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1CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111
HEAT TRANSFER
SME 4463SME 4463
INSTRUCTOR: ASSOC PROF DR. MAZLAN ABDUL WAHID
http://www.fkm.utm.my/~mazlan
TEXT: Introduction to Heat Transfer
by Incropera, DeWitt, Bergman, Lavine
FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
DR. MAZLAN
by Incropera, DeWitt, Bergman, Lavine5th Edition, John Wiley and Sons
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111TEXT: Inroduction to Heat Transferby Incropera, DeWitt, Bergman, Lavine John Wiley and Sons
FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
DR. MAZLAN
2CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111
Thermodynamics is about: Interaction of energy with system and surroundings.
Thermodynamics
systemsurroundings
boundaryWQ
FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
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Energy can move in and out of a system in two forms Work (W) and Heat (Q)
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111ObjectivesWhen you finish studying this chapter, you should be able to: Understand how thermodynamics and heat transfer are related to
each other, Distinguish thermal energy from other forms of energy, and heat Distinguish thermal energy from other forms of energy, and heat
transfer from other forms of energy transfer, Perform general energy balances as well as surface energy balances, Understand the basic mechanisms of heat transfer, which are
conduction, convection, and radiation, and Fourier's law of heat conduction, Newton's law of cooling, and the StefanBoltzmann law of radiation,
Identify the mechanisms of heat transfer that occur simultaneously in
FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
DR. MAZLAN
Identify the mechanisms of heat transfer that occur simultaneously in practice,
Develop an awareness of the cost associated with heat losses, and
3CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Thermodynamics and Heat Transfer The science of thermodynamics deals with the
amount of heat transfer as a system undergoes a process from one equilibrium state to another, and process from one equilibrium state to another, and makes no reference to how long the process will take.
The science of heat transfer dealswith the determination of the rates of energy that can be transferred from one system to another as a
FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
DR. MAZLAN
from one system to another as a result of temperature difference.
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
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Thermodynamics deals with equilibrium states and changes from one equilibrium state to another. Heat
Thermodynamics and Heat Transfer
changes from one equilibrium state to another. Heat transfer, on the other hand, deals with systems that lack thermal equilibrium, and thus it is a nonequilibriumphenomenon.
Therefore, the study of heat transfer cannot be based on the principles of thermodynamics alone.
However, the laws of thermodynamics lay the
FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
DR. MAZLAN
However, the laws of thermodynamics lay the framework for the science of heat transfer.
4CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Heat Transfer
The basic requirement for heat transfer is the presence of a temperature difference.
The second law requires that heat The second law requires that heat be transferred in the direction of decreasing temperature.
The temperature difference is the driving force for heat transfer. The rate of heat transfer in a certain direction depends on the
magnitude of the temperature gradient in that direction.
FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
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The rate of heat transfer in a certain direction depends on the magnitude of the temperature gradient in that direction.
The larger the temperature gradient, the higher the rate of heat transfer.
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111But thermodynamics ..deals with the end states of the process
or
when the system reach equilibrium at the end states
It provides no information concerning
The nature of the interactions The time rate at which it occurs
Heat transfer describes the nonequilibrium phenomena of the
FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
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Heat transfer describes the nonequilibrium phenomena of the transfer of energy due to temperature difference.
5CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111EXAMPLE
Consider a can of drinks which you want to cool down you would put it in a refrigerator.
20oCSurrounding Air
We know from experience that if we leave it in the fridge ultimately it will reach equilibrium with its surroundings AT WHAT RATE ? HOW?
Surrounding AirT = 4oC
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AT WHAT RATE ? HOW?Thermodynamics can not answer that.
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When there is temperature difference between two medium, energy will transfer from a hotter medium to a colder medium in a form of HEAT.
The nature of heat transfer
So heat transfer will occur when there is an energy difference (temperature difference) in a medium or between mediums
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6CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
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Heat transfer is thermal energy in transit due to
temperature difference
The topic of Heat Transfer is about
All of Heat Transfer study is about answering the
understanding, determining and predicting flows of heat
temperature difference
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All of Heat Transfer study is about answering the question:
What is the heat flow rate from A to B?
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11111111What is temperature ?
