Physics 110 Lecture 38 from Chapter 11 Sections 5 to 6

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Physics 110 Lecture 38 from Chapter 11
Sections 5 to 6

• Heat Transfer

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Homework Assignment 38

• Conceptual Question
• Chapter 11, CQ 12 on page 378
• Problems
• Chapter 11, Problem 36 on page 381
• Chapter 11, Problem 42 on page 382
• Chapter 11, Problem 66 on page 384

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Heat Transfer

• When two objects of different temperatures are
  placed in thermal contact, the temperature of the
  warmer decreases and the temperature of the
  cooler increases
• However, this doesn't happen instantaneously, it
  takes time for the transfer of energy to take
  place.
• Different materials transfer the heat at
  different rates.

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3 Methods of Heat Transfer

• Conduction heat transfer which occurs by atoms
  and molecules bumping into each other and passing
  momentum and energy through collisions.
• Convection heat transfer which occurs due to
  molecules moving about and mixing while carrying
  the energy along with them.
• Radiation heat transfer which occurs due to the
  emission and absorption of electromagnetic
  radiation between bodies.

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Conduction

• The transfer can be viewed on an atomic scale
• It is an exchange of energy between microscopic
  particles by collisions
• Less energetic particles gain energy during
  collisions with more energetic particles
• Rate of conduction depends upon the
  characteristics of the substance

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Conduction example

• The molecules vibrate about their equilibrium
  positions
• Particles near the stove coil vibrate with larger
  amplitudes
• These collide with adjacent molecules and
  transfer some energy
• Eventually, the energy travels entirely through
  the pan and its handle

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Conduction, cont.

• In general, metals are good conductors
• They contain large numbers of electrons that are
  relatively free to move through the metal
• They can transport energy from one region to
  another
• Conduction can occur only if there is a
  difference in temperature between two parts of
  the conducting medium

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Conduction

• Heat Transfer Rateby Conduction

where heat transfer rate (in Watts) k
thermal conductivity A cross sectional area L
thickness along direction of heat transfer ?T
Th-Tc temperature difference.
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Thermal Conductivity of Materials

• Good Conductors have high k values
• Good Insulators have low k values

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Home Insulation

• Insulation is rate by R value which refers to the
  resistance to heat flow per unit area.
• where L is the thickness of the layer and
• k is the thermal conductivity of the
  material
• For multiple layers, the total R value is the sum
  of the R values of each layer

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Table of R values
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Example 1

• A house has an average thermal conductivity of
  4.8x10-4kW/m-oC for its 21 cm thick walls and
  roof.The house is heated with natural gas
  (heat of combustion is 9300 kcal/m3). How
  many cubic meters of gas are burned each day to
  maintainan inside temperature of 25oC if the
  outside temperatureis 0oC?

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Example 1

• k 0.48 W/m-oC
• L 21 cm 0.21m
• Th-TC 25oC
• A Aends AsidesAroof
• 2x52m2 2x50m2 100m2 304m2
• t 1 day 86400 s
• Qfuel/Vol 9300 kcal/m3).

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Cost of Natural gas Nov. 2007 7.50 per 1
million BTU
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Example 1

• k 0.48 W/m-oC
• L 21 cm 0.21m
• Th-TC 25oC
• A 304m2
• t 86400 s
• Qfuel/V 9300 kcal/m3).
• Cost 7.50 per million BTU

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Convection

• Energy transferred by the movement of a substance
• When the movement results from differences in
  density, it is called natural conduction
• When the movement is forced by a fan or a pump,
  it is called forced convection

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Convection example

• Air directly above the flame is warmed and
  expands
• The density of the air decreases, and it rises
• The mass of air warms the hand as it moves by

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Convection Current Example

• The radiator warms the air in the lower region of
  the room
• The warm air is less dense, so it rises to the
  ceiling
• The denser, cooler air sinks
• A continuous air current pattern is set up as
  shown

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Convective Heat Transfer

• Convective Heat transfer is usually measured by
  how well heat is removed from a surface of known
  temperature and dissipated out into the fluid.
• The equation is given by
• where hc is the coefficient of convection
  A is contact surface area Tsurface-Tfluid is
  the temperature difference

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Coefficient of convection
Table taken from Basic Heat Transfer by Kreith
and Black
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Radiation

• Radiation does not require physical contact
• All objects radiate energy continuously in the
  form of electromagnetic waves due to thermal
  vibrations of the molecules
• Rate of radiation is given by Stefans Law

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Radiation equation

• The power is the rate of energy transfer, in
  Watts
• s is Stefan-Boltzmann constant s
  5.6696 x 10-8 W/m2.K4
• A is the surface area of the object
• e is a constant called the emissivity
• e varies from 0 to 1
• T is the abolute temperature in K degrees

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Energy Absorption and Emission by Radiation

• With its surroundings, the rate of heat flow from
  an object at temperature T with surroundings at
  temperature To isWhen an object is in thermal
  equilibrium with its surroundings, it radiates
  and absorbs at the same rate
• Its temperature will not change

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Absorber or Reflector

• Black Body an ideal absorber is an object that
  absorbs all of the energy incident on it.
  e 1
• White Body an ideal reflector is an object which
  reflects all the energy incident upon it.
  e 0
• The terms white and black body don't necessarily
  refer to the actual color of the object.

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Emissivity and Absorptivityof selected surfaces.
Table taken from Handbook of Tables for
Engineering Science by Bolz and Tuve
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Applications of Radiation

• Clothing
• Black fabric acts as a good absorber
• White fabric is a better reflector
• Thermography
• The amount of energy radiated by an object can be
  measured with a thermograph
• Body temperature
• Radiation thermometer measures the intensity of
  the infrared radiation from the eardrum

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Example 2

• At high noon, the Sun delivers 1.00 kW to each
  square meter of a blacktop road. If the hot
  asphalt loses energy only by radiation, what is
  its equilibrium temperature?

Qabsorb/?t
Qemitted/?t
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Example 2

• At high noon, the Sun delivers 1.00 kW to each
  square meter of a blacktop road. If the hot
  asphalt loses energy only by radiation, what is
  its equilibrium temperature?

Qabsorb/?t
Qemitted/?t
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Example 2
Qabsorb
Qemitted