NAOE 2205: HEAT TRANSFER
CONDUCTION
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.
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.
