Chapter 1 Introduction

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Chapter 1 Introduction

• In this introductory chapter, we will
  discuss
• (1) The importance of thermal management
• (2) The principle of conservation of energy
• (3) A brief review of the heat transfer
  mechanism

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1. The importance of thermal management in
electronics
1-1 The trend of heat dissipation in electronics
The heat generation rate by a microprocessor
is proportional to clock frequency f, chip size
A, number of metal layers L, the density of
transistors per unit area, n, and the square
operating voltage V. It can be expressed as
Power (P) ? f x A ? n x L ? V2 It is
reported by International Technology Roadmap for
Semiconductor (ITRS) the on-chip clock frequency
and the transistor density will increases
exponentially over the next decade. The power
supply voltage will decrease continually, its
decrease is not sufficient enough to compensate
for the increase in power generation due to the
increase in transistor density and the on-chip
clock frequency. As predicted by ITRS, chip
power generation will continue to increase over
the next decade, as shown in figure 1.
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Figure 1 the trend of chip power dissipation rate
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1-2 The difficulties in handling thermal
management in electronic

• High power dissipation rate in a small area
• Small temperature difference between heat sink
  and the operation temperature of the device. The
  maximum operation temperature of the devices is
  limited, usually between 80 to 120oC
• The heat dissipation rate is described
  by
• A surface area of the device
• h heat transfer coefficient
• ?T The difference between
  junction and ambient temperatures
• For the problem of heat dissipation in
  electronics, both ?T and A are small. If the heat
  dissipation rate is large, it requires a very
  large heat transfer coefficient. Its value has
  already exceeded the maximum limits of some of
  the convectional cooling techniques.

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• 1-3 The importance of thermal design in
  electronics
• If the heat generated by semiconductor is not
  removed, its
• temperature will go up
• If the temperature is too high, the device
  may fail. The failure
• rate will increase with the increasing of
  operation temperature.
• There are several types of failures due to
  high operation
• temperature, such as crosstalk noise
  between the cells and
• interconnects and mechanical failures.
• The mechanical failure is due the difference
  of thermal expansion
• coefficients between the bonded materials,
  such as the die and
• substrate bond failure and cracking, etc.
• Therefore, thermal design is an integral part
  of the whole
• electrical system design.

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2 The principle of conservation
of energy

• 2-1 Heat and unit of heat
• Heat is a form of energy. In SI units, the
  unit of heat is joule, J (J Nm). In
• some cases, other units, specifically, the
  calorie (cal) and the British
• thermal units (Btu) are still in use today.
  They are related to Joule by
• 1 cal 4.186J heat required to raise 1
  gram of water by 1C at 14.5C
• 1 Btu 1,055.056J 1.055056kJ heat
  required to raise 1lbm of water By
• 1oF at 60oF
• 2-2 Heat transfer rate and heat flux
• Q The amount of heat transfer to an
  object during a period of time, (J)
• q The amount of heat transfer of unit
  mass of the substance, (J/kg)
• The heat transfer rate or the amount
  of heat transfer per unit time
• (J/s W). It relates to total heat
  transfer by
• 
  (W J/s)
• Heat flux or heat transfer rate per unit
  surface area (W/m2 or W/cm2),

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• 2.3 Similarity of heat flow rate and other forms
  of flow rate equations
• Heat flow from a hot object (say, a electronic
  component) to its environment, must exist a
  temperature difference between them. There exists
  an analogue relationship among the flow of heat,
  the flow of electrical current and the flow of
  fluids.
• The flow rate of heat, electrical current, and
  fluid from one point to another is equal to the
  ratio of potential difference between the two
  points in the system to the flow resistance
  between the two points. If there exists no
  potential difference, there is no flow. The
  general flow rate equations of heat, electrical
  current and fluid are
• Rate of heat flow (W)
• Rate of electric current flow (Amp)
• Rate of fluid flow ( )
• where Rh, Ri, Rf are the flow resistance of
  heat, electric current and flow of fluid,
  respectively.

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2.4 Specific heat and internal energy

• The heat required to change the temperature of
  unit mass of the substance by
• one degree is called specific heat. Its value
  depends on the substance and the
• process of the temperature change
• Constant volume specific heat (cv, J/kg.K)
• cv is defined as the amount of heat required
  to change the temperature of unit mass (1 kg) of
  a substance by one degree as the volume of the
  substance is held constant. For a temperature
  change of ?T degree, the heat required is
• q ?u cv ?T,
  (J/kg)
• Under such condition, the total heat
  supplied is used to change the internal energy of
  the substance, ?u. The internal energy is the
  total microscopic mode of energies of all the
  molecules of the substance, which is proportional
  to the temperature. The total change of internal
  energy of mass m kilogram is,
• Q ?U mcv ?T, (J)
• Constant pressure specific heat (cp , J/kg.K)
• cp is defined as the heat required to change
  the temperature of unit mass of the substance by
  one degree as the pressure is held constant. In
  this case, part of the heat supplied is used to
  change the temperature or the internal energy of
  the substance and the rest is used to perform
  some works. The combination of the two parts is
  also called the change in enthalpy ?h.
• q ?h cp ?T
  cv ?T p ?v, (J/kg)

