Modes of Heat Transfer

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Modes of Heat Transfer

• P M V Subbarao
• Professor
• Mechanical Engineering Department

Accounting of Natural Happenings ..
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Radiation from a Thermodynamic System
Spectral integration of Planks distribution law
estimates the total energy emitted by a real
system as

• where esys is the emissivity of the system,
• Asys-surface is the surface area,
• Tsys is the temperature, and
• s is the Stefan-Boltzmann constant, equal to
  5.6710-8 W/m2K4.
• Emissivity is a material property, ranging from 0
  to 1, which measures how much energy a surface
  can emit with respect to an ideal emitter (e 1)
  at the same temperature

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Radiative Heat Transfer between System and
Surroundings
Consider the heat transfer between system surface
with surroundings, as shown in Figure. What is
the rate of heat transfer into system surface ?
To find this, we will first look at the emission
from surroundings to system.
Surrounding Surface emits radiation as described
in
This radiation is emitted in all directions, and
only a fraction of it will actually strike system
surface.
This fraction is called the shape factor, F.
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The amount of radiation striking system surface
is therefore
The only portion of the incident radiation
contributing to heating the system surface is
the absorbed portion, given by the absorptivity
aB
Above equation is the amount of radiation gained
by System from Surroundings. To find the net
heat transfer rate for system, we must now
subtract the amount of radiation emitted by
system
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The net radiative heat transfer (gain/loss) rate
at system surface is
Similarly, the net radiative heat transfer
(loss/gain) rate at surroundings surface is
What is the relation between Qsys and Qsur ?
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An Universe consisting of System Surroundings
only
According to Reciprocity theorem
If both system and surroundings are ideal bodies
If system completely engulfs the surroundings.
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Nature of Convection Heat Transfer

• Convection involves the transfer of heat by the
  motion and mixing of "macroscopic" portions of a
  fluid.
• This mixing is called as the flow of a fluid past
  a solid boundary leading to Heat Convection.
• The term natural convection is used if this
  motion is generated within.
• The term forced convection is used if this motion
  and mixing is caused by an outside force, such as
  a pump/fan.
• Heat transfer by convection is more difficult to
  analyze than heat transfer by conduction because
  no single property such as thermal conductivity,
  can be identified to describe the convection
  mechanism.

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Natural Convection

• Natural convection (or free convection) refers to
  a case where the fluid movement is created by the
  warm fluid itself.
• The density of fluid decrease as it is heated
  thus, hot fluids are lighter than cool fluids.
• Warm fluid surrounding a hot object rises, and is
  replaced by cooler fluid.
• The result is a circulation of air above the warm
  surface

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Forced Convection

• Forced convection uses external means of
  producing fluid movement.
• Forced convection is what makes a windy, winter
  day feel much colder than a calm day with same
  temperature.
• The heat loss from your body is increased due to
  the constant replenishment of cold air by the
  wind.
• Natural wind and fans are the two most common
  sources of forced convection.

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Newtons Law of Cooling
Newton, when asked once about how he gained his
insight into the problems of nature, replied By
constantly thinking unto them. Historians of
science agree that Newtons paper incorporated
two important generalizations on law of cooling.
The first was that the rate of cooling of a hot
body at any moment is proportional to the
difference between the temperature of the body
and of the surrounding fluid. This generalization
has the most far-reaching effect and became the
genesis of the convective heat transfer. The
second was that when a body melts or evaporates,
its temperature remains constant.
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A plausible 'wind tunnel' for Newton's
coolingexperiments.
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Rate of Convection Heat Transfer

• Convection involves the transfer of heat between
  a system at a given temperature (Ts) and fluid at
  a bulk temperature (Tb).
• The exact definition of the bulk temperature (Tb)
  varies depending on the details of the situation.
• For flow adjacent to a hot or cold surface, Tb
  is the temperature of the fluid "far" from the
  surface.
• For boiling or condensation, Tb is the saturation
  temperature of the fluid. For flow in a pipe, Tb
  is the average temperature measured at a
  particular cross-section of the pipe.
• Newtons law of cooling suggests a basic
  relationship for heat transfer by convection

h is called as Convection Heat Transfer
Coefficient, W/m2K
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Possible Actions During a change of state?

• Work transfer
• Heat transfer
• Mass transfer
• How to Account for these actions?

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Net Work During a Cycle process
The net work done by the system in the process
a1b2a is
Change in any property during a cycle is zero! Is
Conservation of Energy valid here?
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Net Heat Transfer During a Cycle
The absolute value of heat transfer during one
cycle is
Change in any other property during a cycle is
zero. Is Conservation of Energy valid here?
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Conservation of Energy

• Energy can neither be created nor be destroyed.
• In a Cycle, Net work Transfer Net Heat
  Transfer.
• This is notes as the First Law of Thermodynamics.

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Combined Heat Work Transfer Sign Conventions
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The First Law of Thermodynamics
If a control mass undergoes a cyclic process, the
cyclic integral of the heat is proportional to
the cyclic integral of work.
Cyclic Integral of Heat ? Cyclic Integral of Work

• This is a law of nature.
• Can be described only for control mass.
• Basis is only experimental evidence.
• The first law can never be disproved.

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Engineering View of First Law

• Any machine which violates first law is called as
  Perpetual Motion Machine of first kind.
• A PMM-1 is a control mass which works
  continuously in a cycle and
• generates only work or
• consumes only work or
• accepts only heat or
• rejects only heat.
• It is impossible to construct A Perpetual Motion
  Machine of first kind (PMM 1).

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Analysis of Cycles using First Law