NAOE 2205: HEAT TRANSFER
INTRODUCTION
MEHRAN ISLAM
Lecturer, Department of Offshore Engineering,
BANGABANDHU SHEIKH MUJIBUR RAHMAN
MARITIME UNIVERSITY, BANGLADESH
INTRODUCTION
• We defined heat as the form of energy that can be transferred from one
system to another as a result of temperature difference.
• A thermodynamic analysis is concerned with the amount of heat
transfer as a system undergoes a process from one equilibrium state to
another.
• The science that deals with the determination of the rates of such
energy transfers is the heat transfer.
• The transfer of energy as heat is always from the higher-temperature
medium to the lower-temperature one
• Heat transfer stops when the two mediums reach the same
temperature.
• Energy can be transferred to or from a given mass by two mechanisms:
heat transfer Q and work W.
• An energy interaction is heat transfer if its driving force is a
temperature difference.
• Otherwise, it is work. A rising piston, a rotating shaft, and an electrical
wire crossing the system boundaries are all associated with work
interactions.
• In daily life, we frequently refer to the sensible and latent forms of
internal energy as heat, and we talk about the heat content of bodies.
• In thermodynamics, however, those forms of energy are usually
referred to as thermal energy to prevent any confusion with heat
transfer.
• we will refer to the thermal energy as heat and the transfer of thermal
energy as heat transfer.
• The amount of heat transferred during the process is denoted by Q.
• The amount of heat transferred per unit time is called heat transfer rate,
and is denoted by 𝑄.
• The overdot stands for the time derivative, or “per unit time.”
• The heat transfer rate 𝑄 has the unit J/s, which is equivalent to W.
• When the rate of heat transfer 𝑄 is available, then the total amount of heat
transfer Q during a time interval ∆t can be determined from:
• For the special case of 𝑄 =constant, the equation above reduces to:
• 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:
• where A is the heat transfer area.
• Note that heat flux may vary with time as well as position on a
surface.
Application Areas of Heat Transfer
• The human body
• Electric or gas range,
• the heating and air-conditioning system,
• the refrigerator and freezer, Air-conditioning, the water heater, the
iron,
• the computer, the TV, electronics.
• car radiators, solar collectors, various components of power plants,
and even spacecraft
• Heat exchanger, IC engines, machineries
MODES OF HEAT TRANSFER
• Heat can be transferred in three different modes: conduction, convection, and
radiation.
• All modes of heat transfer require the existence of a temperature difference
• All modes are from the high-temperature medium to a lower-temperature one.
Reference (text, images, and equations) : HEAT AND MASS TRANSFER: FUNDAMENTALS & APPLICATIONS, FIFTH EDITION- YUNUS A.
ÇENGEL and AFSHIN J. GHAJAR (McGraw-Hill Education)
CONDUCTION
• 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.
• 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.
• In solids, it is due to the combination of vibrations of the molecules in a
lattice and the energy transport by free electrons.
• For example A cold canned drink in a warm room, eventually warms up to
the room temperature as a result of heat transfer from the room to the
drink through the aluminum can by conduction.
• The rate of heat conduction through a medium depends on the:
Geometry of the medium,
Its thickness,
and the material of the medium,
as well as the temperature difference across the medium.
• Consider steady heat conduction through a large plane wall of
thickness ∆x= L and area A, as shown in Fig.
• The temperature difference across the wall is ∆T =T2 -T1.
• Experiments have shown that the rate of heat transfer 𝑄 through the
wall is doubled when the temperature difference ∆T across the wall or
the area A normal to the direction of heat transfer is doubled,
• but is halved when the wall thickness L is doubled.
• Thus we conclude that the rate of heat conduction through a plane
layer is proportional to the temperature difference across the layer and
the heat transfer area, but is inversely proportional to the thickness of
the layer.
• That is,
• Where the constant of proportionality k is the thermal conductivity of
the material, which is a measure of the ability of a material to conduct
heat.
• In the limiting case of ∆x0, the equation above reduces to the differential form:
• This is called Fourier’s law of heat conduction after J. Fourier.
• Here dT/dx is the temperature gradient, which is the slope of the temperature
curve on a T-x diagram (the rate of change of T with x), at location x.
