Fins Introduction, Efficiency & Effectiveness HMT Tutorial- 21, Heat and Mass Transfer, GATE Video Lecture | Study Topper Handwritten Notes & Videos for GATE ME - Mechanical Engineering | Best Video for Mechanical Engineering

- so welcome to this total and in this
short well I'm going to share with you
theme or this is all about things right
what is themes and what we can do with
is how to solve numerical problems if
you will get related to this topic right
so what is means basically so basically
what happens we use fins in case of
automobile refrigerator condenser you
can say a refrigerator condenser you can
say such type of you know such type of
robot type and come with a structure in
the bad side of the refrigerator most of
the time right but nowadays it's you can
say such type of structure in the whole
ref heater but nowadays it's covered
okay now now the thing is that what is
feels basically so fins it is you know
it we use it for increasing heat
transfer rate heat transfer rate we use
themes for increasing heat transfer rate
okay what know while we used
I mean auto mobile means I'm talking
about bite we used in bike right so this
is this is all about fin
but now the most important factor is
that that is most important what is that
that is what we exactly do with the
things right so first of all things we
use to increase the heat transfer first
second what kind of things we used so
now I am going to draw a diagram which
diagram will help you to discover the
basic concept of this if you want it
solves no medical problems
related to being fiend so you must have
been things right so you record
something amazing right this is the
Tyler suppose it is the diagram of
things and here this thickness here Q X
is entering to this thing and we get in
Q X plus DX okay suppose that length of
the fin is a and this chair at and
thickness is T and here and this is a
base world let's say this is a base one
right this is you can say this one is
Road okay now route or base were both
route or base of teen both the same now
here what is going on at conviction is
point one why suppose that you will see
some kind of things in bike and because
bike will be run that means the
temperature that heat will transfer from
it's surrender or engine to things and
things will transfer hey lead to the
surrounding air that's which process is
going on there convection process is
going on there
okay so this is the diagram and this is
a typical thing and he must say this is
a rectangular thing will be mess of just
a lysosome paralyzes okay so here with a
thickness of the plane chad is weak of
the field now most important thing what
are our gently objectives from this
derivation or must say this this comes
about this video exactly in this video i
am going to share with you temperature I
mean how to find out slow how to find
out it transfer rate real things I am
going to share with you here only okay
now what happened we have in Q X and Q X
plus B X what is Q X and what is Q X
plus DX we need to know Q X means hit
can
into element that means K a DT by DX it
conducted into the element and QX + TS
hit conducted out of the element okay so
here QX + curly by curly X key works
into DX so this our two equations we are
using here now if you wanted to write
energy balance equation for steady state
condition of diamonds suppose that we
wanted to write energy balance equation
for the steady state condition of this
of these elements of this element that
means of this Fein then what we should
write the so we he'd he'd conducted it
conducted into the element is equal to
heat conducted heat conducted out of the
element out of the element plus heat
conducted from our heat convicted from
the surface of element heat convicted
from the surface or element right so
where we going power Q X is equal to Q X
plus BX plus Q convection because
convection process is going on there
right now let's go for the next step
that is why you can understand about it
what exactly going okay so here what
what is going on your Q X is equal to u
X plus thirdly by thirdly X Q X into DX
h P DX t minus 10 fit because of this
convection process now if you we will
simplify this
now if we'll simplify this what we are
going to get QX plus we cancel right
this one Ichiro this one Ichiro and
jiwoo is equal to curly white curly X
cube X into DX plus h P DX t minus
tinfinity
we can transfer this DX takes to this
side that means this will become again
zero so d if we will again differentiate
this equation other than ugly just okay
1 and 1 cancel out right so D Square t
be X square H P by ka t minus T infinity
is equal to 0 right and one the most
important thing you know what is that we
know m is equal to root under H K by K G
so slope this is a slow and it's unit is
per meter or you can say meter minus one
so so what exactly I am trying to say
we're just going to put to the value of
this here in this equation so Li square
T DX square M square t minus T infinity
is equal to zero right now and till this
point we can get this one right now
suppose that we are putting t minus T
infinity is equal to theta
is equal to FX after differentiating can
say DX is equal to D theta by DX and D 2
squared is equal to least capita by DX
square so we can put this value here so
what we get D 2 theta by DX square minus
M square theta is equal to 0 and this is
a standard format of second order
differential equation you know that ok
