using the principles of thermodynamics we can study the interactions of a
system with its surroundings these interactions are in the form of heat and
work however there is something missing did you notice none of these
thermodynamic relations have time in them
and they do not contain any information about how these interactions are taking
place now you may ask why is this important why do I need time or the
nature of these interactions especially then I can get the amount of heat
transfer or the work done by simply using these thermodynamic principles
while that is entirely true have you ever wondered why does the
metal tumbler feel colder to touch than a ceramic mug even though they are at
the same temperature, temperature of your room. Or perhaps you would have noticed
how blowing over a hot cup of coffee cools it down faster, or why on a hot
summer day you feel more comfortable in the shade and not out in the open under
the Sun. Questions like these can't be answered using thermodynamics alone and
that is because the science of thermodynamics deals with the amount of
heat transfer or the work done for a system that is undergoing a process from
one state to the other and it does not care about how long the
process takes or its inherent nature but in
engineering we are often interested in the rate of heat transfer and the means
with which we can make it happen
this is the focus of this lesson so let's get started.
Simply put heat
transfer is the thermal energy in transit due to a temperature difference
if there is a temperature difference in a medium or between different media heat
transfer will occur the transfer of energy as heat is always from the higher
temperature medium to the lower temperature one and this transfer stops
when the two media reach the same temperature this state is also known as
thermodynamic equilibrium heat transfer is the phenomena which keeps our car
engines from overheating it is what keeps our homes warm during cold winter
days and cool during hot summer days heat transfer helps us keep our food and
drinks cool and fresh it helps power our cities and keeps our electronics cool
and running now this transfer of thermal energy can
occur in three ways it can happen via conduction convection or radiation these
are the three modes of heat transfer so let's look into them in detail
the first mode of heat transfer we'll be looking at is conduction conduction is
the heat transfer that occurs and the temperature difference exists across a
stationary medium at the very fundamental level it can be described as
the transfer of energy from more energetic to less energetic particles of
a substance via interaction between these particles at molecular levels
conduction can take place in solids liquids or gases in order to understand
this mechanism let's consider a gas occupying a space between two surfaces
these surfaces are being maintained at different temperatures and due to this
we get a temperature gradient across the gas but without any bulk motion remember
the gas is stationary temperature at any point in this gas can be associated with
the energy of random translational internal rotational and vibrational
motion of the gas molecules and as one might expect higher molecular energies
are associated with higher temperatures now these random motions will certainly
lead to molecular collisions which helps in the transfer of energy from more
energetic molecules to the less energetic ones and in this way the
energy is transferred by conduction in the direction of decreasing temperature
in the case of liquids the mechanism of conduction is the same as the molecules
are closely spaced and the molecular interactions are stronger and even more
frequent than gases however in the case of solids conduction is not associated
with the motion of the particles but with the atomic activity in the form of
lattice vibrations if the solid happens to be an electrical conductor the
translational motion of free electrons also contributes towards energy transfer
now that we have an understanding of the mechanism of conduction heat transfer
let's formalize it in more specific engineering terms generally any heat
transfer process can be quantified in terms of appropriate rate equations
these are used to compute the amount of energy being transferred per unit time
in the case of heat conduction this rate equation was first formulated by Fourier
in 1820 to consider a one-dimensional ball which has two surfaces being
maintained at t1 and t2 and a distance Delta X part free observed that the heat
transfer was from the hotter side with the colder side and it was higher when
the temperature difference was higher on the other hand if the distance between
the two sides was large or in the other words if the wall was thick the heat
transfer was lower
this is the four years law of heat conduction but states that the heat flux
resulting from thermal conduction is proportional to the temperature gradient
the negative sign is due to the fact that heat transfer is in the direction
of decreasing temperature that is opposite to the positive gradient
consider a steady-state condition now then the temperature gradient is linear
and the heat flux is simply given by this relation the parameter K is a
material property known as thermal conductivity materials that have higher
thermal conductivity allow a higher heat transfer through them compared to
materials that have lower heat conductivity and that is why that metal
tumbler feels colder to hold compared to that ceramic mug
so far we have talked about heat transfer via molecular interactions only
and fill out any bulk motion of the fluid
remember the medium was stationary now if we add some bulk motion of the fluid
or in other words the high-energy particles not only provide energy to the
neighboring particles by a collision but now they move and they take that energy
from one place to the other then this mode of heat transfer is
called convection convection refers to the heat transfer between a surface and
a moving fluid then there is a temperature difference between the two
if the surface temperature is greater than the temperature of the fluid flow
convection heat transfer occurs from the surface and into the outer flow if the
