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Prandtl Number (GATE Previous Year Question) With Solution, Heat and Mass Transfer, GATE Video Lecture | Topper Handwritten Notes & Videos for GATE ME - Mechanical Engineering
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FAQs on Prandtl Number (GATE Previous Year Question) With Solution, Heat and Mass Transfer, GATE Video Lecture - Topper Handwritten Notes & Videos for GATE ME - Mechanical Engineering
| 1. What is the Prandtl Number? |  |
The Prandtl Number is a dimensionless number that represents the ratio of momentum diffusivity to thermal diffusivity in a fluid. It is defined as the ratio of the kinematic viscosity to the thermal diffusivity.
| 2. How is the Prandtl Number calculated? | |
The Prandtl Number (Pr) can be calculated using the formula: Pr = ν/α, where ν is the kinematic viscosity of the fluid and α is the thermal diffusivity of the fluid.
| 3. What does the Prandtl Number signify in heat and mass transfer? | |
In heat and mass transfer, the Prandtl Number signifies the relative importance of heat transfer to momentum transfer. A low Prandtl Number indicates that heat transfer is dominant, while a high Prandtl Number indicates that momentum transfer is dominant.
| 4. What is the significance of the Prandtl Number in engineering applications? | |
The Prandtl Number is significant in engineering applications as it helps in determining the heat transfer characteristics of a fluid. It is used to analyze and design heat exchangers, determine convective heat transfer coefficients, and predict flow regimes in various fluid flow systems.
| 5. How does the Prandtl Number affect boundary layer thickness? | |
The Prandtl Number affects boundary layer thickness by influencing the rate of heat transfer in the fluid. A low Prandtl Number results in a thinner boundary layer and faster heat transfer, while a high Prandtl Number leads to a thicker boundary layer and slower heat transfer.
Text Transcript from Video
this is welcome arson and in this video
tutorial I'm going to share with you how
to find out the thickness of thermal
boundary layer but the same question has
been asked in gate previous year and the
question was a Viking one month in 2008
they have asked this question that's why
I'm sharing with you so how you can find
out basically the boundary layer
thickness of the same location whatever
they have given in the question but it
seems very difficult for the question I
mean if you will see the portion
oh it's lengthy and oh please that thing
will come in your mind but if will come
to know that how he can basically solve
the problem it's really simple you just
need to know what is that number and its
relationship with a hydrodynamic
boundary layer and the thermal boundary
layer once you will come to know about
it you can do it just like that it's
really simple okay
it will take hardly 1 or 2 minutes if
you are familiar with that relationship
will it she right now I am going to
share with you alright so here is it so
Pentel number PR is equal to we know
that mu mu CP by what is mu mu basically
you know that dynamic viscosity k is
thermal conductivity and CP is a
specific heat at constant pressure so
and another relation we have here only
Prandtl number is equal to del by Del T
whole to the power 3 this is the
relation you need to know to solve this
this numerical problem if you know this
relation you can solve it quite easily
okay so what they have given basically
just look at this you know look at this
a question in the question what we have
even basically for flow of fluid over a
heated plate a heated plate flowing
fluid properties are known these casa t
is this so just write it down what they
have given viscosity is 0.001 and
following heat transfer heat is specific
heat at constant pressure is this so 1
kilo joule that means 1,000
and thermal conductivity is one so we
got everything here so P R is equal to
we got this now 1000 is this will cancel
so we'll get parental number is equal to
1 is equal to Delta by delta T whole to
the power 3 so we can write okay with
right after I mean first of all we need
to know what we need to find out in this
question then we'll proceed further so
what we have even in this question now
hydrodynamic boundary layer thickness at
a specified location on the plate is 1mm
thermal boundary layer thickness at the
same location is what we have to find
out that so so what they have said
basically hydrodynamic boundary layer
thickness both in one way they have said
this right so what we got basically
thermal boundary layer okay you know
there is it diagram I must share with
you if you harvested about convention
then probably you can recall the diagram
this a diagram we have studied when we
do relation between Prandtl number as
well as you know I as well as the
hydrodynamic boundary layer burn oh
sorry bounder number hydrodynamic
boundary layer and thermal boundary
layer I must say that so suppose that
for this case PR is equal to 1 right and
if PR is equal to 1 then what will
happen
del is equal to delta T that what is Del
basically and what is delta T thermal
boundary layer and tell is hydrodynamic
boundary layer if you know in the below
line we have what PR is greater than 1
in the above line what we have PR is
less than 1 so this diagram we have is
studied in case of you know in case of
convection in st peter our st or attempt
