INTRODUCTION TO HEAT AND MASS TRANSFER
At the high
level when we think of heat or mass transfer we need to think about the flux equation there's this general equation that applies time and again
to everything we're going to be doing and that
is this rule that tells us that flux is
equivalent to some kind of coefficient which we'll just abbreviate times some driving force and so
without looking at any numbers or any greek
letters this is all it's telling us is that
we've got some flux is
equal to this coefficient times a driving
force and i was beginning to depict these
terms what we're going to know is that flux is equivalent to a quantity per area per
time and then this coefficient is generally
something that's in a form of like a k or some some literally just a constant or coefficient that depends
on some other factors and then this driving
force is usually some kind of difference
between two things or
a differential and so when we take this kind of template breadboard and look at the heat
transfer equation that we may have learned in
high
school chemistry or physics class usually what you'll see people write is this
stuff where you've got you to know q dot is equivalent to k times a times delta t
or something like this and as you introduce differentials into these equations we
look at the dt kind of temperature gradient and so this flux if we look at this
equation here is really just dividing both sides of this equation by area so
flux here corresponds to this q dot over a term I'm sorry my, uh computer's
acting up a little bit but you get the point so flux is equal to this
coefficient times this driving force and specifically this heat flux is
equivalent to this coefficient of heat transfer times a difference in
temperature some kind of temperature gradient and what we also remember from
the fundamental laws of thermo is that heat is transferred from hot objects to cold
objects so we know the directionality of this heat transfer
so
very important to remember that heat moves from hot to cold objects and we can
say something very similar to things regarding mass transfer and when we look
at mass transfer we'll say that mass moves from high to low concentrations so
if I took a ball pit of many
different
colored balls just like we used to have a chuck e cheese and we had all these
red balls stuck in the corner that's an area of high concentration and what do
I expect to happen over time is we have mass transfer occurring in my ball pit as
I expect to see a bunch of my red balls eventually diffuse through the ball pit
and then they'll be widely distributed everywhere just the same thing can be
said with heat or this energy it's that energy doesn't like to be jammed up in
this one spot it wants to kind of diffuse through systems and if we ask ourselves
the big question here why is because it's how we maximize entropy how do we
give something the most degrees of freedom it can possibly have in our closed system
and so um this is the very important conceptual overview of everything we're
going to be discussing in heat and mass transfer classes as engineers and
scientists now the next
the thing
we're going to be looking at is the units that we're going to be using or the
dimensions that are going to be in all of our equations and so when we talk
about a rate of heat transfer like how many joules per second of something are
moving through an object we usually define the term watts so w I'll just write
it out watts one watt is equal to one joule per second so it's a rate of energy
how much energy have I just transferred in this given period is equal to
one watt and so commonly when we're talking about a heat flux which I'll put a
little hat on top of our cube just so we know that q q hat which is really
equivalent to this q dot
over the area this heat flux is equal to q dot which q dot is just going to have units
of watts per area so if we look at the dimensions on this equation we'll have
watts per and we can go with like meter squared area will be equal to some coefficient
of heat transfer and my computer sucks today anyway um some kind of coefficient
of heat transfer which I'll just leave it to ask for now and we'll keep these
dimensions the same and we can actually do a dimensional analysis determine
what, uh k is so it's going to be equal to some coefficient
times
a difference in temperature this difference in temperature will have units of
something like degrees Celsius or degrees Kelvin for instance and I'll go with
degrees c just so that I am sticking to not having too many k's present so this
thing here will have units of
times
you know degrees c so you'd have like 0 and 100 degrees celsius would be this difference
in temperature that is causing a movement of energy in your system and so if we
wanted to do a dimensional analysis and say like okay tell me what are the
units of uh k in this equation it's literally just rearranging it k your
coefficient of heat transfer is going to have units of watts per meter squared
per degree celsius and so these can have a lot of different dimensions to them depending
on what units you're doing within your specific problem statement and so when
we look at something like mass transfer i'm going to try to keep this video short
too by the way but when we look at units of mass mass transfer well what do we
measure mass in we measure mass usually in stuff like kilograms or kilomoles so
we've got kilograms and we're carrying about some rates so this would be a
kilogram of something moved per second for instance would be equivalent to what
is our heat flux or i'm sorry our mass flux and then we're going to be dividing
this whole thing by the an area so we'd say you know how many kilograms per
second are moving through this material in one square meter of space for instance
and so this would be the left side of our general flux equation
and
on the right side we're going to have again some kind of coefficient of mass
transfer which i'll again just say let's call it k sub m k sub m times and then
a driving force for this mass transfer and this driving force is going to have
units of concentration differences so how many you know kilograms per given
volume are we going to have of something that is resulting in this mass exchange
and so if we begin to think about well what is units of concentration as we
were saying this is usually equivalent to you know we can think of stuff in
terms of like moles per uh something so i'd say like kilomoles per cubic meter
and then if we do some kind of dimensional analysis on this and for the sake of
uh simplicity i will keep things in units of kilograms per cubic meter so it's
amount of stuff for a given volume and if we were to now do a dimensional analysis
on what is k sub m k sub m would be equivalent to the following so we would
have kilograms per second per square meter and we would multiply this by the
reciprocal we would have kilograms per cubic meter so the dimensions on the following
here would be meters per second which is actually equivalent to velocity which
is very interesting but anyway so these are the dimensions we're going to be
working with in our mass and heat transfer equations and these are the core
concepts that we should just get right from the start and then to give an
example problem of something that you know i think all of us can relate to if
we think about the following in which we are sweating I think it's an excellent
example of something that shows how connected rates of heat and mass transfer
are to one another and uh to set up some kind of example problem that can be
food for thought let's say that the human body has an area of two square meters
so you've got two square meters of exposed skin and when we are sweating what's
happening to this sweat so if I was to take a section of skin exposed skin and
we've got this sweat right here on the surface i'll just label this skin and
sweat and we think about what is the objective of sweating it's to cool us down
right so the objective here is to cool down the body as soon as possible because
you're really hot and what is happening here is when we think about the two
things that are happening with the sweat is number one we are changing the thermal
properties of our skin by having this fluid on its surface it's making this
fluid much more conductive and or it's making this surface a lot more
conductive which is allowing a lot more heat to go from your body to the
outside world assuming that you know if you had t sub b and t sub a where t sub
b was greater than t sub a which is generally the case because your body
temperature is 98.6 outside temperature is probably 70 degrees c or i'm sorry
70 degrees f you're going to have temperature flowing you're going to have heat
flowing in the direction from your body to the outside world so this would be q
sub dot right there and so the two equations here to think about would be in
terms of this heat transfer that is occurring at this moment in time we can say
that q dot will be equivalent to some kind of coefficient of heat transfer
which i'll just call k and then this would be q dot per area by the way just we
stick to what we were talking about earlier.
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