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Summary Extended and Description of Formula List - Process Heat Transfer (CHEN 10092) $7.10
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Summary Extended and Description of Formula List - Process Heat Transfer (CHEN 10092)

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This document provide a explaination, description of nomenclatures in the given formula list. Since some variables can be used differently for each course, this will help make sure that you totally understand what each variable really meant.

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  • December 24, 2024
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  • 2023/2024
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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

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