The effects of temperature are everywhere in our daily lives.
I bet that you often check the temperature outside before going out. [1] [2]
Or, do you feel the heat from your smartphone when you charge it, or when you overuse it? [3]
If you heat a slice of pizza in a microwave, will you be annoyed by
the uneven temperature of the food? [4] In fact, heat is generated or utilized by many
engineered structures or machines. The performance of these structures
may depend greatly on the temperature experienced during its operation.
Conducting heat transfer analyses allow us to understand the temperature distribution over the
domain, which can help us evaluate whether or not specific requirements are met for the product.
Before talking about what is heat transfer, let’s have a quick review of structural
analysis with force and displacement. You will see why it is needed very soon.
In a typical structural analysis, for example, we are pulling this simple paper clip,
the input is the load we applied on the edge of the paper clip, and we are looking for the
displacement as the unknown caused by this load. Of course, for dynamic analysis, we are also
looking for the derivatives of displacement that are velocity and acceleration.
As structural analysis relates forces to displacements, heat transfer is no
more than the study of the relationship between heat flow and temperature.
For heat transfer, you will see a similar but different governing equation. The variables are
different, but the format is similar. On the left side of the equation,
we have a matrix multiplied to a vector, the vectors are our unknowns. On the right side,
it’s a single vector representing the “load” (use hand gesture for quote).
In heat transfer problem, our unknowns are temperature
and its time derivative. And our input “load” (use hand gesture for quote) is heat flow.
With this governing equation, a simple heat transfer problem could be the following: when
we turn on the oven, how long does it take for the cookies to reach 190 Celsius degree? Here,
the oven is the heat source, and the temperature of our cookies
is what we want to determine. [5] Since we are going to study heat transfer,
let’s first answer the question, what is heat? And What’s the format of heat?
Heat is a form of energy. It is produced when a rise in temperature causes atoms
and molecules to move faster. As a form of energy,
the unit of heat is Joule (J). For heat flow, the quantity Q,
in the governing equation, is also called heat flow rate. It is the
amount of heat that is transferred per unit of time. Then, naturally,
the unit for heat flow is Joule per second, which is also called a Watt.
I believe Temperature is a much more familiar quantiy to all of us.
There are various of temperature scales. The most commonly used scales are Celsius scale, Kelvin
scale, Fahrenheit scale and Rankine scale. For Celsius and Fahrenheit degree, you might see
them often from weather report, depending on which country you are living in.
For kelvin scale and Rankine scale, they are mostly used in Astronomy and Theoretical physics.
Temperature values in Kelvin and Rankine scales are always positive, because they use absolute
zero as 0 K and 0 R. Absolute zero is the coldest conceivable temperature, at which no
more energy can be removed from the system. There is a corresponding relationship between
Kelvin degree and Celsius degree. That is, a temperature difference of one Kelvin degree is
defined as equal to one Celsius degree. As 0 K equals to -237.14 Celsius degree, we can see that
1Keiven equals to -236.14 Celsius degree. Same relationship between Rankine scale
and Fahrenheit scale, as 0 Rankine degree equals to -458.67 Fahrenheit degree, 1 Rankine degree
equals to -457.67 Fahrenheit degree. Let’s have a look of what kind of application
requires heat transfer analysis. In many cases, heat is the enemy. And we want to
reduce or limit it for the mechanical system. For example, when the computer is running,
excessive heat may damage the electric components. Or for a car engine,
the overheating of the components can be a safety hazard or lead to other issues.
Sometimes, heat transfer analysis is needed for the design of an insulated space. For example,
how long can the cooler keep your beverages cold? Or how quickly should the pizza in an insulated
bag be delivered before it is no longer hot? Or even for a house with insulation,
what temperature can be maintained in the living space during a harsh winter?
Of course, heat is not always the enemy. It can be an important energy source that
we want to utilize. For example, without heat, how can we me bake delicious cookies?
For an engineer, to design an efficient oven, we need to understand the temperature
distribution within it to make the most efficient use of heat.
Or for the solar energy industry, the heat from the sun is transformed to electricity energy.
So in designing and analyzing solar panels, our goal is to maximize the sun’s incident energy
while minimizing heat loss. As we mentioned, the effects of
temperature are everywhere, and the applications of heat transfer are definitely not limited
to what we have shown here. Therefore, heat transfer is a very
important subject for engineers to be familiar with.