temperature of the flowing fluid is greater than the surface then the
convection heat transfer occurs from the outer flow and into the surface
just like the hydrodynamic boundary layer when the surface and the flow
temperature differs there will be a region of fluid where the temperature
will vary from the surface temperature to the temperature of the outer flow
this region is called the thermal boundary layer within the boundary layer
convection heat transfer is carried out via both random molecular motion and the
bulk motion of the fluid the contribution due to the random molecular
motion dominates near the surface where the fluid velocity is low due to the no
slip condition at the surface the fluid velocity is zero and heat is transferred
by a diffusion only the contribution due to the bulk motion comes from the fact
that the boundary layer grows as the flow progresses in the X direction in
effect the heat that is conducted into this layer is swept downstream and is
eventually transferred to the fluid outside the boundary layer
and it is for this reason that fluid mechanics plays a vital role in our
analysis of convection the rate of the convection heat transfer process is
given by the Newton's law of cooling as shown here
here PS is the temperature of the solid surface and be infinity represents the
temperature of the fluid flowing over this surface in this equation H is the
convection heat transfer coefficient and it depends on the conditions in the
boundary layer this can be influenced by surface geometry the nature of the fluid
flow and various fluid thermodynamic and transport properties based on the nature
of the fluid flow simulation heat transfer can be classified into two
categories the first type is known as force convection where the flow is
caused by external means such as by a fan a pump or atmospheric vents remember
that cup of hot coffee blowing air over it to cool it down
that's basically forced convection free or natural convection on the other hand
deals with convection heat transfer where flow is induced by buoyancy forces
which are caused by density differences arising due to the temperature
variations in the fluid the simplest example of this type of convection is
boiling of water in a kettle or a saucepan
till now we have talked about heat transfer in a stationary medium and heat
transfer in a medium in motion but what if there is no medium present between
the hot and the gooey bodies can we get any heat transfer when there is no
medium between the two the answer is yes and this brings us with the third type
of heat transfer called radiation radiation is the emission of
energy in the form of electromagnetic waves all matter at non zero temperature
emits thermal radiation this emission is due to changes in the
electron configurations of the atoms or molecules and this energy is transported
by our electromagnetic waves or photons in the absence of an intervening medium
there is a net heat transfer by radiation between two surfaces at
different temperatures this is how the thermal energy from Sun reaches Earth
the rate of energy release per unit area is called the surface emissive power the
maximum rate of radiation that can be emitted from a surface at an absolute
temperature of T s is given by a Stefan Boltzmann law as shown here
here Sigma is the stefan-boltzmann constant the idealized surface that
emits radiation at this maximum rate is called a blackbody and the radiation
emitted by a black body is called blackbody radiation the heat flux
emitted by a real body is always less than that of a black body and this is
given by this equation here epsilon is the emissivity which is a measure of how
effectively a surface emits energy relative to a blackbody it depends on
the material of the surface and its finish just like the emissivity there is
another important property of a surface called absorptivity it is the fraction
of the radiation energy incident on the surface that is absorbed by the surface
just like emissivity its value also lies between 0 and 1 and the maximum value of
1 is associated with you guessed it right the blackbody
so in other words a blackbody is a perfect absorber and also a perfect
emitter interesting the rate at which radiant energy is absorbed by unit
surface area can be evaluated using this equation if the surface is opaque
portions of the irradiation are reflected however if the surface is
semi-transparent portion of the irradiation
may also be transmitted now that we have an idea of the underlying mechanisms of
radiation let's formalize the radiation heat transfer consider the radiation
exchange between a small surface at t1 and a much larger isothermal surface
which is completely surrounding the smaller surface at t2 we assume that the
surface is a gray surface meaning the absorptivity is equal to the emissivity
for the surface the net rate of radiation heat transfer
per unit area from the surface can be expressed by the expression shown here
this equation represents the difference between the thermal energy being
released due to radiation emission and that which is being absorbed
so to summarize in this lesson we talked about three modes of heat transfer which
are conduction convection and radiation we also discussed their underlying
physics and the means to compute the heat transfer flux corresponding to each
of these three modes heat transfer is a complex phenomenon and more often than
not multiple modes of heat transfer are at play at the same time to consider for
example the cooling of a CPU as you CPU works it generates heat it starts to
make it hot if this heat is left unchecked the temperatures can get so
high that it can burn the chip causing permanent damage
therefore engineers design cooling systems which first draws the heat from
the chip into the heatsink and fins via conduction and then a mechanical fan
blows air over these fins in order to cool the fringe down by our convection
and of course not to mention the radiation heat transfer that is always
taking place the entire time
this is just one example among numerous
engineering applications and you can find all around you which rely on the
principles of heat transfer
you