Thermal energy: atomic/molecular/electronic kinetic energyenergy
Measure to determine how hot/cold a material is (intensity of thermal energy)
Criterion to determine the direction of thermal-energy transport
From a microscopic view, temperature represents atomic ormolecular kinetic energy (translation / vibration / rotation)
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molecular kinetic energy (translation / vibration / rotation)
7CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Where is heat transfer falls at?There are three principle laws upon which Engineering studies are derived Conservation of Momentum (Fluid Mechanics, Conservation of Momentum (Fluid Mechanics, Mass Transfer) Conservation of Energy (Thermodynamics, Heat Transfer)Conservation of Mass (Continuity, Mass Transfer)
FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
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In this course we are primarily interested in the
Conservation of Energy in Heat Transfer
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11111111Application Areas of Heat Transfer
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8CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Importance of heat transfer in engineering
Power High turbine inlet temperatures desired for efficiency. Heat transfer from gas or steam to turbine blades (convection, radiation) blades may fail. Predict/control temperature of blades. Cooling strategies internal cool air passages,cool air bleed through perforated blade surface.
Power
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cool air bleed through perforated blade surface.
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Turbine blade cooling
FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
DR. MAZLANFaculty of Mechanical EngineeringUniversiti Teknologi Malaysia81310 Skudai, Johor, Malaysia
9CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Biomedical
Thermal cancer treatments electromagnetic radiation (laser, radio), ultrasonic waves, etc used to heat tumor.
Necessary to predict tumor temperature and understand heat transfer to surroundingtissue (conduction, convection). Sometimes whole body temperature needs to be raised, lowered, maintained water
ultrasonic waves, etc used to heat tumor.
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maintained waterand air blanket devices (convection and conduction), IR lamps (radiation).
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Building
Heat is transferred through walls (conduction) to outside air (convection), through(convection), throughwindows (radiation, convection, conduction), open doors/windows (convection) Heat loss (or gain) determines heating (air-conditioning) requirements.
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Heat exchangers devices designed specifically to promote heat transfer between two fluids car radiators, boilers, condensers, chip cooling, equipment cooling and so onand so on
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Fuel cells
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
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FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Energy Transfer
Energy can be transferred to or from a given mass by two mechanisms: heat transfer, and work.
The amount of heat transferred during a process is denoted by Q. The amount of heat transferred during a process is denoted by Q. The amount of heat transferred per unit time is called heat
transfer rate, and is denoted by Q. The total amount of heat transfer Q during a time interval t can
be determined from
0
(J)t
Q Qdt
= &
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The rate of heat transfer per unit area normal to the direction of heat transfer is called heat flux, and the average heat flux is expressed as
0
2 (W/m )Qq
A=
&
&
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111The First Law of Thermodynamics
The first law of thermodynamics states that energy can neither be created nor destroyed during a process; it can only change forms.Total energy Total energy Change in the
The energy balance for any system undergoing any process can be expressed as (in the rate form)
Total energyentering the
system
Total energyleaving the
system
Change in thetotal energy of
the system- =
(W)E E dE dt =& &
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(W)in out systemE E dE dt =& &
Rate of net energy transfer
by heat, work, and mass
Rate of change in internal kinetic, potential,
etc., energies
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Notation used in this course
Notation
Q - energy transfer in the form of heat (same as in thermo), Jq - heat transfer rate, Wq - heat transfer rate, per unit length, W/mq - heat flux, heat transfer rate per unit area, W/m2.
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q - rate of energy generation per unit volume, W/m3.
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Methods of Heat Transfer
Objectives are to: describe the three methods of heat transfer give practical/environmental examples of each
FACULTY OF MECHANICAL ENGINEERINGUNIVERSITI TEKNOLOGI MALAYSIASKUDAI, JOHOR, MALAYSIA HEAT TRANSFER INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Modes of Heat Transfer
Heat transfers across the systems boundary in three modes
Conduction
Convection
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Radiation
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Conduction
Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles.particles.
Conduction can take place in solids, liquids, or gases In gases and liquids conduction is due to
the collisions and diffusion of the molecules during their random motion.
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In solids conduction is due to the combination of vibrations of the molecules in a lattice and the energy transport by free electrons.