so after solving this differential
equation we'll get the value will get
the value that is theta 1 is equal to C
1 it will be per MX plus C 2 e to the
power MX after solving the whole
equation ok now this is all about all
about and yes you see once into constant
this is all about finding out theta
I mean slope right now we have your
cases we have in cases in fins and what
type of things we are going to use right
so we need to understand of all those
cases also so let's go for the first
step first case case first right so it
tastes fast what happened suppose that
fin is in finitely long ok very long by
long FINA can say then what will happen
for its heat transfer rate so heat does
permit Q is equal to K ay M e naught
minus T infinity is equal to we can say
also based ad say I of H a P K right T
naught minus T infinity this is the
formula if we are trying to solve the
inside finish in fact long and we wanted
to find out heat transfer rate now next
if we say this is this is it ok this is
it
if will say finite the length is finite
length is finite
and tip keep is insulated tip of the fin
is insulated okay if length is inclined
and T piece of the thing is insulated
then how we are going to find out it's a
heat transfer rate so for this we are
having formula Q is equal to HP K ay T
not minus infinity M hypo m l-c this is
most important and one of the most
secret yeah yeah that is most important
I would like to share with you secret is
here if in the problem we don't have
given any case then we have to consider
this case by default remember this okay
this is important right so let me use on
the same okay now now now most important
yeah most important yeah yeah most
important that is yeah let me show you
first
yeah I'm sorry if fired tip is not
insulated I must say that then we'll
have this one now Third Point if T P is
this is finite length finite length and
tip is insulated
if TP is insulated then what we are
going to get this I mean how we can find
out so Q is equal to HP K ay T naught
minus T infinity and hypo ml now one
thing I haven't shared with you that is
LC what is L see L is length of the
field as I have already shared with you
but what is else is LT else is
characteristic length okay so we are
having two types of fins one is
rectangular type and another one is a
pin fin or you can say circular type so
in case of rectangular field LC
is equal to n plus T upon 2 T is
thickness and in case of circular LC is
equal to L plus D PI for base diameter
of that circle so this is how you can
find out heat transfer rate in case of
thin alright now if you wanted to find
out any other things just like suppose
that efficiency then that's also simple
okay now what I am going to share with
you that is the effectiveness of thing
right so let's go foil with a thickness
of thing effectiveness of thing but
suppose that you wanted to find out
effectiveness of cream and you know why
we use thin because of its effectiveness
it increases heat transfer rate then
without using fin so if we are using
thin that means it must increase heat
transfer rate okay so if if activeness
of the field is greater than 2 or equal
to 2 then we use only thin if it is not
greater than or equal to 2 then we are
not going to use fin remembers that this
is tricky I mean this is important most
of our time objective type ocean you can
see okay now most important thing if if
we wanted to find out effectiveness that
is that is epsilon then what what is the
formula for this so for a definition you
will both definition then the formula is
C liters per day to the heat transfer
rate of the fin to the heaters per date
without existing the thing suppose that
heat transfer rate is 20s with film and
without finished M then is equal to 2 so
that means according to our standard we
are going to use fin in that system if
it is less than 2 we are not going to
use Fein in our system okay no
let's go for the efficiency of the fiend
so what would be the formula for
efficiency of the Ring fecl see my
friends efficiency of Fame efficiency is
equal to Q actual heat transfer it
actually actual I know you must say
actual heat transfer rate taking place
to the theme by maximum possible heat
transfer rate that can open to the thing
okay
so maximum possible heat transfer rate
of the things so actual means root under
HP ka
tan theta minus P infinity T naught
minus T infinity 10 hypo ml 5 by you
must say that yeah so it is H P L P not
minus infinity so we can say that tell
hypo ml root under HP k a into L you can
say this okay so this is how you can
find out efficiency or efficiency of
thing now other thing is mostly
important that is word that is also I
need to share with you in this case is
applicable only for you know only for
general type now if insulated teeth if
we we are we are considering a thin
which is having inserted and insulated P
then what would be the efficiency of fin
efficiency is equal to 10 hypo ml by ml
and and if fill is infinitely long if
fin is infinitely long then what would
be the efficiency of the fin infinitely
long then it will have 1 PI ml m in
slope ll is
so I hope this is a lambda lecture I
think so we have you maybe you got bored
but yeah I had to share with you this
lecture so this is all about themes and
hope you enjoy the lecture you have
blonde lot of things from this lecture
so thank you very much for watching see
you soon in my next video bye bye