Mechanical Engineering Exam > Mechanical Engineering Videos > Topper Handwritten Notes & Videos for GATE ME > Radial Conduction Heat Transfer Through Hollow Cylinders HMT Tutorial- 16, Heat and Mass Transfer, Mechanical Engineering, GATE
Radial Conduction Heat Transfer Through Hollow Cylinders HMT Tutorial- 16, Heat and Mass Transfer, Mechanical Engineering, GATE Video Lecture | Topper Handwritten Notes & Videos for GATE ME
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FAQs on Radial Conduction Heat Transfer Through Hollow Cylinders HMT Tutorial- 16, Heat and Mass Transfer, Mechanical Engineering, GATE Video Lecture - Topper Handwritten Notes & Videos for GATE ME
| 1. What is radial conduction heat transfer? |  |
Ans. Radial conduction heat transfer refers to the transfer of heat through a hollow cylinder in a radial direction. It occurs when there is a temperature difference between the inner and outer surfaces of the cylinder, causing heat to flow from the hotter side to the colder side.
| 2. How is radial conduction heat transfer calculated through hollow cylinders? | |
Ans. The radial conduction heat transfer through hollow cylinders can be calculated using the formula:
Q = 2πkL(T1 - T2) / ln(r2/r1)
where Q is the heat transfer rate, k is the thermal conductivity of the cylinder material, L is the length of the cylinder, T1 and T2 are the temperatures at the inner and outer surfaces of the cylinder, and r1 and r2 are the inner and outer radii of the cylinder.
| 3. What factors affect radial conduction heat transfer through hollow cylinders? | |
Ans. Several factors affect radial conduction heat transfer through hollow cylinders, including:
- Thermal conductivity of the cylinder material: Higher thermal conductivity leads to a higher heat transfer rate.
- Temperature difference between the inner and outer surfaces of the cylinder: A larger temperature difference results in a higher heat transfer rate.
- Length of the cylinder: Longer cylinders have a larger surface area and therefore higher heat transfer rates.
- Inner and outer radii of the cylinder: Larger radii result in higher heat transfer rates.
| 4. How does radial conduction heat transfer through hollow cylinders impact engineering applications? | |
Ans. Radial conduction heat transfer through hollow cylinders is relevant in various engineering applications, such as heat exchangers and thermal insulation systems. Understanding and calculating radial conduction heat transfer is crucial for designing efficient systems that require controlled heat transfer between different mediums.
| 5. What is the significance of studying radial conduction heat transfer in the context of mechanical engineering exams like GATE? | |
Ans. The study of radial conduction heat transfer through hollow cylinders is important for mechanical engineering exams like GATE as it tests the candidate's understanding of fundamental heat transfer principles and their ability to apply them to practical engineering problems. Questions related to radial conduction heat transfer help evaluate the candidate's knowledge of heat transfer calculations, thermal conductivity, and the impact of various parameters on heat transfer rates.
Text Transcript from Video
alright - so in this video I'm going to
share with you yeah you can read right
now the radial conduction heat transfer
through a hollow cylinder right and as
you can see me we have a power symbol in
front of us and that's why you can
understand about it quite easily so in
this toter well I'm going to share with
you the concept of hollow cylinder first
and second I'm going to also going to
share with you a problem which has been
asked in cage 2007 Sam Smith
I hope you wanted to learn numerical
problems with along with theoretical
right so first of all in case of
cylinder in case of cylinder we need to
learn what is the formula for finding
out area office later so you know area
is 2 PI R M now if we see this this is a
follows in the right and internal radius
is R 1 outer radius is R 2 so if you say
a1 is equal to 2 PI R 1 L and a2 is
equal to 2 PI R 2 L right
so if you want that I think you can
understand what I am talking right now
so now for finding out he tasks per
weight we need to learn at least in case
of conduction that is Fourier law here
is equal to minus K DT by DX right now
what is DX but in case of silver we have
to consider this as DT by D F because DX
we used in case of slab right but in
case of cylinder we have to use BR
because we are dealing with radius okay
our diameter you can see but we are
considering here radius there so I am
putting here are right now next what is
next that is minus kV
we know t2 minus t1 right this has
happened T 2 minus T 1 be our Thanks no
no till now we have done we have done
but here we have to do some extra work
because we are finding out heat transfer
for follow cinder so you know area any
is what - a a a means 2 pi k means 2 pi
RL right now this would be T 2 minus T 1
okay okay let's it with DP y dr q is
equal to this now if I will indicate
both sides I'll integrate both sides
like this let me write I am letting with
Aron's in that way there so you can
understand so Q send this dr to this
side and our to this side so d r by r
minus K 2 pi L DT and this will be what
to do this would be do you want to do I
hope you what it is okay no no
integration of this what will happen Q
natural rock here - let us say 2 K pi L
T 2 minus P 1 because you th n of DT
will be T and DT by sorry d ry
R would be natural log R 2 by R 1 ok
this is a simple formula for finding out
integration right now what I am going to
do I am going to multiple this minus