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Conduction
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Conduction
-Usually in solid(s) , maybe liquids -Rarely gases (negligible to convection)
Straightforward transmission of heat within a stationary medium Solid, liquid, or gas (usually most important in solids)
Mechanisms are on molecular/atomic level: molecular vibrations,
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Mechanisms are on molecular/atomic level: molecular vibrations, motion of free electrons
Can often come up with exact mathematical solutionsNeed a temperature gradient
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Conduction
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Conduction is simply:Transfer of energy from more energetic to lessenergetic particles of a substance due to interactionsbetween particles
Conduction
Fouriers Law
between particles
From empirical observations (experiments)
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111
LTkAqcond
=
Conduction
q: heat transfer rate A: cross-sectional area L: length
LkAqcond =
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L: length k: thermal conductivity T: temperature difference across conductor
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Thermal Conductivity
The thermal conductivity of a material is a measure of the ability of the material to conduct measure of the ability of the material to conduct heat.
High value for thermal conductivity good heat conductor
Low value
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Low valuepoor heat conductor or insulator.
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Thermal Conductivities of Materials
The thermal conductivities of gasesconductivities of gasessuch as air vary by a factor of 104 from those of pure metals such as copper.
Pure crystals and metalshave the highest
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thermal conductivities, and gases and insulating materials the lowest.
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Thermal Conductivities and Temperature
The thermal conductivities of materials vary with temperature.
The temperature dependence of thermal conductivity causes considerable complexity in
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conduction analysis. A material is
normally assumed to be isotropic.
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Thermal diffusivity
2Heat conducted (m s)
Heat stored pkc
= =
The thermal diffusivity represents how fast heat diffuses through a material.
Appears in the transient heat conduction analysis. A material that has a high thermal conductivity or a low heat
Heat stored pc
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A material that has a high thermal conductivity or a low heat capacity will have a large thermal diffusivity.
The larger the thermal diffusivity, the faster the propagation of heat into the medium.
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Example
A plain carbon steel rod of diameter 15 mm and length 420 mm has its ends held at steady temperatures of 20C and 90C, respectively. What is
Conduction
ends held at steady temperatures of 20C and 90C, respectively. What is the heat flow rate?
k = conductivity = 60.5 W/m.K for plain carbon steel(Fouriers Law).
q = -kAdT/dx = kA(T - T )/L
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q = -kAdT/dx = kA(T1- T2)/L= 60.5 pi (0.015)2/4 (90 20) / 0.42= 1.78 W
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11111111Under steady state conditions where temperature distribution is linear, the temperature gradient may be expressed as
and the heat flux is then
or
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Note: heat flux is rate per unit area. The heat rate by conduction, qx (W), through a plane wall of area A is qx = qx " A
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Example
The heat flow rate through a wood board of 2 cm thick for a temperature difference of 25oC between the two surfaces is 150 W/m2. Calculate
Conduction
between the two surfaces is 150 W/m2. Calculate the thermal conductivity of the wood.
T
50oC25oC
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25oC
Convection
Convection is the mode of energy transfer between a
CONVECTION = Conduction + Advection (fluid motion) Convection is the mode of energy transfer between a
solid surface and the adjacent liquid or gas that is in motion.
Convection is commonly classified into three sub-modes: Forced convection, Forced convection, Natural (or free) convection, Change of phase (liquid/vapor,
solid/liquid, etc.)
21
ConvectionT
T s
The convection heat transfer mode is comprised two mechanisms:
1. Energy transfer due to random molecular motion (diffusion)
2. Energy transfer due to bulk (or macroscopic) motion of the fluid(called advection)
If both transport of energy is present, the term CONVECTION is generallyused.If transport of energy due only to bulk motion of the fluid, the termADVECTION is used.
h is the convection heat transfer coefficient in W/m2C.
Convection
W/m C. h depends on variables such as the
surface geometry, the nature of fluidmotion, the properties of the fluid, and the bulk fluid velocity.
22
Convection is what happens when the motion of a heat conductingfluid increases the rate of heat transfer.
Convection
heat transfer.
In other words, the convective air currents increase the rate
of heat transfer by improving of heat transfer by improving the conduction at the surface.
