Conduction Through Composite Wall Heat Transfer HMT Tutorial- 14, Heat and Mass Transfer, Mechanical Engineering, GATE Video Lecture | Topper Handwritten Notes & Videos for GATE ME

all right Maria so in this video I am
going to share with you conduction of
heat transfer through a composite slab
well if you are be bearing for any
university examination or maybe gate
examination then this topic is most
important alright so let me share with
you what what is that the mission we are
going to take for deriving the equation
what equation we require to solve
numerical problems right so for the
assumption is a complete state is
complete condition and the state will be
one dimensional complete state will be
one dimensional this is the summation we
are taking for solving the problem you
know let me first draw the circuit the
circuit which is really important for
this portion right this is the circuit
and here t1 is the temperature and here
you can see this one one resistance t2
is the intermediate temperature and t3
is here now as you can you know this is
thermal resistance rth one or pH two
let's say this right now as you know
according to four years law of heat
transfer what we know he was equal to
minus ka DT by DX right again we know
what DT DX DX is equal to V we have
already I have already share with you so
DT means t2 minus t1 so because we will
just multiply this minus here so things
will change so we can write B by K T so
we can write this equation like this T 1
minus T 2 B by K D so this B by K a is
the thermal resistance so here if we see
the first slab first slab this is the
first lab and this is the second slab if
we will see this first slab then RT h1
is equal to k1 k1 a and the same that
should be seen for this second slab RTS
2 is equal to B 2 K 2 a so this is this
is all about thermal resistance now once
we get the thermal resistance for this
lab we can easily find out the heat
transfer or rate of heat transfer
through this slab right so we know Q is
equal to Q is equal to D 1 minus D
things by the total resistance B 1 K 1 a
plus P 2 K 2 a right so this is the
total heat transfer rate now if it is
heat transfer rate and the unit of this
is what all right now cushion may be
asked that heat transfer rate okay let
me write first heat transfer rate per
unit area that means what per meter
square or sometimes we said W per meter
square right
so if quotient in the question is like
this what we should do we'll have to
transfer this area to this side that
means Q by a is equal to t1 minus t2 by
B 1 by K 1 plus B 2 by K 2 that's it
so this is the formula for finding out
heat transfer rate per area and this is
the formula for finding out heat
transfer rate for any composite slab for
composite slab only you need to invert
this and this is all about finding out
heat transfer rate through composite
slab well in my next in the last I mean
in this video only I'm going to share
with you a question which questions
already asked engaged 2006 I hope you
can read the question right so that's it
2006 okay
so in this portion what we have given
exactly we need to understand first we
are we have given a composite slab that
is important because we need to think
about composite slab
I have already shared with you what is
composite slab and now I will I'm going
to share with you how to solve the
question right away that's why if
anywhere you will get cushion related to
these you can solve the question quite
easily so first of all we have to draw a
composite slab so I have already to the
position so you need to read the
question first right so because you know
you don't know what about this tempo is
level now on that right so already they
have been asked that this side is W so
so this is David I'm just marking with
red line that's what you can identify
this is that we thought they said is
double and this side is single right now
the temperature is like this t1 and T I
and t2 here in the question will have
given di is equal to t1 plus DP by P
that means average average of these two
right so based on this diagram based on
this diagram what we have to do we have
to draw the resistance I mean the metal
diagram you must say okay Network once
you will come to know how to tow a
thermal circuit or you can social
network diagram the thermal circuit I
must say that because this is the
technical name of this thermal circuit
once you will come to know how to draw a
thermal circuit then the solve the
problem solve in a lawsuit or thinking
all much better for you ok I mean the
you can easily solve the question you
don't have any problem not this problem
once you will come to know how to draw a
thermal circuit so it's simple first
start here because you are having one
only one resistance here one type of
okay now second and then another
material because this is a composite
slab of two two that's why we have drawn
thermal circuit like this
here temperature one here temperature I
say temperature fridge here here we are
having something right
you know Q is equal to minus ka DT by DX
right this is the formula for four years
ago I mean this is a four tips law and
we have been studied couple of times
maybe have also gone through this
formula okay but here D X is me and all
those things are same here changing
temperature that means if I would say
from here to here what I have to write
for here for in this case T 1 minus TI
by be a by K a so the resistance would
be like this here to be because
thickness is here to be by K B K is
thermal conduction so suppose that this
is K 1 this is K 2 so k1 a right now for
this is B by K 2 a B by K 2 a okay now
let's go I'll go for the question okay
so this quotient will have given that
will have already a month off some dr.
we have to find out a relation like this
okay
so for this we don't need to find out
any numerical values so the thing is
that we the probability of doing mistake
is very less but here what is the case
here heat transfer it here in the first
lab is equal to it does parade in the
second slab so we can write the equation
like this Q is equal to t1 minus TI y to
be k1 K is equal to TI minus t2 by B by
K 2
okay now as we know T I is equal to t1
plus t2 by two because we have all day
live in this condition in the question
right so we have to put values TI and TI
here only
so let's write e1 minus TI t 1 plus t 2
by 2 and here also to be by k1 is equal
to t1 plus t2 by 2 minus t2 by b k2 e
now we will solve this quotient but we
caught here would be caught here that is
important that is important right so
what we got here after solving this we
can say I mean this down this idea to t1
minus t1 plus t2 right and t1 plus t2
minus 2 D 2 y 2 right so this is the
question I mean you know after what we
are getting here what we are getting
here these terms these two terms are
same okay so so what happened what
happen okay so and as you know if we
solve case and this what we want to get
this let me write so clapping will
happen to t1 minus T 1 minus T 2 by 2 so
here what will be meaning T 1 minus T 2
by 2 so let me first okay on the face
that's what we share with you
it's not so what we can write here that
is 1 minus T 2 T 1 minus T 2 by 2 B so
to give to be by K 1 a for the first or
a second second one is what here this
let me share with you so this is the we
have to simplify this one right so T 1
plus T 2 minus 2 T 2 by 2 so it will
happen T 1 minus T 2 by 2 so I can write
the same equation here T 1 minus T 2 by
2 divided by 2 so it will be by K 2 e so
this will this will cancel out now what
we can write to be 1 K 1 e and V by K 2
cross multiplication it will go cross
multiplication we are going to get like
this right now
AE cancel out be we cancel out so what
we can write Q 1 is equal to 2 K 2 what
we can write k 1 is equal to 2 K 2 so
this is how we can solve quotient if you
will get quotient come for composite
slab ok I hope you understand the
question as well as concept behind it
thanks for watching see you soon in my
next video bye