Mechanical Engineering Exam > Mechanical Engineering Videos > Topper Handwritten Notes & Videos for GATE ME > Dimensionless Numbers in Heat Transfer HMT Tutorial- 13, Heat and Mass Transfer, Mechanical Engineering, GATE
Dimensionless Numbers in Heat Transfer HMT Tutorial- 13, Heat and Mass Transfer, Mechanical Engineering, GATE Video Lecture | Topper Handwritten Notes & Videos for GATE ME
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FAQs on Dimensionless Numbers in Heat Transfer HMT Tutorial- 13, Heat and Mass Transfer, Mechanical Engineering, GATE Video Lecture - Topper Handwritten Notes & Videos for GATE ME
| 1. What are dimensionless numbers in heat transfer? |  |
Ans. Dimensionless numbers in heat transfer are mathematical ratios that provide information about the relative importance of different physical phenomena in the heat transfer process. They are used to simplify and analyze complex heat transfer problems by reducing the number of variables involved. Examples of dimensionless numbers in heat transfer include the Nusselt number, Reynolds number, Prandtl number, and Peclet number.
| 2. How do dimensionless numbers help in heat transfer analysis? | |
Ans. Dimensionless numbers play a crucial role in heat transfer analysis as they allow engineers and researchers to compare and predict the behavior of different heat transfer systems. By using dimensionless numbers, it becomes possible to identify the dominant factors influencing heat transfer, assess the relative importance of conduction, convection, and radiation, and design efficient heat transfer systems. They also facilitate the scaling of laboratory experiments to real-world applications.
| 3. What is the significance of the Nusselt number in heat transfer? | |
Ans. The Nusselt number is a dimensionless number used to determine the convective heat transfer coefficient in fluid flow. It relates the convective heat transfer rate to the conductive heat transfer rate. The value of the Nusselt number provides information about the efficiency of heat transfer in a system, with higher values indicating more efficient heat transfer. It is widely used in the design and analysis of heat exchangers, cooling systems, and other heat transfer devices.
| 4. How can the Reynolds number be calculated in heat transfer? | |
Ans. The Reynolds number is a dimensionless number used to determine the flow regime (laminar or turbulent) in a fluid flow system. It is calculated by dividing the product of the fluid velocity, characteristic length, and fluid density by the fluid viscosity. The formula for Reynolds number is Re = (ρ * V * L) / μ, where Re is the Reynolds number, ρ is the fluid density, V is the fluid velocity, L is the characteristic length, and μ is the fluid viscosity.
| 5. What is the significance of the Prandtl number in heat transfer? | |
Ans. The Prandtl number is a dimensionless number used to characterize the relative importance of momentum and thermal diffusivity in a fluid flow system. It is calculated by dividing the fluid viscosity by the thermal conductivity. The Prandtl number provides information about the relative rates of momentum and heat transfer in a system, with higher values indicating that heat transfer occurs more rapidly compared to momentum transfer. It is used in the analysis of boundary layer flows, convection heat transfer, and flow visualization techniques.
