viscosity into account Cuse when Hoid's viscosity change significantly with terp (
&
𝜇𝑏 0.14 My =
dynamic viscosity of bullo frid cinside the
pipe)
𝑁𝑢𝑚 = 0.027 𝑅𝑒𝐿0.8 𝑃𝑟 0.333
(𝜇 ) Mw =
dynamic viscosity of fluid near the wall Con outer surface of the pipel
𝑤
Range of application: 𝑅𝑒 > 10,000, 0.7 < 𝑃𝑟 < 16,700 , 𝐷𝐿 > 60 , smooth pipes
Heat transfer with phase change: Meg at Tsat
= Film condensation & properties at To
,
assume 𝑔 = 9.81 𝑚 𝑠 −2 4)
↓
convection coefficiat for PLATE
& Average
1⁄
Nu 𝑔 𝜌𝑙 (𝜌𝑙 − 𝜌𝑣 )ℎ′𝑓𝑔
1⁄
𝐿3 4 𝑔 𝜌𝑙 (𝜌𝑙 − 𝜌𝑣 )ℎ′𝑓𝑔 𝑘𝑙 3 4
Average
̅̅̅̅𝐿 = 0.943 [
𝑁𝑢 ] ℎ̅𝐿 = 0.943 [ ]
&
number
>
-
𝜇𝑙 𝑘𝑙 (𝑇𝑠𝑎𝑡 − 𝑇𝑠 ) 𝜇𝑙 (𝑇𝑠𝑎𝑡 − 𝑇𝑠 )𝐿
ℎ′𝑓𝑔 = ℎ𝑓𝑔 + 0.80 𝑐𝑝,𝑣 (𝑇𝑠 − 𝑇𝑠𝑎𝑡 ) ℎ′𝑓𝑔 = ℎ𝑓𝑔 + 0.68 𝑐𝑝,𝑙 (𝑇𝑠𝑎𝑡 − 𝑇𝑠 )
↑ but botten
Film pool
same
equation one
boiling is for horizontal tubes & spheres
I I
Steady state
.
2 One dimensional
3
. Constant properties
Formula List 4
. No internal
energy production
5.
5 No heat loss
The following equations and data may be useful:
Radiation -
Boltzman's law
Fourier’s law: ↓
length of tube
Eguy"
&
Eblab :
ESTs" - Emission
𝑇1 − 𝑇2 Cylinder 2𝜋𝑘𝐿(𝑇1 − 𝑇2 )
Plain wall : 𝑄 = 𝑘𝐴 Tubes
i
𝑄= 𝑟
𝐿 ln (𝑟2 ) Q =
&E , A , CTs " -Ts) T is in Kelvin
[Thickness 1
Newton’s law of cooling:
Gainstivity
& :
absorb
𝑄 = ℎ𝐴(𝑇1 − 𝑇2 ) Q hAOTE : = hALTs -Tsat) Celticiency of
absorption
Thermal resistances:
𝐿 𝑟 1
𝑅= ln ( 2 ) 𝑅=
𝑟1 ℎ𝐴
𝑘𝐴 𝑅=
2𝜋𝑘𝐿
Dimensionless terms:
relative thickness
of the two 𝑐𝑝 𝜇 𝑣 momentum diffusivity
=> 𝜌𝑢 𝐿 &ℎ𝐿 significant length dimension that
is in the
boundary -
>
𝑃𝑟 = = 𝑅𝑒 = 𝑁𝑢 = direction of growth/thickness
layers in connection
𝑘 𝛼 Thermal diffusivity
- 𝜇 k ↳ Diameter of Cylinde
𝜇
where 𝑣 = 𝜌 and 𝛼 = 𝜌𝑐
𝑘 ↑ ratio of convection conduction b
x =
dynamic viscosity to
length of plate
𝑝
Colburn equation: heat traster system
I
Both and mass in the
𝑁𝑢 = 0.023 𝑅𝑒 0.8 𝑃𝑟 0.333
Range of application: 𝑅𝑒 > 10,000, 0.7 < 𝑃𝑟 < 160 , 𝐷𝐿 > 60 , smooth pipes
Calculate Nu
Dittus-Boelter equation: Use for
heating or
cooling applications
to find "h" 𝑁𝑢 = 0.023 𝑅𝑒 0.8 𝑃𝑟 𝑛
where 𝑛 =0.4 for heating, 0.3 for cooling.
Range of application: 𝑅𝑒 > 10,000, 0.7 < 𝑃𝑟 < 160 , 𝐷𝐿 > 60 , smooth pipes.
Sieder and Tate equation: Take viscosity into account Cuse when Hoid's viscosity change significantly with terp (
&
𝜇𝑏 0.14 My =
dynamic viscosity of bullo frid cinside the
pipe)
𝑁𝑢𝑚 = 0.027 𝑅𝑒𝐿0.8 𝑃𝑟 0.333
(𝜇 ) Mw =
dynamic viscosity of fluid near the wall Con outer surface of the pipel
𝑤
Range of application: 𝑅𝑒 > 10,000, 0.7 < 𝑃𝑟 < 16,700 , 𝐷𝐿 > 60 , smooth pipes
Heat transfer with phase change: Meg at Tsat
= Film condensation & properties at To
,
assume 𝑔 = 9.81 𝑚 𝑠 −2 4)
↓
convection coefficiat for PLATE
& Average
1⁄
Nu 𝑔 𝜌𝑙 (𝜌𝑙 − 𝜌𝑣 )ℎ′𝑓𝑔
1⁄
𝐿3 4 𝑔 𝜌𝑙 (𝜌𝑙 − 𝜌𝑣 )ℎ′𝑓𝑔 𝑘𝑙 3 4
Average
̅̅̅̅𝐿 = 0.943 [
𝑁𝑢 ] ℎ̅𝐿 = 0.943 [ ]
&
number
>
-
𝜇𝑙 𝑘𝑙 (𝑇𝑠𝑎𝑡 − 𝑇𝑠 ) 𝜇𝑙 (𝑇𝑠𝑎𝑡 − 𝑇𝑠 )𝐿
ℎ′𝑓𝑔 = ℎ𝑓𝑔 + 0.80 𝑐𝑝,𝑣 (𝑇𝑠 − 𝑇𝑠𝑎𝑡 ) ℎ′𝑓𝑔 = ℎ𝑓𝑔 + 0.68 𝑐𝑝,𝑙 (𝑇𝑠𝑎𝑡 − 𝑇𝑠 )
↑ but botten
Film pool
same
equation one
boiling is for horizontal tubes & spheres
I I