Convection heat transfer normally takes place in a moving liquid or gas
Convection
Conduction still takes place
Usually interested in cooling or heating of a solid object by a fluid stream e.g. pipes in a boiler, cooling fin on an engine
Exact mathematical analysis usually impossible usually rely on empirical correlations
23
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Convection
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111
Convection
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Convection at Home
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111
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11111111
We are interested mainly in cases where there is heat transfer between a fluid in motion and a bounding surface.a. Velocity boundary layer
Convection
a. Velocity boundary layerb. Thermal boundary layerThere are two types of convection:
Forced convection - flow caused by external means
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Forced convection - flow caused by external means
Free convection - caused by buoyancy forces
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Newtons Law of Cooling:
Convection
q is the convective heat flux (W/m2), and is proportional to the
difference between surface and fluid temps. h (W/m2 K) is convective heat transfer coefficient -depends on
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depends onconditions in boundary layer, surface geometry, nature of
fluid motion, and fluid thermo and transport properties.
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Convection
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111RADIATION
Radiation is energy emitted by matter that
is at a finite temperature.
The emission is due to changes in
electron configurations of constituent
atoms or molecules.
Transported by electromagnetic radiation.
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Does not require a material medium,
occurs most efficiently in vacuum.
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Radiation Radiation is the energy emitted by matter in the form of
electromagnetic waves (or photons) as a result of the changes in the electronic configurations of the atoms or molecules.molecules.
Heat transfer by radiation does not require the presence of an intervening medium.
In heat transfer studies we are interested in thermal radiation (radiation emitted by bodies because of their temperature).
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temperature). Radiation is a volumetric phenomenon. However, radiation
is usually considered to be a surface phenomenon for solids that are opaque to thermal radiation.
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Ideal Radiator
The maximum rate of radiation that can be emitted from a surface at a thermodynamic temperature Ts (in K) is given by the StefanBoltzmann law as
Ideal radiatoror Blackbody
where,
Ts is the absolute temp (K) of the surface is the Stefan Boltzmann constant (5.67 x 10-8 W/m2K4)
The idealized surface that emits radiation at this maximum rate is called a blackbody.
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blackbody.
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CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111
Heat flux emitted by a real object (less than that of a blackbody)
0 1
: emissivity, a radiative property of surface, how efficient radiation emission is compared to blackbody
Determination of the net rate at which radiation is
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Determination of the net rate at which radiation is exchanged between surfaces is complicatedMost often, we only need to know the net exchange between a small surface and the surroundings.
CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER
11111111Small Surface and Large Surroundings
The net rate of radiation heat exchange between a small surface and a large surroundings per a unit area of the small surface
: emissivity
T su r
T s
A
A su r
( )44 SURS TTAq =
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: emissivityMaximum = 1.00, black charcoal surface,Minimum = 0.01, shiny gold surface
: Stefan-Boltzmann constant, 5.67 x 10-8 W/m2K4
0 1
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Above eqn. can also be written in the following form,
( )44 SURS TTAq = Above eqn. can also be written in the following form,
q = hrA(Ts Tsur)Where hr is the radiation heat transfer coefficient
h = (T + T ) (T 2 + T 2)
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hr= (Ts + Tsur) (Ts2 + Tsur2)where we have linearized the equation shown earlier.
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Greenhouse Greenhouse Greenhouse Greenhouse EffectEffect
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11111111Conservation of Energy
Control Volume
Surroundings, S
-Accumulation (Storage) stE&
Energy conservation on a rate basis:
Control Volume (CV)
Boundary, B (Control Surface, CS)
(Storage) -GenerationAddition
through inletLossthrough outlet
stst
outgin EdtdEEEE &&&& ==+
inE& outE&gE&
stE&
Units W=J/s
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basis: dt
Inflow and outflow are surface phenomena Generation and accumulation are volumetric phenomena
Units W=J/s
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Conservation of energy
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= dEst/dt =
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st=
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11111111Surface Energy Balance
For a control surface:
qrad
0
0
"""
=
=
radconvcond
outin
qqq
or
EE &&T1
T2
qcondqrad
qconv
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T
x
T2
T
control surface
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Surface energy balance
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11111111The surface energy balance
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11111111Analysis of h.t problem Mesti buat seperti ini !!!
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11111111Important!
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