one of the easiest ways to solve a
one of the easiest ways to solve a

problem that has more than one mode of
problem that has more than one mode of

heat transfer or different conduction or
heat transfer or different conduction or

convection coefficients is the use of
convection coefficients is the use of

thermal circuits what is an example of
thermal circuits what is an example of

this well let's look at a plain wall
this well let's look at a plain wall

here it has a thermal conductivity of K
here it has a thermal conductivity of K

then we have out here some surrounding
then we have out here some surrounding

temperature will call T infinity 1 and
temperature will call T infinity 1 and

then a surface temperature TS 1 a
then a surface temperature TS 1 a

surface temperature TS 2 and finally a
surface temperature TS 2 and finally a

surrounding temperature of T infinity to
surrounding temperature of T infinity to

the surrounding temperature on the left
the surrounding temperature on the left

has a heat transfer coefficient of H 1
has a heat transfer coefficient of H 1

and out here is H 2 and H 1 does not
and out here is H 2 and H 1 does not

equal H 2 in this particular problem how
equal H 2 in this particular problem how

do we solve for Q in this situation so
do we solve for Q in this situation so

what we're going to do is use an analogy
what we're going to do is use an analogy

between heat and electrical charge both
between heat and electrical charge both

of them have a driving force divided by
of them have a driving force divided by

resistances for example current has
resistances for example current has

change in voltage over an electrical
change in voltage over an electrical

resistance here our heat rate is a
resistance here our heat rate is a

change in temperature over a thermal
change in temperature over a thermal

resistance how do we find our
resistance how do we find our

resistances let's start with our
resistances let's start with our

conductive resistance so we go back to
conductive resistance so we go back to

that equation for Q conductive
that equation for Q conductive

resistance equals delta T over Q we just
resistance equals delta T over Q we just

rearrange this which is delta T over Q
rearrange this which is delta T over Q

conductive which is K a delta T divided
conductive which is K a delta T divided

by L so
by L so

our conductive resistance is l / k times
our conductive resistance is l / k times

a where L is the length of the wall and
a where L is the length of the wall and

a is the area right here that Q goes
a is the area right here that Q goes

through now let's look at our convective
through now let's look at our convective

resistance here we use delta T over Q or
resistance here we use delta T over Q or

our convective resistance which is delta
our convective resistance which is delta

T and now convection is H our heat
T and now convection is H our heat

transfer coefficient times this area as
transfer coefficient times this area as

shown before times delta T so our
shown before times delta T so our

convective resistance is 1 over H times
convective resistance is 1 over H times

a for trying to find our Q again its
a for trying to find our Q again its

delta T divided by our total resistances
delta T divided by our total resistances

so if we go back here and look at our
so if we go back here and look at our

picture the first resistance is the
picture the first resistance is the

convective resistance when we're looking
convective resistance when we're looking

for our total we start with 1 over H 1 a
for our total we start with 1 over H 1 a

now we go to TS 1 and the next thing we
now we go to TS 1 and the next thing we

have is our conductive resistance
have is our conductive resistance

because we have conduction through the
because we have conduction through the

wall we had convection that caused the Q
wall we had convection that caused the Q

between the temperatures of T infinity 1
between the temperatures of T infinity 1

and TS 1 now we're going to look at the
and TS 1 now we're going to look at the

difference between TS 1 and t s 2 and
difference between TS 1 and t s 2 and

its resistance we have a conductive
its resistance we have a conductive

resistance now we have this third
resistance now we have this third

resistance between T s 2 and T infinity
resistance between T s 2 and T infinity

2 and this is a convective resistance so
2 and this is a convective resistance so

it is 1 over H 2 a because we have a
it is 1 over H 2 a because we have a

different heat transfer coefficient
different heat transfer coefficient

and so now when we find Q our delta T is
and so now when we find Q our delta T is

from T infinity 1 minus T infinity 2
from T infinity 1 minus T infinity 2

because those are the two temperatures
because those are the two temperatures

that we're going from over the sum of
that we're going from over the sum of

the resistances the beauty of using
the resistances the beauty of using

thermal circuits is that we can find the
thermal circuits is that we can find the

temperature difference between any two
temperature difference between any two

points the reason for this is that Q of
points the reason for this is that Q of

X is a constant how do we know that Q
X is a constant how do we know that Q

sub X is a constant in other words it's
sub X is a constant in other words it's

not a function of X well let's go back
not a function of X well let's go back

to our temperature profile which is T of
to our temperature profile which is T of

x equals a constant times X plus a
x equals a constant times X plus a

second constant we determine this from a
second constant we determine this from a

previous screencast which use the heat
previous screencast which use the heat

diffusion coefficient and simplified it
diffusion coefficient and simplified it

for a plane wall remember that Q is
for a plane wall remember that Q is

minus K a DT DX and when we take the
minus K a DT DX and when we take the

derivative of T with respect to X what
derivative of T with respect to X what

we end up with is c1 which is a constant
we end up with is c1 which is a constant

which is not a function of X so let's
which is not a function of X so let's

see how we can use something like that
see how we can use something like that

if we go back to our picture we want to
if we go back to our picture we want to

find out something between T infinity 1
find out something between T infinity 1

and T s 2 then we know that Q equals T
and T s 2 then we know that Q equals T

infinity 1 minus T s 2 over the total
infinity 1 minus T s 2 over the total

resistances between the two of those
resistances between the two of those

temperatures and the resistance is our
temperatures and the resistance is our

first our convective resistance and then
first our convective resistance and then

our conductive resistance so once you
our conductive resistance so once you

determine Q then you can figure out
determine Q then you can figure out

another temperature just using the idea
another temperature just using the idea

of thermal circuits
of thermal circuits