Notation and symbols commonly used in conduction theory are summarized below:

Independent Parameters

Quantity

Symbol

Units

temperature

T

K

time

t

s

thermal conductivity

k

W/m-K

specific heat

c

J/kg-K

density

r

kg/m^{3}

internal heat generation

q_{gen}

W/m^{3}

Dependent Parameters

Quantity

Symbol

Units

thermal diffusivity

a

m^{2}/s

heat flux

q

W/m^{2}

1-D heat flux

q

W/m^{2}

heat transfer rate

W

total heat

J

A Note on the q's

Confusion can arise over the notation used to describe heat flux, total heat flow, and total heat, especially since they all involve some permutation of the letter q.

In an effort to fully clarify the usage of q here, please note the following interdependencies, explained both with math and with words:

Mathematical Relationships

q

q_{gen}

q

Interpretations

q

q_{gen}

Total heat tranfered is the heat tranfer rate summed over the time interval.

Total heat tranfered through area A is the heat flux integrated over A and the time interval.

Total heat generated in volume V is the heat generation rate integrated over V and the time interval.

Heat transfer rate across an area A is the heat flux integrated over A.

Steady-state heat transfer rate out of a volume V is the heat generation rate integrated over V.

q

One-dimensional version of the conservation of energy statement, where e is the internal energy density reflected in the body's temperature.