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• q ?h cp ?T cv ?T p ?v,
  (J/kg) w
• 
  A
  L
• 
  
• W is the weight on top of the piston and A
  is the piston area.
• The total change in enthalpy of a substance
  with a mass of m (kg) is ?H.
• Q ?H mcp ?T
  (J)
• For solid or liquid, cp cv
• 
  
• For ideal gas, p v RT ?p?v R?T
  
• cp ?T cv ?T p
  ?v cv ?T R ?T
• cp cv R
• where R is gas constant. For air, R
  287J/kgK
• 
  

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2.4 General equations of conservation of
energy

• The principle of conservation of energy is
• In any process, the rate of total energy
  entering a system, less the
• rate of total energy leaving the system, is
  equal to the rate of change of energy within the
  system. Mathematically
• 
  
  (J/s W )
  
• An alternative form can be obtained by
  integrating the above equation over a time
  interval ?t.
• In any process during a time interval ?T,
  the total energy entering a system, less the
  total energy leaving the system, is equal to the
  change of energy within the system
• Ei Eo ?Esys
  (J)

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2.5 Energy
balance for a closed system

• A closed system consists of a fixed mass there
  is no mass flow across the boundary of the
  system. Electrical components, such as resistor,
  can be considered as closed system.
• The only inflow and outflow of energies are due
  to heat transfer process across the boundary of
  the system and it may have energy generation
  within the system, for example, resistance
  heating,
• Neglecting the change in other types of energies,
  such as the kinetic and potential energies, the
  thermal energy balance equation, in the rate from
  
• the net rate of heat input to the system is
  equal to the rate of change of internal energy of
  the system.
• Over a time interval (?t), the thermal energy
  balance equation is
• Under steady-state condition,

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Example 1-1 Heating of a circular resistor

• To turn on a circular resistor of diameter 1cm
  and length 2cm from temperature 10oC to 70oC in
  30 sec. The density and specific heat of the
  resistor are 1000kg/m3 and 500J/kg.K,
  respectively. Assume there is no heat loss form
  the external surface of the resistor.
• Find a. the total heat supplied, J
• b. the heating rate, J/s W
• Solutions

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Energy balance for an open
system

• In open system, both mass and heat may flow in
  and out from the boundary of the system. In
  steady state condition, the rate of mass flow or
  the rate of energy flow to the system must be
  equal to these flow out from the system.
• The over-head projector and computers with
  air cooling are typical examples of open systems,
  because there are cooling fluids that flows
  through these devices
• The term steady, means that there is no
  physical quantity that changes with time at any
  position in the system. However, physical
  quantities, such as pressure, temperature, and
  flow velocity may change from one point to
  another. The opposite of steady is unsteady or
  transient.
• The mass flow rate, in a duct of cross-sectional
  area, A, can be calculated
• by
  kg/s
  

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• The volume flow rate
• The flow of fluids involves pressure
  loss. But, relatively, the change of the absolute
  pressure between inlet and outlet ports is very
  small in the applications of cooling electronic
  systems.Therefore it may considered as a constant
  pressure process.
• In a steady state, the energy balance equation,
  on the rate basis
• It indicates that the net heat input to
  a steady flow system is converted to the rate of
  increase in enthalpy of the fluid.
• Note
• 1. mass flow rate in a steady flow
  system is constant
• 2. volumetric flow rate may change from
  one point to another.

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Example 2- Cooling a electrical system

• An electronic system contains 10 printed circuit
  boards each dissipates 30W. A 20W
• fan is installed at the inlet port to draw air
  into the system to cool the boards. The total
• heat loss through the casing of the system is
  40W. The air pressure at both ports is
• approximately 1bar ?105Pa. The constant specific
  heat of air is 1000J/kgoC. If the
• inlet and outlet air temperatures are,
  respectively, 30oC and 40oC, what is the air flow
  
• rate in kg/s? The diameter of the inlet port is
  equal to 10cm, what is the inlet air
• velocity? The diameter outlet port is also equal
  to 10cm, what is the outlet air velocity?
• Assumption Steady state operation and air
  behaves as ideal gas.
• To calculate outlet air velocity

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3. Heat transfer mechanism

• Heat transfer is energy in transit due to there
  exists a temperature gradient. If there exists no
  temperature gradient, there is no heat flow.
• Three modes of heat transfer, conduction,
  convection, and radiation.
• 3-1 Conduction
• For a one-dimensional heat conduction
  through a plane wall, the rate of heat flow is
  proportional to the surface area, A, the
  temperature difference across the plane wall, and
  inversely proportional to the thickness of the
  wall
• The proportional constant ,k, is called thermal
  conductivity of the material of
• the wall. Physically, it means that the heat
  transfer rate across a plate of area
• 1m2 and thickness 1m and under 1 degree
  temperature difference across the
• two sides of the wall. It is a material
  property.