Text Transcript from Video
well my dear so in this video total
we'll learn about and nusselt number
parental number and holds number their
sub number and Biot number all these
numbers are most important as you know
that that's why I am sharing with you
and if you learn these numbers and these
numbers are most important for
completing summation just like it I mean
most of our time they ask formula as
well as you know if you are repeating
for any other examination just like GE
then even you are going to get questions
from these numbers and I have ID'd
analyzes most of our time to ask
question from all these numbers so let's
get started from nusselt number so what
is basically nusselt number
so basically if you prepare for I mean
if you preparing for convection then
this number is most important I mean you
will definitely get this number what is
it how is it what is the formula of it
you will need to know so basically
formula this is s Delta upon T and Delta
is known as correct a stick length
basically corrector sticks left H is
heat transfer coefficient and basically
it does work off is the intent it is
edge it transfer coffees the end and it
seemed it is what permitted square
centigrade okay now other than this K is
thermal conductivity okay so this is all
about nusselt number now interesting
fact is that with handle number prandtl
number is a fabulous mu nu upon alpha nu
is known as kinematic viscosity alpha is
known as thermal Definity so you can say
it is the ratio of kinematic viscosity
to the thermal difficulty one another
formula I mean one other thing or
another way we can learn or we can come
to know its ratio that is molecular
defect diffusivity or momentum to the
Mollica molecular diffusivity of heat so
diffusivity is
most common term for this case so
basically new is known as kinematic
viscosity so what is dynamic viscosity
that is diameter is 40 is equal to
dynamic viscosity by Rho Rho means
density here and alpha is thermal
difficulty its formula is K by Rho CP
okay I mean conductivity by heat
capacity Rho CP is known as heat
capacity if you do some calculation or
simplification then what we are going to
get just let me share with you Rho and
Rho CP k sorry this will go up so this
will be Rho CP by K so Rho cancel the
remaining will be mu CP by K so this is
the formula for repented number right
now let's move to the Reynolds number
well most your time people ask about
Reynolds number because according to
this number we can come to know that
fluid is what type of flow the fluid is
exactly laminar flow transition flow or
even turbulent flow so that's why the
application of Reynolds number is quite
wide okay now the formula for for
Reynolds number is inertia force inertia
force by viscous force and it is known
as also we can we know about it as Rho
VL through VL by mu okay so basically
what is Rho Rho is density and V is
velocity L is length this
characteristics lanthanum he is
viscosity okay now if Reynolds number if
an also number is about mm is about mm
then it is known as then flow is known
as laminar flow if Ron's number in
between 2000 to 4000 40,000 then it is
known as transition flow if Reynolds
number is above 4000 it is known as
turbulent flow turbulent flow basically
such type of things we
in FM okay such things we study in FM
clear mechanics because you know in
through if you are talking about flow
fluid flow they know they usually study
fluid mechanics in that case we we know
or we studied about it what is RAM your
flow what is transition flow what is
even turbulent flow if you are asking
for example of turbulent flow then I
must say smoke or cigarette that's the
real example of turbulent flow so this
is all about Reynolds number so do you
know what we have is that it nusselt
number parental number and Ravens number
these three numbers are really important
now what we call the next number that is
known as brush-up number so the formula
for guess of number E is buoyancy force
divided by this force force there is
little difference between inertia
Reynolds number and recip number in the
TVs in the divide division we have
discussed number discus number both but
on the upper side energy of force is for
Reynolds number and when sea force is
Fergus of numbers show so what we got
here
G beta T s minus the DVD LCQ by Union
Square now you can see new its kinetic
me to viscosity else's sky testings
length and that is a surface temperature
tinfinity is temperature far from the
surface temperature and these you know
gravity gravitational force or sorry
grab with registration be program
especially to gravity can say and this
is a beta is a coefficient of volume
expense and this is all about
rajab number now all these numbers after
all these numbers at the end we are
studying about biotin umber because you
know I have seen positions the APIs they
have s in the case of tunnel rental
numbers right all right so let's study
about Biot number five number is its
formula is conducts on the disk
to the convection resistance conduct
some resistance to the convection
resistance well I cannot remember in
which a book I have or probably in the
examination I have seen they have
directly asked the question from this
topic that is Biot number I mean they
have as just simply as what is the ratio
of ratio or Biot number that is
conduction resistance to the convection
resistance they got they have even
multiple of Sun just like conversely
resistance by conduction resistance then
conduction by convection or both or
