Symbols and Formulas Staff 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.

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}

1-D 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.