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3-1 Conduction

• The thermal conductivity of the substance has the
  unit of W/moC, or W/mK.
• It depends on the material and the temperature.
  The minus sign is a
• consequence of the fact that heat flow is in the
  direction of decreasing
• Temperature, or in the direction of negative
  temperature gradient.
• The thermal conductivity of some common
  substances at room temperature are
• Substance Thermal conductivity,
  W/mK (25oC)
• Diamond 2300
• Copper 401
• Gold
  317
• Aluminum 237
• Silicon 148
• Epoxy-glass 0.26
• Water 0.613
• Helium 0.152
• Air
  0.026

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3-2 Convection Heat
Transfer

• It is comprised of two mechanisms
• Conduction heat transfer due to random molecular
  motion of the fluid.
• Bulk or macroscopic motion of the fluid.
• It can be represented by the convection heat
  transfer coefficient, h (W/m2K), the difference
  between the the surface temperature and the bulk
  fluid temperature, ?T (K or oC), and the wetted
  surface area, A (m2), or
• Physically, the convection heat
  transfer coefficient means that the heat transfer
  rate of wetted surface area 1m2 and under 1
  degree temperature difference between the the
  surface temperature that at the ambient, T8.
• Natural forced convections
• (1) Natural or free convection the
  current of the bulk motion is induced
• by buoyancy force, which arises
  from the density gradient of the fluid
• in the presence of gravitational
  field.
• (2) Forced convection the current is
  caused by external means, such as
• by fan, pump, and others, such as
  the natural wind

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3-2 Convection

• Typical values of convection heat transfer
  coefficient are listed in below
• Type of Convection
  h( W/m2K )
• Free convection of gases
  225
• Free convection of liquids
  101000
• Forced convection of gases
  25250
• Forced convection of liquids
  5020,000
• Boiling and condensation
  2500100,000

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3-3 Radiation

• The energy of radiation is transported by
  electromagnetic wave.
• Radiation does not require the presence of
  material medium in between the two surfaces
• The rate of radiation energy released per unit
  area (W/m2) is termed as the surface emissive
  power, E.
• There is an upper limit of the surface emissive
  power from ideal radiator or blackbody. It is
  prescribed by Stefan-Boltzmann law
• Ts is the absolute temperature (K) of the surface
  and s is called as the Stefan-Boltzmann constant.
  It is equal to
• s 5.67x10-8 (W/m2K4)

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3-3 Radiation

• The heat flux emitted by a real surface is less
  than that of a blackbody at the same temperature
  is given by
• is termed emissivity of the surface. It
  provides a measure of how efficiently a
  surface emits energy relative to a blackbody. It
  is a positive value less than unity.
• A special case that occurs frequently involves
  radiation exchange between a small object at
  temperature Ts and a large surroundings at
  temperature Tsurr. The radiation heat exchange
  between the two is
• where A and are the surface area and
  emissivity of the small object.
• For two black parallel plates with very small gap
  between them. The radiation heat transfer rate
  from the higher temperature plate to the lower
  temperature plate is

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Example 1-11 Heat transfer between two isothermal
boards

• Two parallel boards of dimension 50cm x 50cm and
  temperatures of T1200K
• and T2300K,respectively. The distance between
  them is 2mm. The two surfaces
• are black surfaces (e 1.0). What are the rate
  of heat transfer between the two
• boards assuming the gap between the two board is
  (a) filled with air at pressure 1
• atmosphere and (b) vacuum.
• Solution (a) the average temperature is 250K,
  the air thermal
• conductivity is 0.0219W/mK
• Conduction heat transfer rate through the air
  layer is
• Radiation heat transfer between the two boards
  with small
• distance apart is
• The total heat transfer rate is 273.7592265.75W
• (b) In vacuum there is not conduction heat
  transfer. The total heat transfer rate is 92W

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• The following pages will not be taught

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Example 1-2 heat loss from heating duct in
basement

• Given L 5m, Ac 20cm x 25cm, Pi 100kPa, Ti
  60oC, Vi 5m/s, To54oC
• Find rate of heat loss from the surface of the
  duct
• Assumptions
• - Steady state operation
• - Air behaves as ideal gas
• The solution
• - The average air temperature
• - The properties of air, form Table
• Cp 1007J/kgK
• - The mass flow rate
• Radiation heat transfer across the air
  layer
• The total rate of heat transfer is 588W

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A long circular resistor has a diameter 2mm
generates 2W per meter long. The ambient fluid
temperature is 20oC the convection heat
transfer coefficient is 100W/m2K. What is the
surface temperature of the resistor?

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