maybe any other option and another
option was I think none of these so
based on these they have is the pushin
but here the formula HLC by K the
formula for this Biot number is L at MC
by K so H is edges what heat transfer
caucus and else is characteristic length
and kgs because of thermal conductivity
so here as you can see this is for
conduction that is K this is a
convection it is for H so basically
these two terms we generally study in
case of four years flow as well as
Newton's law of cooling
I have already shared with you let me
share with you what is that I mean how
how we are relating this convection and
conduction actually if we say in broadly
in case of conduction well this is one
of the mode of heat transfer there are
three modes of heat transfer with
harvested one is conduction another H
convection and under and last one is
radiation so in conduction we follow
with all of Fourier slow it will follow
for yet slow in case of convection we
follow Newton's law of cooling Newton's
law of cooling so in case of Fourier
slow we flow this Q equal to minus K DT
by DX and in case of let me share with
you yeah you can see you know yeah in
case of Newton's law of cooling we
follow Q is equal to HC
t s minus TF so ta surface temperature
TF is flute temperature as GC transfer
coefficient is area and here K is a
thermal conductivity days area and this
is known as temperature gradient which
change difference in temperature and
this is a width you can see right maybe
sometimes record is thickness also right
so basically based on these two formula
we we studied over B Sol further things
in these basically so what we studied we
we need to know its basic concept of
conduction as low conversion these two
formulas play mostly important role in
you must remember this so what we have
stated till now in this tutorial we will
have the static nusselt number we have
stirred Prandtl number we have
astronauts number we have instead also
said aggressive number as well as Biot
number so M one testing fact is that all
these numbers all these numbers are
dimensionless remember that all these
numbers are diamonds and nails diamonds
unless they don't have in dimension so
one that is that another fact if will
ask which one is most important out of
all these numbers then I must say one is
trundle number another one is Reynolds
number most of the time people over most
of time in the completed summation we
have seen question from Penta number as
well as an acid number so don't forget
to understand all these numbers because
it take less than you can one minute I
mean what one period exactly about 50
minutes or one hour will you study for
one hour definitely you can get the
question well thanks for watching see
you soon in my next video bye bye
we'll learn about and nusselt number
parental number and holds number their
sub number and Biot number all these
numbers are most important as you know
that that's why I am sharing with you
and if you learn these numbers and these
numbers are most important for
completing summation just like it I mean
most of our time they ask formula as
well as you know if you are repeating
for any other examination just like GE
then even you are going to get questions
from these numbers and I have ID'd
analyzes most of our time to ask
question from all these numbers so let's
get started from nusselt number so what
is basically nusselt number
so basically if you prepare for I mean
if you preparing for convection then
this number is most important I mean you
will definitely get this number what is
it how is it what is the formula of it
you will need to know so basically
formula this is s Delta upon T and Delta
is known as correct a stick length
basically corrector sticks left H is
heat transfer coefficient and basically
it does work off is the intent it is
edge it transfer coffees the end and it
seemed it is what permitted square
centigrade okay now other than this K is
thermal conductivity okay so this is all
about nusselt number now interesting
fact is that with handle number prandtl
number is a fabulous mu nu upon alpha nu
is known as kinematic viscosity alpha is
known as thermal Definity so you can say
it is the ratio of kinematic viscosity
to the thermal difficulty one another
formula I mean one other thing or
another way we can learn or we can come
to know its ratio that is molecular
defect diffusivity or momentum to the
Mollica molecular diffusivity of heat so
diffusivity is
most common term for this case so
basically new is known as kinematic
viscosity so what is dynamic viscosity
that is diameter is 40 is equal to
dynamic viscosity by Rho Rho means
density here and alpha is thermal
difficulty its formula is K by Rho CP
okay I mean conductivity by heat
capacity Rho CP is known as heat
capacity if you do some calculation or
simplification then what we are going to
get just let me share with you Rho and
Rho CP k sorry this will go up so this
will be Rho CP by K so Rho cancel the
remaining will be mu CP by K so this is
the formula for repented number right
now let's move to the Reynolds number
well most your time people ask about
Reynolds number because according to
this number we can come to know that
fluid is what type of flow the fluid is
exactly laminar flow transition flow or
even turbulent flow so that's why the
application of Reynolds number is quite
wide okay now the formula for for
Reynolds number is inertia force inertia
force by viscous force and it is known
as also we can we know about it as Rho