if you guys said their states and few
people said at mt
so from here what we can say basically
Delta by delta T is equal to 1 and what
we have to find out
thermal boundary layer we have given
this hydrodynamic boundary layer so
delta T is equal to 1 basically okay so
what is answer here now after looking at
the I mean up
looking at the option given in this
quotient you can easily mark the right
answer so which one is the right answer
that is one meter is the light answer
for this course earth is the one it
should be mm right because it's given ml
so 1 mm is the right answer for this
question yeah I hope you understand the
question and if you are getting any
problem in any other question just let
me know how to try to solve it and make
a video on that and definitely I will
upload to my youtube channel thanks for
watching thank you very much and if you
like that order and share with your
friends they will also get help from
this daughter but why
tutorial I'm going to share with you how
to find out the thickness of thermal
boundary layer but the same question has
been asked in gate previous year and the
question was a Viking one month in 2008
they have asked this question that's why
I'm sharing with you so how you can find
out basically the boundary layer
thickness of the same location whatever
they have given in the question but it
seems very difficult for the question I
mean if you will see the portion
oh it's lengthy and oh please that thing
will come in your mind but if will come
to know that how he can basically solve
the problem it's really simple you just
need to know what is that number and its
relationship with a hydrodynamic
boundary layer and the thermal boundary
layer once you will come to know about
it you can do it just like that it's
really simple okay
it will take hardly 1 or 2 minutes if
you are familiar with that relationship
will it she right now I am going to
share with you alright so here is it so
Pentel number PR is equal to we know
that mu mu CP by what is mu mu basically
you know that dynamic viscosity k is
thermal conductivity and CP is a
specific heat at constant pressure so
and another relation we have here only
Prandtl number is equal to del by Del T
whole to the power 3 this is the
relation you need to know to solve this
this numerical problem if you know this
relation you can solve it quite easily
okay so what they have given basically
just look at this you know look at this
a question in the question what we have
even basically for flow of fluid over a
heated plate a heated plate flowing
fluid properties are known these casa t
is this so just write it down what they
have given viscosity is 0.001 and
following heat transfer heat is specific
heat at constant pressure is this so 1
kilo joule that means 1,000
and thermal conductivity is one so we
got everything here so P R is equal to
we got this now 1000 is this will cancel
so we'll get parental number is equal to
1 is equal to Delta by delta T whole to
the power 3 so we can write okay with
right after I mean first of all we need
to know what we need to find out in this
question then we'll proceed further so
what we have even in this question now
hydrodynamic boundary layer thickness at
a specified location on the plate is 1mm
thermal boundary layer thickness at the
same location is what we have to find
out that so so what they have said
basically hydrodynamic boundary layer
thickness both in one way they have said
this right so what we got basically
thermal boundary layer okay you know
there is it diagram I must share with
you if you harvested about convention
then probably you can recall the diagram
this a diagram we have studied when we
do relation between Prandtl number as
well as you know I as well as the
hydrodynamic boundary layer burn oh
sorry bounder number hydrodynamic
boundary layer and thermal boundary
layer I must say that so suppose that
for this case PR is equal to 1 right and
if PR is equal to 1 then what will
happen
del is equal to delta T that what is Del
basically and what is delta T thermal
boundary layer and tell is hydrodynamic
boundary layer if you know in the below
line we have what PR is greater than 1
in the above line what we have PR is
less than 1 so this diagram we have is
studied in case of you know in case of
convection in st peter our st or attempt
if you guys said their states and few
people said at mt
so from here what we can say basically
Delta by delta T is equal to 1 and what
we have to find out
thermal boundary layer we have given
this hydrodynamic boundary layer so
delta T is equal to 1 basically okay so
what is answer here now after looking at
the I mean up
looking at the option given in this
quotient you can easily mark the right
answer so which one is the right answer
that is one meter is the light answer
for this course earth is the one it
should be mm right because it's given ml
so 1 mm is the right answer for this
question yeah I hope you understand the
question and if you are getting any
problem in any other question just let
me know how to try to solve it and make
a video on that and definitely I will
upload to my youtube channel thanks for
watching thank you very much and if you
like that order and share with your
friends they will also get help from
this daughter but why
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Dec 24, 2024 Last updated |
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