Introduction to Heat transfer
MEL 202
Heat & Mass Transfer
Dr. Amit Arora
Department of Mechanical Engineering
NORTHCAP UNIVERSITY, GURUGRAM
Modes of Heat Transfer
• Heat can be transferred via three different modes
1. Conduction,
2. Convection,
3. Radiation
• All three modes require the existence of temperature
difference
• Conversely, heat transfer stops when the medium reaches
isothermal state
Conduction
• Conduction heat transfer depends on the activities at atomic
and molecular levels in a (single) quiescent medium
• What do you understand by ‘quiescent medium’ ?
– Examples !!!
– Apparently, conduction can take place in solids, liquids, or gases
• Conduction may be viewed as transfer of energy from more
energetic particles, of a substance, to the adjacent less
energetic particles as a result of interactions b/w its particles
• Mechanism of conduction depends on the phase of substance
due to interactions b/w the particles being phase dependent
• In quiescent fluids, conduction is only due to random molecular
motion which constitute collisions and diffusion of its particles
• Consider a gas occupying space b/w two surfaces, at different
temperatures, such that temperature gradients are prevailing in
it but no bulk motion
– All the molecules keep on constantly colliding with the neighbouring
molecules
What is
temperature ?
– Molecules with higher kinetic energies (higher-temperature) transfer a
part of their kinetic energies to the adjacent less energetic molecules
(lower temperature) as a result of random molecular collisions and
diffusion
– Conversely, conduction heat transfer occurs in the direction of
decreasing temperature
– Net transfer of heat in the direction of decreasing temperature, due to
random molecular motions, may also be referred to as heat diffusion
• Compared to gases, heat conduction in liquids is of higher order
– Why ?
– Molecules in liquids are more closely spaced leading to stronger
and more frequent molecular interactions
• Unlike fluids, atoms and molecules of solids exhibit only
vibrational motions
– Due to their fixed positions relative to each other in a periodic
manner (grid) called lattice
• In solids, an additional mechanism facilitates heat conduction,
which is attributed to the migration of free electrons
• Apparently, conduction in solids is due to the combined effect
of two mechanisms i.e.
– Vibrations of atoms and molecules in a lattice (lattice vibration/
waves) and energy transport due to the flow of free electrons,
– Latter mechanism is more effective for the heat transport, if
present
• In pure metals, conduction is mainly due to the flow of free
electrons; and in non-metals, conduction is due to lattice
vibration only
– As conduction due to the flow of free electrons is more effective,
that is why pure metals are generally good conductors of heat
• Rate of heat conduction through a medium is found
to depend on four factors
1. Geometry of the medium,
2. Thickness of the medium,
3. Material of the medium,
4. Temperature difference across the medium
• What is the functional relationship b/w heat transfer
rate and the four independent parameters ?
– Consider heat transfer across the wall of a room
exposed to solar radiation
• Functional dependence of conduction heat transfer
rate is defined as, Area x Temp. diff .
Rate of heat conduction
Thickness
• Rate of heat conduction is expressed as
T2 T1
Q cond kA
x
– Referred as Fourier’s law of heat conduction
– Physical law that governs heat conduction
– Here, ‘k’ is the constant of proportionality
– What is the significance of (-ve) sign ?
Fourier’s law of
• In the limiting case of Δx → 0, above heat conduction
equation reduces to differential form after J. Fourier,
dT who expressed it
Q cond kA (W)
dx first in his heat
transfer text in 1822
– Temperature gradient is the slope of
temperature distribution at a given location ‘x’
dT
Q cond kA (W)
dx
• Conditions for applying the Fourier’s law of
heat conduction
– Steady state
– Bounding surfaces are isothermal
– Heat flow is uni-directional (1 D)
– Temperature gradient is constant
– No internal heat generation
– Material is homogeneous and isotropic
Thermal Conductivity
• Thermal conductivity ‘k’ is the measure of a material’s ability
to conduct heat
dT
• Its units are ‘W/m-K’ Q cond kA (W)
dx
• At room temperature,
– k ≈ 0.608 W/m-K for water and
– k ≈ 80.2 W/m-K for iron,
• Iron conducts heat more than 100 times faster than water
– Conversely, water is a poor heat conductor compared to iron
• Thermal conductivity of a material depends on its physical state
and is a function of pressure, temperature, humidity and structure
• Thermal conductivity of gases is smaller than liquids due to
intermolecular spacing being much larger
Range of Thermal Conductivity
• Thermal conductivity of selected
engineering materials at room
temperature is compared
• Thermal conductivity of gases (say air)
is lower than pure metals (say copper)
by a factor of the order 104
• Pure crystals and metals have the
highest thermal conductivities
• Gases and insulating materials have
the lowest thermal conductivities
Range of thermal
conductivity of
various
engineering
materials at
room temperature
A simple experimental
setup to determine the
thermal conductivity
of a material...
L
K .Q
A (T1 T2 )
CONVECTION
Forced Convection
Natural
Convection
Boiling
Condensation
Newton’s Law of Cooling
(Physical law governing Convection)
• Convection is the mechanism of heat transfer b/w a solid
surface and adjacent fluid (in motion)
– Both are at different temperatures
• Faster the fluid motion, greater
the rate of heat convection
• Convection heat transfer involves energy transfer due to both
– Random molecular motions (conduction) and
– Bulk motion of the fluid (advection)
• In the absence of bulk motion of the fluid, heat transfer b/w the
solid surface and adjacent fluid is by pure conduction
• Rate of convection heat transfer is given by Newton’s Law of
Convection
Q conv h A s (Ts T )
– Where ‘h’ is called convection heat transfer coefficient
– Units: W/m2-K
– It is an experimentally determined parameter
– Its value depends on several independent variables influencing
the amount of convection heat transfer
– Conditions for applying the law !
Typical values of convection heat transfer coefficient
Type of convection ‘h’
process (W / m2 K)
Free Convection
Gases 2-25
Liquids 50 -1000
Forced Convection
Gases 35 -250
Liquids 50 -20,000
Phase Change
Boiling/ 2500 -100,000
Condensation
