The Engineer posted on October 23, 2006 
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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.

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.

Independent Parameters 
Quantity

Symbol

Object

Units

Temperature 
T

scalar

K

Time 
t

scalar

s

Thermal conductivity 
k

scalar

W/m · K

Specific heat 
c

scalar

J/kg · K

Convection heat transfer coefficient 
h

scalar

W/m^{2}K

Emissivity 
e

scalar

W/m^{2}K

Density 
r

scalar

kg/m^{3}

Internal heat generation 
q_{qen}

scalar

kg/m^{3}


Dependent Parameters 
Quantity

Symbol

Object

Units

Heat flux

q"

vector

W/m^{2}

1D heat flux

q

scalar

W



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) 
Parameter

Formula

Interpretation

Prandtl number 

Ratio of fluid velocity boundary layer thickness to the fluid temperature boundary layer thickness. 
Nusselt number 

Ratio of heat transferred from surface to heat conducted away by fluid. 
Forced Convection Only 
Parameter

Formula

Interpretation

Reynold's number 

Ratio of fluid inertia stress to viscous stress (for flow over flat plates). 
Reynold's number 

(Reynold's number for pipe flow) 
Stanton number 


Free Convection Only 
Parameter

Formula

Interpretation

Grashof number 

Ratio of fluid buoyancy stress to viscous stress. 
Rayleigh number 



Heat Transfer Coefficient 
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

Process

h
(W/m^{2} · K)

Free convection


Gases

2–25

Liquids

50–1000

Forced convection


Gases

25–250

Liquids

50–20,000

Convection with phase change


Boiling or condensation

2500–100,000

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.

