Natural (Free) Convection Heat transfer Video Lecture | Heat Transfer - Mechanical Engineering

recall from our previous module we noted
that free convection or sometimes it's
called natural convection occurs when a
fluid comes into contact with heated
surface and due to buoyancy since the
the density of the fluid will decrease
when it is in contact with a higher
temperature or solid due to that
buoyancy that fluid will rise and colder
fluid will take its place so that sets
up a natural current around the solid
object so in this case there are three
dimensionless numbers that are used to
develop these correlations nusselt
number grashof number and parental
number the correlation is actually quite
simple nusselt number equals a constant
a times grashof number times parental
number raised to power constant M now
this quantity grashof number times
Prandtl number is also called Raliegh
number the grashof number is given by
this equation
DC raised to power three Rho squared G
beta delta T divided by mu square where
DC is the characteristic dimension now
this characteristic dimension will
depend on what is the shape of the
object and we will see that in a minute
Rho is the density of the fluid G is the
acceleration due to gravity beta is the
coefficient of volumetric expansion
recall that when the temperature of the
fluid increases
it is going to expand so this
coefficient tells us something about how
much expansion of the fluid will take
place delta T is the temperature
difference between the surface of a
solid and the surrounding bulk fluid
temperature mu is the viscosity now the
grashof number can be also written as a
ratio between the buoyancy forces and
viscous forces similar to Reynolds
number a grashof number is also useful
in telling us something about what is
the state of fluid flow over an object
for example if grashof number is greater
than 10 raised to power 9 for fluid flow
over vertical plates then that indicates
a turbulent flow now in the calculations
of physical properties of the fluid we
use the film temperature where the film
temperature we call it TF equals
TS which is the surface temperature of
the solid plus T infinity bulk
temperature of the fluid divided by 2
next let's see how to obtain constants a
and M table for point to where we see
different shapes of objects to determine
the value of these constants a and M for
example for a vertical plate the
characteristic dimension is the length
or the height of that plate
now if the Rowley number is between 10
raised to power 4 and 10 raised to power
9 then the constant a is 0.5 9 and the
constant M is 0.25 if the range of
Rowley number is determined to be 10
raised to power 9 to
13 then constant a will be 0.1 and
constant M will be 0.333 so again
depending on the shape and the
orientation of the object we determine
the value for Rowley number and then
select the appropriate constants a and M
in our equation Nestle number equals a
in parentheses grashof number times
parental number which is the Rowley
number raised to power M in the textbook
you will see other shapes as well as
orientations of different objects and
appropriate relationships between the
Rowley number and Nussle number so that
one can calculate an appropriate Nestle
number and from nussle number we can
find out the convective heat transfer
coefficient since you know that Nestle
number equals H DC over K