• The relation above indicates that the rate of heat conduction in a given direction is
proportional to the temperature gradient in that direction.
• Heat is conducted in the direction of decreasing temperature, and the temperature
gradient becomes negative when temperature decreases with increasing x.
• The negative sign in Eq. ensures that heat transfer in the positive x direction is a
positive quantity.
• The heat transfer area A is always normal to the direction of heat
transfer.
• For heat loss through a 5-m-long, 3-m-high, and 25-cm-thick wall, for
example, the heat transfer area is A=15 m2.
• Note that the thickness of the wall has no effect on A.
THERMAL CONDUCTIVITY
• we have defined the property specific heat cp as a measure of a
material’s ability to store thermal energy.
• For example, cp = 4.18 kJ/kg·°C for water and cp = 0.45 kJ/kg·°C for
iron at room temperature
• which indicates that water can store almost 10 times the energy that
iron can per unit mass.
• Likewise, the thermal conductivity k is a measure of a material’s
ability to conduct heat.
• For example, k=0.607 W/m·K for water and k =80.2 W/m·K for iron
at room temperature,
• which indicates that iron conducts heat more than 100 times faster
than water can.
• Thus we say that water is a poor heat conductor relative to iron,
although water is an excellent medium to store thermal energy.
• The thermal conductivity of a material can be defined as the rate of
heat transfer through a unit thickness of the material per unit area
per unit temperature difference.
• The thermal conductivity of a material is a measure of the ability of
the material to conduct heat.
• A high value for thermal conductivity indicates that the material is a
good heat conductor,
• A low value indicates that the material is a poor heat conductor or
insulator.
• The thermal conductivity of pure copper at room temperature is
• k = 401 W/m·K, which indicates that a 1-m-thick copper wall will
conduct heat at a rate of 401 W/m2 area per K temperature difference
across the wall.
• Materials such as copper and silver that are good electric conductors
are also good heat conductors, and have high values of thermal
conductivity.
• Materials such as rubber, wood, and Styrofoam are poor conductors of
heat and have low conductivity values.
• Unlike metals, which are good electrical and heat conductors,
crystalline solids such as diamond and semiconductors such as silicon
are good heat conductors but poor electrical conductors.
• As a result, such materials find widespread use in the electronics
industry.
• Despite their higher price, diamond heat sinks are used in the cooling
of sensitive electronic components because of the excellent thermal
conductivity of diamond.
• Silicon oils and gaskets are commonly used in the packaging of
electronic components because they provide both good thermal contact
and good electrical insulation.
• The thermal conductivity of an alloy of two metals is usually much
lower than that of either metal.
• Even small amounts in a pure metal of “foreign” molecules that are
good conductors themselves seriously disrupt the transfer of heat in
that metal.
• The thermal conductivity of steel containing just 1 percent of chrome
is 62 W/m·K, while the thermal conductivities of iron and chromium
are 83 and 95 W/m·K, respectively.
• The temperature dependence of thermal conductivity causes
considerable complexity in conduction analysis.
• Therefore, it is common practice to evaluate the thermal conductivity
k at the average temperature and treat it as a constant in calculations.
• In heat transfer analysis, a material is normally assumed to be
isotropic.
• That is, to have uniform properties in all directions. This assumption is
realistic for most materials,
• Except those that exhibit different structural characteristics in different
directions, such as laminated composite materials and wood
(anisotropic materials).
• The thermal conductivity of wood across the grain, for example, is
different than that parallel to the grain.
HEAT CAPACITY
• The product cp, which is frequently encountered in heat transfer
analysis, is called the heat capacity of a material.
• Both the specific heat cp and the heat capacity cp represent the heat
storage capability of a material.
• But cp expresses it per unit mass whereas cp expresses it per unit
volume,
• As can be noticed from their units J/kg·K and J/m3·K, respectively.
THERMAL DIFFUSIVITY
• Another material property that appears in the transient heat conduction
analysis is the thermal diffusivity, which represents how fast heat
diffuses through a material and is defined as:
• Note that the thermal conductivity k represents how well a material
conducts heat, and the heat capacity cp represents how much energy a
material stores per unit volume.
