So I'd like to describe some of the fundamental parameters associated with heat transfer and
their respective meanings.
I'll make a table of the particular quantity we're interested in, their respective meanings,
the symbols that we typically use in heat transfer, and then the respective units.
The first quantity that is important is thermal energy.
And what I mean by that is, it's the energy associated with the microscopic behavior of
matter, and I mean more specifically the vibrations and rotations and different types of energy
associated with the molecules themselves, and I'm not talking about bulk movement of
molecules.
They're stationary, and we just quantify this conceptually as their internal energy.
The internal energy of matter is directly related to the temperature, and the symbol
that we typically use for internal energy is the capital letter U, and we can draw a
relationship between U and the temperature by using this equation, which says that the
internal energy is proportional to what we call the heat capacity at constant volume
multiplied by the temperature, which can be above or below some reference temperature.
All molecules have internal energy associated with them if the temperature is above absolute
zero.
So we say that the internal energy is defined arbitrarily, that if the temperature is equal
to the reference temperature, there are still molecular vibrations associated with it, there
is still some absolute energy associated with it, but we arbitrarily call that 0 when T
equals T ref.
The units associated with this are, we can either say joules, and extensive variable,
or we can say joules per kilogram, so the total amount of energy by some amount of matter,
or we can say the total amount of energy per unit mass of matter.
So the second quantity is temperature, and as I said, the internal energy is directly
proportional to the temperature of some amount of matter.
So we say that the temperature is a means of indirectly assessing the amount of thermal
energy stored in matter, so when you hear things like "a large temperature," what we're
really saying is that the matter has a large amount of internal energy, and we say when
the absolute temperature in Kelvin or degrees Rankine, that equals zero, then we effectively
are saying that that amount of matter has no internal energy.
The symbol that we always see is that temperature is symbolized by a capital letter T, and the
units associated with it in absolute units is degrees Kelvin or degrees Rankine In more
common units we say the temperature is in degrees Centigrade or degrees Fahrenheit.
What's meant by the term "heat transfer" is the thermal energy transport due to temperature
gradients.
So you know that heat flows from a high temperature to a cold temperature, so hot things tend
to cool off and cool things tend to warm up.
We'll eventually figure out that the total amount of heat transfer is symbolized by the
capital letter Q, and the units of this, we're talking about a total amount of energy, so
the amount of energy transport over some period of time for example, the units of this are
in joules.
When we talk about the heat rate, what we mean is the thermal energy transfer per unit
time, so we mean the rate at which heat is being transferred, and the symbol that's typically
used is a lowercase q, and the units are in joules per second, or watts.
And the difference between heat rate and heat transfer, what we're really saying is, we're
not concerned with the total amount of time or the total amount of energy that was transferred,
for example there would be 1000 joules transferred over a minute.
What we're really saying is over that minute, there is a rate associated with heat transfer,
so we say something like joules per second, so it's independent of the length of time
over which heat transfer is occurring.
What we're effectively doing to get between heat transfer and heat rate is we're taking
the total amount of heat transfer and dividing by delta T, and that will give us the average
rate at which heat was transferred over this time interval.
Let's take this one step further and define what is known as the heat flux.
Heat flux is defined as the thermal energy transfer per unit time, and per unit surface
area.
So what I've drawn is a small surface area and a large surface area, and if all things
remain the same, we would consider that the rate of heat transfer in watts would we greater
for the larger surface area than the small surface area, simply because there's a larger
amount of area for heat transfer to occur.
But what we're really interested in is accounting for this difference in surface area, so we
take it and we want to normalize by it, we want to know, is there a parameter that would
hold true for both of them?
Is there a parameter that is essentially intensive and independent of the surface area?
So let's do this: we're going to take the heat rate, q, and divide it by the surface
area.
If we doubled the surface area, the rate of heat transfer, q, would also double.
So this q over A is a way to normalize for the surface area, and the notation that we
use is q'', where the double prime represents the flux.
The units of this are in watts, the total rate of heat transfer, divided by meters squared,
for example, or we could say watts per foot squared.