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Symbols and FormulasStaff posted on October 23, 2006 |
Symbols and Formulas
A simple definition of heat transfer is energy in transit due to a temperature difference. If there is a temperature difference in a medium or between media, heat transfer must occur.
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| Commonly Used Symbols |
The follow tables are a list of variables, their symbols, and the associative units commonly used in heat transfer expressions. All the equations present in the heat transfer section have the same quantity denoted by the symbols in the table.
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| Independent Parameters |
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Quantity
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Symbol
|
Object
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Units
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| Temperature |
T
|
scalar
|
K
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| Time |
t
|
scalar
|
s
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| Thermal conductivity |
k
|
scalar
|
W/m · K
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| Specific heat |
c
|
scalar
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J/kg · K
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| Convection heat transfer coefficient |
h
|
scalar
|
W/m2K
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| Emissivity |
e
|
scalar
|
W/m2K
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| Density |
r
|
scalar
|
kg/m3
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| Internal heat generation |
qqen
|
scalar
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kg/m3
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Dependent Parameters |
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Quantity
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Symbol
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Object
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Units
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Heat flux
|
q"
|
vector
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W/m2
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1-D heat flux
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q
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scalar
|
W
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| Table of Dimensionless Parameters |
As is common with fluid mechanics analysis, a number of dimensionless parameters are employed to describe convective heat transfer. A summary of these variables is included in the following tables:
General Convection (Forced and Free) |
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Parameter
|
Formula
|
Interpretation
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| Prandtl number |
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Ratio of fluid velocity boundary layer thickness to the fluid temperature boundary layer thickness. |
| Nusselt number |
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Ratio of heat transferred from surface to heat conducted away by fluid. |
Forced Convection Only |
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Parameter
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Formula
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Interpretation
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| Reynold's number |
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Ratio of fluid inertia stress to viscous stress (for flow over flat plates). |
| Reynold's number |
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(Reynold's number for pipe flow) |
| Stanton number |
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Free Convection Only |
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Parameter
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Formula
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Interpretation
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| Grashof number |
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Ratio of fluid buoyancy stress to viscous stress. |
| Rayleigh number |
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| Heat Transfer Coefficient |
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The heat transfer coefficient encompasses all of the parameters that influence convection heat transfer. It depends on conditions in the boundary layer, which are influenced by surface geometry, the nature of the fluid motion, and other fluid thermodynamic and transport properties. Convection heat transfer will frequently appear as a boundary condition in the solution of conduction problems. The table below is the typical values of the convection heat transfer coefficient.
Typical Values of Convection Heat Transfer Coefficient
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Process
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h
(W/m2 · K)
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Free convection
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Gases
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2–25
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Liquids
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50–1000
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Forced convection
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Gases
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25–250
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Liquids
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50–20,000
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Convection with phase change
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Boiling or condensation
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2500–100,000
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Some material excerpted from: Incroprera, Frank and De Witt, David P. Introduction to Heat Transfer. Second Edition. New York: John Wiley & Sons, Inc. 1985, 1990.
Copyright © 1985, 1990, by John Wiley & Sons, Inc.
This material is used by permission of John Wiley & Sons, Inc.
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