sign here so - okay 5l t1 minus t2 right
now I am going to send this to this side
so Q is equal to Q is equal to D 1 minus
D 2 Phi natural log R 2 by R 1
even this I can write this one like this
is 1 by 2 pi 2 pi jl 2 pi clear so this
is this is the formula this is the
formula for finding out heat transfer
rate in a hollow cylinder I hope you
understand and here we are assuming one
thing we are assuming these area and one
more thing steady state condition first
and second one dimensional one
dimensional heat transfer we're
considering these two things here for
finding out heat transfer rate of him
follows the endurance I hope you
understand the question right so would
you like to do would you like to learn
that problem which problem has been as
engaged 2007 and that is totally based
on that is totally based on this formula
I hope you are interested right and one
more thing if you wanted to learn if you
wanted to learn this thing in writing I
must see one thing that is to learn
thermal circuit how to draw a thermal
circuit this is t1 this is t2 and this
is H and you know the formula for rth in
this case that is just amazing that is
just amazing you need to understand the
formula which formula you required right
so that would be RTS is equal to natural
log log R 2 minus R 1 by 2 pi here this
is the formula for thermal resistance
for thermal resistance for finding out
thermal resistance in case of also
follow and this pretty formula I am
going to
use to solve the numerical problem which
has been asking get 2007 right I would
understand it right so let's go for that
for that potion that's why you can
understand wait yeah yeah we caught the
question and I hope you can right now
you can treat the quotient the whole
portion so here what we have even a long
glass cleaner of inner diameter is this
and outer diameter is this so suppose
that this inner this is outer okay so
this in no time
victory is 0.03 meter and it's outer
diameter is 0.05 meter simple now K is a
hot fluid inside it in thermal
conductivity of class this class K is
equal to one point zero five what meter
Kelvin per meter can the thermal
resistance scale K resistance R yes you
need to find out Kelvin per watt okay
now as we know thermal resistance for
almost Linda I have already share with
you natural rock R 2 minus R 1 by 2 pi K
L here we have given all just we need to
find out what per unit length and this
is R th you need to understand the
quotient right so we have we have given
R 2 by R 1
that means 0.05 by 0.03 okay 2 pi K
means how much cake 1.05 all unit we
have checked okay now L is remaining but
we don't have given the value of L with
even don't require because it is s here
only kilo per word per unit length that
means we have to send this L don't here
got it now after the solution well right
now I don't have calculator I have a
Miss somewhere right so let me share
with you what would be the answer for
this question that is for discussion
here 1 0 7 7 g open 0 7 7 know the
approximate answer is zero point zero
seven so 0 1 yeah this is the
approximate answer so the most important
factoring need to understand that is are
th for always in them now hollow
cylinder in case of hollow Center where
we are going to make mistake let me
share with you to babble to ask you
they're going to ask you
thermal resistance tests and they will
give you the value the value you make
one is an emitter and another one maybe
in centimeter so what we'll have to see
you will have to see all the unit first
we have to see all that unit the asking
need as well as given unit once you will
understand this concept then probability
of doing mistake in the commit
examination would be very less let me
share with you one of the interesting
fact okay after checking almost thousand
examination paper itself I have analyzed
and I said I have done analysis that
forty percent students make mistake here
what I am doing I am sharing with you
right now
they don't cheat the don't check that in
mean of the given things and what will
have a need to find out once they will
come to work once you will miss you are
about the unit then go for it and firm
the play mostly two important tools for
solving numerical problems I hope you
understand the questions as well as
concept of hollows ender for finding out
heat transfer rate alright so thanks for
watching see you soon in my next video
bye
share with you yeah you can read right
now the radial conduction heat transfer
through a hollow cylinder right and as
you can see me we have a power symbol in
front of us and that's why you can
understand about it quite easily so in
this toter well I'm going to share with
you the concept of hollow cylinder first
and second I'm going to also going to
share with you a problem which has been
asked in cage 2007 Sam Smith
I hope you wanted to learn numerical
problems with along with theoretical
right so first of all in case of
cylinder in case of cylinder we need to
learn what is the formula for finding
out area office later so you know area
is 2 PI R M now if we see this this is a
follows in the right and internal radius
is R 1 outer radius is R 2 so if you say
a1 is equal to 2 PI R 1 L and a2 is
equal to 2 PI R 2 L right
so if you want that I think you can
understand what I am talking right now
so now for finding out he tasks per
weight we need to learn at least in case
of conduction that is Fourier law here
is equal to minus K DT by DX right now
what is DX but in case of silver we have
to consider this as DT by D F because DX
we used in case of slab right but in
case of cylinder we have to use BR
because we are dealing with radius okay