VL through VL by mu okay so basically
what is Rho Rho is density and V is
velocity L is length this
characteristics lanthanum he is
viscosity okay now if Reynolds number if
an also number is about mm is about mm
then it is known as then flow is known
as laminar flow if Ron's number in
between 2000 to 4000 40,000 then it is
known as transition flow if Reynolds
number is above 4000 it is known as
turbulent flow turbulent flow basically
such type of things we
in FM okay such things we study in FM
clear mechanics because you know in
through if you are talking about flow
fluid flow they know they usually study
fluid mechanics in that case we we know
or we studied about it what is RAM your
flow what is transition flow what is
even turbulent flow if you are asking
for example of turbulent flow then I
must say smoke or cigarette that's the
real example of turbulent flow so this
is all about Reynolds number so do you
know what we have is that it nusselt
number parental number and Ravens number
these three numbers are really important
now what we call the next number that is
known as brush-up number so the formula
for guess of number E is buoyancy force
divided by this force force there is
little difference between inertia
Reynolds number and recip number in the
TVs in the divide division we have
discussed number discus number both but
on the upper side energy of force is for
Reynolds number and when sea force is
Fergus of numbers show so what we got
here
G beta T s minus the DVD LCQ by Union
Square now you can see new its kinetic
me to viscosity else's sky testings
length and that is a surface temperature
tinfinity is temperature far from the
surface temperature and these you know
gravity gravitational force or sorry
grab with registration be program
especially to gravity can say and this
is a beta is a coefficient of volume
expense and this is all about
rajab number now all these numbers after
all these numbers at the end we are
studying about biotin umber because you
know I have seen positions the APIs they
have s in the case of tunnel rental
numbers right all right so let's study
about Biot number five number is its
formula is conducts on the disk
to the convection resistance conduct
some resistance to the convection
resistance well I cannot remember in
which a book I have or probably in the
examination I have seen they have
directly asked the question from this
topic that is Biot number I mean they
have as just simply as what is the ratio
of ratio or Biot number that is
conduction resistance to the convection
resistance they got they have even
multiple of Sun just like conversely
resistance by conduction resistance then
conduction by convection or both or
maybe any other option and another
option was I think none of these so
based on these they have is the pushin
but here the formula HLC by K the
formula for this Biot number is L at MC
by K so H is edges what heat transfer
caucus and else is characteristic length
and kgs because of thermal conductivity
so here as you can see this is for
conduction that is K this is a
convection it is for H so basically
these two terms we generally study in
case of four years flow as well as
Newton's law of cooling
I have already shared with you let me
share with you what is that I mean how
how we are relating this convection and
conduction actually if we say in broadly
in case of conduction well this is one
of the mode of heat transfer there are
three modes of heat transfer with
harvested one is conduction another H
convection and under and last one is
radiation so in conduction we follow
with all of Fourier slow it will follow
for yet slow in case of convection we
follow Newton's law of cooling Newton's
law of cooling so in case of Fourier
slow we flow this Q equal to minus K DT
by DX and in case of let me share with
you yeah you can see you know yeah in
case of Newton's law of cooling we
follow Q is equal to HC
t s minus TF so ta surface temperature
TF is flute temperature as GC transfer
coefficient is area and here K is a
thermal conductivity days area and this
is known as temperature gradient which
change difference in temperature and
this is a width you can see right maybe
sometimes record is thickness also right
so basically based on these two formula
we we studied over B Sol further things
in these basically so what we studied we
we need to know its basic concept of
conduction as low conversion these two
formulas play mostly important role in
you must remember this so what we have
stated till now in this tutorial we will
have the static nusselt number we have
stirred Prandtl number we have
astronauts number we have instead also
said aggressive number as well as Biot
number so M one testing fact is that all
these numbers all these numbers are
dimensionless remember that all these
numbers are diamonds and nails diamonds
unless they don't have in dimension so
one that is that another fact if will
ask which one is most important out of
all these numbers then I must say one is
trundle number another one is Reynolds
number most of the time people over most
of time in the completed summation we
have seen question from Penta number as
well as an acid number so don't forget
to understand all these numbers because
it take less than you can one minute I
mean what one period exactly about 50
minutes or one hour will you study for
one hour definitely you can get the
question well thanks for watching see
you soon in my next video bye bye
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