• Therefore, the thermal diffusivity of a material can be viewed as the
ratio of the heat conducted through the material to the heat stored per
unit volume.
• A material that has a high thermal conductivity or a low heat capacity
will obviously have a large thermal diffusivity.
• The larger the thermal diffusivity, the faster the propagation of heat
into the medium.
• A small value of thermal diffusivity means that heat is mostly
absorbed by the material and a small amount of heat is conducted
further.
CONVECTION
• Convection is the mode of energy transfer between a solid surface and
the adjacent liquid or gas that is in motion,
• and it involves the combined effects of conduction and fluid motion.
• The faster the fluid motion, the greater the convection heat transfer.
• In the absence of any bulk fluid motion, heat transfer between a
solid surface and the adjacent fluid is by pure conduction.
• The presence of bulk motion of the fluid enhances the heat transfer
between the solid surface and the fluid, but it also complicates the
determination of heat transfer rates.
• Consider the cooling of a hot block by blowing cool air over its top
surface.
• Heat is first transferred to the air layer adjacent to the block by
conduction.
• This heat is then carried away from the surface by convection.
• Convection is called forced convection if the fluid is forced to flow over
the surface by external means such as a fan, pump, or the wind.
• In contrast, convection is called natural (or free) convection if the fluid
motion is caused by buoyancy forces that are induced by density
differences due to the variation of temperature in the fluid.
• In the absence of a fan, heat transfer from the surface of the hot block in
is by natural convection since any motion in the air in this case is due to
the rise of the warmer (and thus lighter) air near the surface and the fall
of the cooler (and thus heavier) air to fill its place.
• Heat transfer processes that involve change of phase of a fluid are also
considered to be convection because of the fluid motion induced during
the process, such as the rise of the vapor bubbles during boiling or the
fall of the liquid droplets during condensation.
• the rate of convection heat transfer is observed to be proportional to
the temperature difference, and is conveniently expressed by Newton’s
law of cooling as:
• Here h is the convection heat transfer coefficient in W/m2·K
• As is the surface area through which convection heat transfer takes
place,
• Ts is the surface temperature, and Tꝏ is the temperature of the fluid
sufficiently far from the surface.
• Note that at the surface, the fluid temperature equals the surface
temperature of the solid.
• The convection heat transfer coefficient h
is not a property of the fluid.
• It is an experimentally determined
parameter whose value depends on all the
variables influencing convection such as
the surface geometry,
the nature of fluid motion,
the properties of the fluid,
and the bulk fluid velocity.
• Typical values of h are given in Table.
RADIATION
• 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.
• Unlike conduction and convection, the transfer of heat by radiation
does not require the presence of an intervening medium.
• In fact, heat transfer by radiation is fastest (at the speed of light) and it
suffers no attenuation in a vacuum.
• In heat transfer studies we are interested in thermal radiation, which is
the form of radiation emitted by bodies because of their temperature.
• It differs from other forms of electromagnetic radiation such as x-rays,
gamma rays, microwaves, radio waves, and television waves that are
not related to temperature.
• All bodies at a temperature above absolute zero emit thermal radiation.
• Radiation is a volumetric phenomenon, and all solids, liquids, and gases
emit, absorb, or transmit radiation to varying degrees.
• usually considered to be a surface phenomenon for solids that are
opaque to thermal radiation such as metals, wood, and rocks
• The maximum rate of radiation that can be emitted from a surface at a
thermodynamic temperature Ts (in K or R) is given by the Stefan–
Boltzmann law as:
• where = 5.67*10-8 W/m2·K4 is the Stefan–Boltzmann constant.
• The idealized surface that emits radiation at this maximum rate is called a
blackbody, and the radiation emitted by a blackbody is called blackbody
radiation.
• The radiation emitted by all real surfaces is less than the radiation emitted
by a blackbody at the same temperature, and is expressed as:
• where ԑ is the emissivity of the surface whose value is in the range 0 ≤ ԑ ≤ 1
• When a surface of emissivity ԑ and surface area As at a thermodynamic
temperature Ts is completely enclosed by a much larger (or black)
surface at thermodynamic temperature Tsurr separated by a gas (such as
air) that does not intervene with radiation,
• the net rate of radiation heat transfer between these two surfaces is
given by:
