ME 259 Heat Transfer Lecture Slides I

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ME 259Heat TransferLecture Slides I

• Dept. of Mechanical Engineering,

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Introduction

• Reading Incropera DeWitt
• Chapter 1

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Heat Transfer as a Course

• Has a reputation for being one of the most
  challenging courses in ME
• Why??
• Physically diverse thermodynamics, material
  science, diffusion theory, fluid mechanics,
  radiation theory
• Higher-level math vector calculus, ODEs, PDEs,
  numerical methods
• Physically elusive heat is invisible developing
  intuition takes time
• Appropriate assumptions required to simplify and
  solve most problems
• However, Heat Transfer is interesting, fun, and
  readily applicable to the real world

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Relevance of Heat Transfer

• Electric Power Generation
• Alternate Energy Systems
• Combustion/Propulsion Systems
• Building Design
• Heating Cooling Systems
• Domestic Appliances
• Materials/Food Processing
• Electronics Cooling Packaging
• Cryogenics
• Environmental Processes
• Space Vehicle Systems

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Definition of Heat Transfer

• Flow of energy due solely to a temperature
  difference
• all other forms of energy transfer are
  categorized as work
• from 2nd Law of Thermodynamics, heat flows in
  direction of decreasing temperature
• heat energy can be transported through a solid,
  liquid, gas, or vacuum

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Heat Quantities
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Relationship Between the Study of Heat Transfer
Thermodynamics

• 1st Law of Thermodynamics for Closed System
• Thermodynamics - allows calculation of total heat
  transferred (Q) during a process in which system
  goes from one equilibrium state to another (i.e.,
  the big picture)
• Heat Transfer - provides important physical laws
  that allow calculation of instantaneous heat
  rate, length of time required for process to
  occur, and temperature distribution within
  material at any time (i.e., the details
  required for design)

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Heat Transfer Modes

• Conduction
• transfer of heat due to random molecular or
  atomic motion within a material (aka diffusion)
• most important in solids
• Convection
• transfer of heat between a solid surface and
  fluid due to combined mechanisms of a) diffusion
  at surface b) bulk fluid flow within boundary
  layer
• Radiation
• transfer of heat due to emission of
  electromagnetic waves, usually between surfaces
  separated by a gas or vacuum

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Heat Transfer Modes - Conduction

• Rate equation (Fourier Biot, ?1820) is known as
  Fouriers law for 1-D conduction,
• where qx heat rate in x-direction (W)
• qx heat flux in x-direction (W/m2)
• T temperature (C or K)
• A area normal to heat flow (m2)
• k thermal conductivity of material
• (W/m-K) see Tables A.1-A.7

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Heat Transfer Modes - Conduction

• Steady-state heat conduction through a plane
  wall

T1
T2
k
L
q? (T1gtT2)
x
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Heat Transfer Modes - Conduction

• Example What thickness of plate glass would
  yield the same heat flux as 3.5? of glass-fiber
  insulation with the same S-S temperature
  difference (T1-T2) ?

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Heat Transfer Modes - Conduction

• Insulation R-value
• where 1 W/m-K 0.578 Btu/hr-ft-F

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Heat Transfer Modes - Convection

• Rate equation (Newton, ?1700) is known as
  Newtons law of cooling
• where q heat flux normal to surface
• q heat rate from or to
  surface As
• Ts surface temperature
• T? freestream fluid
  temperature
• As surface area exposed to fluid
• h convection heat transfer coefficient
• (W/m2-K)

q?
Fluid flow, T?
Ts (gtT?)
As
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Heat Transfer Modes - Convection

• The convection heat transfer coefficient (h)
• is not a material property
• is a complicated function of the many parameters
  that influence convection such as fluid velocity,
  fluid properties, and surface geometry
• is often determined by experiment rather than
  theory
• will be given in most HW problems until we reach
  Chapter 6

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Heat Transfer Modes - Convection

• Types of Convection
• Forced convection flow caused by an external
  source such as a fan, pump, or atmospheric wind
• Free (or natural) convection flow induced by
  buoyancy forces such as that from a heated plate
• Phase change convection flow and latent heat
  exchange associated with boiling or condensation

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Heat Transfer Modes - Radiation

• Rate equation is the Stefan-Boltzmann law which
  gives the energy flux due to thermal radiation
  that is emitted from a surface for a black body
• For non-black bodies,
• where E emissive power (W/m2)
• ? Stefan-Boltzmann constant
• 5.67x10-8 W/m2-K4
• ? emissivity (0lt ?lt1) of surface
• Ts surface temperature in absolute
• units (K)

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Heat Transfer Modes - Radiation

• Radiation incident upon an object may be
  reflected, transmitted, or absorbed
• where
• G irradiation (incident radiation)
• ? reflectivity (fraction of G that is
  reflected)
• ? transmissivity (fraction of G that is
  transmitted
• ? absorptivity (fraction of G that is
  absorbed)
• ? emissivity (fraction of black body
  emission)
• E and the interaction of G with each
  participating object determines the net heat
  transfer between objects

G
?G
?G
?G
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Heat Transfer Modes - Radiation

• Heat transfer between a small object and larger
  surroundings (AsltltAsur)
• where ? emissivity of small object
• As surface area of small object
• Ts surface temperature of small
• object (K)
• Tsur temperature of surroundings (K)

Tsur
q
Ts
? , As
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Conservation of Energy Control Volume

• Control volume energy balance
• from thermodynamics
• Incropera DeWitt text notation

Q
mass out
W
mass in
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Conservation of Energy Control Volume

• Energy rates
• where

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Conservation of Energy Control Surface

• Surface energy balance
• since a control surface is a special control
  volume that contains no volume, energy generation
  and storage terms are zero this leaves

Eout
Ein
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Summary The Laws Governing Heat Transfer

• Fundamental Laws
• Conservation of mass
• Conservation of momentum
• Conservation of energy
• Heat Rate Laws
• Fouriers law of heat conduction
• Newtons law of convection
• Stefan-Boltzmann law for radiation
• Supplementary Laws
• Second law of thermodynamics
• Equations of state
• ideal gas law
• tabulated thermodynamic properties
• caloric equation (definition of specific heat)

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Objectives of a Heat Transfer Calculation

• ANALYSIS
• Calculate T(x,y,z,t) or q for a system undergoing
  a specified process
• e.g., calculate daily heat loss from a house
• e.g., calculate operating temperature of a
  semiconductor chip with heat sink/fan
• DESIGN
• Determine a configuration and operating
  conditions that yield a specified T(x,y,z,t) or
  q
• e.g., determine insulation needed to meet a
  specified daily heat loss from a house
• e.g., determine heat sink and/or fan needed to
  keep operating temperature of a semiconductor
  chip below a specified value

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Classes of Heat Transfer Problems

• Thermal Barriers
• insulation
• radiation shields
• Heat Transfer Enhancement (heat exchangers)
• boilers, evaporators, condensers, etc.
• solar collectors
• finned surfaces
• Temperature Control
• cooling of electronic components
• heat treating quenching of metals
• minimizing thermal stress
• heating appliances (toaster, oven, etc.)