our diameter you can see but we are
considering here radius there so I am
putting here are right now next what is
next that is minus kV
we know t2 minus t1 right this has
happened T 2 minus T 1 be our Thanks no
no till now we have done we have done
but here we have to do some extra work
because we are finding out heat transfer
for follow cinder so you know area any
is what - a a a means 2 pi k means 2 pi
RL right now this would be T 2 minus T 1
okay okay let's it with DP y dr q is
equal to this now if I will indicate
both sides I'll integrate both sides
like this let me write I am letting with
Aron's in that way there so you can
understand so Q send this dr to this
side and our to this side so d r by r
minus K 2 pi L DT and this will be what
to do this would be do you want to do I
hope you what it is okay no no
integration of this what will happen Q
natural rock here - let us say 2 K pi L
T 2 minus P 1 because you th n of DT
will be T and DT by sorry d ry
R would be natural log R 2 by R 1 ok
this is a simple formula for finding out
integration right now what I am going to
do I am going to multiple this minus
sign here so - okay 5l t1 minus t2 right
now I am going to send this to this side
so Q is equal to Q is equal to D 1 minus
D 2 Phi natural log R 2 by R 1
even this I can write this one like this
is 1 by 2 pi 2 pi jl 2 pi clear so this
is this is the formula this is the
formula for finding out heat transfer
rate in a hollow cylinder I hope you
understand and here we are assuming one
thing we are assuming these area and one
more thing steady state condition first
and second one dimensional one
dimensional heat transfer we're
considering these two things here for
finding out heat transfer rate of him
follows the endurance I hope you
understand the question right so would
you like to do would you like to learn
that problem which problem has been as
engaged 2007 and that is totally based
on that is totally based on this formula
I hope you are interested right and one
more thing if you wanted to learn if you
wanted to learn this thing in writing I
must see one thing that is to learn
thermal circuit how to draw a thermal
circuit this is t1 this is t2 and this
is H and you know the formula for rth in
this case that is just amazing that is
just amazing you need to understand the
formula which formula you required right
so that would be RTS is equal to natural
log log R 2 minus R 1 by 2 pi here this
is the formula for thermal resistance
for thermal resistance for finding out
thermal resistance in case of also
follow and this pretty formula I am
going to
use to solve the numerical problem which
has been asking get 2007 right I would
understand it right so let's go for that
for that potion that's why you can
understand wait yeah yeah we caught the
question and I hope you can right now
you can treat the quotient the whole
portion so here what we have even a long
glass cleaner of inner diameter is this
and outer diameter is this so suppose
that this inner this is outer okay so
this in no time
victory is 0.03 meter and it's outer
diameter is 0.05 meter simple now K is a
hot fluid inside it in thermal
conductivity of class this class K is
equal to one point zero five what meter
Kelvin per meter can the thermal
resistance scale K resistance R yes you
need to find out Kelvin per watt okay
now as we know thermal resistance for
almost Linda I have already share with
you natural rock R 2 minus R 1 by 2 pi K
L here we have given all just we need to
find out what per unit length and this
is R th you need to understand the
quotient right so we have we have given
R 2 by R 1
that means 0.05 by 0.03 okay 2 pi K
means how much cake 1.05 all unit we
have checked okay now L is remaining but
we don't have given the value of L with
even don't require because it is s here
only kilo per word per unit length that
means we have to send this L don't here
got it now after the solution well right
now I don't have calculator I have a
Miss somewhere right so let me share
with you what would be the answer for
this question that is for discussion
here 1 0 7 7 g open 0 7 7 know the
approximate answer is zero point zero
seven so 0 1 yeah this is the
approximate answer so the most important
factoring need to understand that is are
th for always in them now hollow
cylinder in case of hollow Center where
we are going to make mistake let me
share with you to babble to ask you
they're going to ask you
thermal resistance tests and they will
give you the value the value you make
one is an emitter and another one maybe
in centimeter so what we'll have to see
you will have to see all the unit first
we have to see all that unit the asking
need as well as given unit once you will
understand this concept then probability
of doing mistake in the commit
examination would be very less let me
share with you one of the interesting
fact okay after checking almost thousand
examination paper itself I have analyzed
and I said I have done analysis that
forty percent students make mistake here
what I am doing I am sharing with you
right now
they don't cheat the don't check that in
mean of the given things and what will
have a need to find out once they will
come to work once you will miss you are
about the unit then go for it and firm
the play mostly two important tools for
solving numerical problems I hope you
understand the questions as well as
concept of hollows ender for finding out
heat transfer rate alright so thanks for
watching see you soon in my next video
bye
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Dec 24, 2024 Last updated |
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