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Heat and Mass Transfer

Introduction

Learning outcomes:
1. Understand the practical importance of heat and mass transfer
2. Describe and quantify heat transfer by conduction

Heat and Mass Transfer

Heat and mass are transferred in practically every process
and event around us. Whether it is boiling water for an afternoon cuppa,
melting a piece of ice you have in your drink, or microwaving your late dinner.

Heat and mass transfer are also often inseparable. Think
about it, what is being transferred when you:

Image: Apple pie

- take out a hot apple pie from an oven? Hint: can you feel
that air around it becomes warm? Can you smell it?

Image: Tea and cream

- put cream to your tea (or coffee, if you anywhere else
than the UK)? Hint: you probably store the cream in the freezer, so it is safe
to assume it was cold while the beverage was hot. Also, can you notice any
changes in the colour?

Image: Hot shower

- take a hot shower? Hint: you probably thought about
flowing water, but how about all that generated steam?

Heat and mass transfer are important in everyday life but
are also at the core of all manufacturing processes. For example, all chemical
reactions require reactants to be delivered to the place of reaction, and
products to be taken away – clearly, some mass transfer needs to happen, or we
will see no reaction or reaction that stops very quickly. Heat transfer is also
important – reactions may need some energy input to happen or may release
energy. If heat is not being efficiently transferred, again, reactions will
stop or, in contrast, release so much energy that the situation can lead to a
thermal explosion!

Challenge! Can you think about 5 specific processes either in industry
or in everyday life where we want to control heat and mass transfer?

Some examples for you, but you can include many more: making
ice cream, producing polymers, for example, nylon, running nuclear reactors
(did you know that submarines have small nuclear engines?), pasteurising food
to kill germs, extracting heat from your laptop, preventing the creation of
pollutants.

So how do we control heat and mass transfer? Firstly, we
need to look into fundamental principles to understand all the possible
mechanisms. You can find more information in the provided resources.

https://www.youtube.com/watch?v=YK7G6l_K6sA

https://www.youtube.com/watch?v=B0CwRyBlt1s

Conduction

A piece of a stainless steel rod is heated on one end until
it becomes red. You take it from another end – currently cold. What do you
expect will happen as time passes? The end of the rod that you hold will slowly
become warmer and warmer, going beyond the point where it will start to burn
your hand, and you will need to drop it.

The reason why one end of the rod starts to heat up was
given by Isaac Newton in 1701 when he was in Cambridge. Newton said that heat
would be transferred from a hot object to its surroundings as long as they have
different temperatures. While this statement concerns an object and its
surroundings, it as well explains the fundamental reason for heat transfer –
and this is the temperature difference. So in our case, even though we have
only one rod, its temperature is different at ends, so heat transfer happens in
the rod itself, through its material – steel.

The heat transfer mechanism through a solid material is
called conduction and was for the first time mathematically described by Joseph
Fourier in 1822. Following Fourier, we can calculate how much heat is being transferred
in a unit of time (so per second):

or
in a mathematical form:

where Q is the rate of heat transfer, A
is the area, k is the thermal conductivity, dT denotes the temperature
difference (the reason for heat transfer), which we observe at the distance dx.

Here, the thermal conductivity represents
the property of the material that allows it to transfer heat. So how do
materials do that, and why some transfer heat quickly (think stainless steel
rod), while others not (Styrofoam). As it turns out, materials transfer heat
through vibrations, movement and collisions of atoms. In metals, the atoms in
the hot region vibrate quickly, affecting neighbours, so passing some energy
further. In gases, molecules are far away from each other, so energy can be
passed only if one molecule collides with another. Hence, stainless steel is a
good heat conductor, while Styrofoam with plenty of air in its porous structure
is a bad heat conductor.

Once we know how quickly heat is
transferred through materials, we can start designing some control techniques.
Think about it – what could we do with the rod situation to transfer heat
faster or slower?

A simple example.

A study room has one external wall
measuring 5 m x 3 m, and is made of 30 cm thick clay brick, for which thermal
conductivity is 0.7 W m-1 K-1. Now, we use a hollow brick
of the same thickness but thermal conductivity of 0.3 W m-1 K-1.
How does this influence the rate of losing heat from the room at 20º to the outside at 5ºC?

Let’s go through this together.

In the situation with the regular clay brick,
we calculate that

In the situation with the hollow brick,

What it means practically is that in the
first case, we need to constantly provide 750 W of heat to the room, for
example, from radiators, to keep the temperature in the room constant. If we
use the hollow brick, we only need to provide 250 W.

Why is silver cutlery not practical?

In the 17th century, the most fashionable
cutlery was made of silver. Nowadays, we use much cheaper stainless steel. But
the reason for switching to steal was also more practical. The thermal
conductivity of silver is 430 W m-1 K-1, and it is one of
the largest values found in metals! What it means is that silver conducts heat
very quickly, and if you use it for eating piping hot food or stirring hot tea
– your fingers will quickly feel the incoming heat! Stainless steel, on the
other hand, has a k of 14 W m-1 K-1. In comparison to
silver, it will conduct 30 times less heat per second, preventing us from
burning our fingers.

Reflective questions

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Task 1

What are the key arguments, concepts, points contained within it?

Task 2

What are you struggling to understand?

What could you do to improve your understanding of these concepts/terminology etc.?

Task 3

What further questions has this resource raised for you?

What else are you keen to discover about this topic and how could you go about learning more?

Can you make any links between this topic and your prior knowledge or school studies?

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