Introduction to heat transfer

➢ Energy can exist in different types (forms).

✓ thermal ✓ potential
✓ chemical ✓ electrical
✓ mechanical ✓ magnetic
✓ kinetic ✓ nuclear and etc
➢ There are two mechanisms for energy to transfer from or to a given system.
✓ Heat
✓ work
➢ Heat is the form of energy that can be transferred from one system to another as a result of
temperature difference.
➢ Heat transfer (or heat) is thermal energy in transit due to a spatial temperature difference.
 Thermodynamics and Heat Transfer
Thermodynamics : Heat transfer:
▪ Thermodynamics" deals with the amount of ▪ Heat Transfer" deals with the rate of heat transfer thus, Heat
energy in form of heat or work during a transfer deals with time and non equilibrium phenomena.
process and only considers the end states in ▪ Heat can only transfer when there is a temperature gradient
equilibrium. exists in a body and which is indication of non equilibrium
▪ How much heat is transferred (dQ) phenomena.
▪ How much work is done (dW) ▪ How (with what modes) dQ is transferred
▪ At what rate dQ is transferred
▪ Temperature distribution inside the body
Application Areas of Heat Transfer
 Mechanisms of heat transfer
✓Heat can be transferred in three different modes:
✓conduction
✓convection
✓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
1. 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.
✓assume that there is no bulk, or macroscopic, motion.

➢In solids;
✓it is due to the combination of vibrations of the molecules in a lattice and the energy
transport by free electrons.
✓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.
 Fig: Conduction heat transfer in gas molecule

▪ Higher temperatures are associated with higher molecular energies, and when
neighboring molecules collide, as they are constantly doing, a transfer of
energy from the more energetic to the less energetic molecules must occur.
▪ random translational motion, as well as to the internal rotational and vibrational
motions, of the molecule
▪ This heat transfer mechanism is much the same in liquids, although the liquid
molecules are more closely spaced and the molecular interactions are stronger
and more frequent.
Quantifying heat transfer processes
• Rate equation may be used to compute the amount of energy being transferred per
unit time.
• For heat conduction, the rate equation is known as Fourier’s law.
• For the one-dimensional plane wall, having a
temperature distribution T(x), the rate equation is expressed as

• The heat flux (W/m2) is the heat transfer rate in the x direction per unit area
perpendicular to the direction of transfer, and it is proportional to the temperature
gradient, dT/dx, in this direction.
• The parameter k is a transport property known as the thermal conductivity (W/m. K)
and is a characteristic of the wall material.
• The minus sign is a consequence of the fact that heat is transferred in the direction
of decreasing temperature.
Temperature gradient

Heat flux

• The heat rate by conduction, 𝑞𝑥 (W), through a plane wall of area A is then the
product of the flux 𝑞𝑥 ′′ and the area, .
2. Convection
✓The convection heat transfer mode is comprised of two mechanisms.
✓due to random molecular motion (diffusion),
✓Due to bulk, or macroscopic, motion of the fluid.
✓When large numbers of molecules are moving collectively or as aggregates,
in the presence of a temperature gradient, contributes to heat transfer.
✓Because the molecules in the aggregate retain their random motion, the
total heat transfer is then due to a superposition of energy transport by the
random motion of the molecules and by the bulk motion of the fluid.
✓It is customary to use the term convection when referring to this cumulative
transport and the term advection when referring to transport due to bulk
fluid motion.
✓ 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.
• 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.
• 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.
• The convection heat transfer process, the appropriate rate equation
is of the form
This expression is known as
Newton’s law of cooling.

▪ The convective heat flux 𝑞𝑥 ′′ (W/m2 ), is proportional to the difference between the
surface and fluid temperatures, 𝑇𝑆 and 𝑇∞ , respectively.
▪ the parameter h (W/m2.K) is termed the convection heat transfer coefficient.
✓ It depends on conditions in the boundary layer, which are influenced by surface
geometry, the nature of the fluid motion, and an as assortments of fluid
thermodynamic and transport properties.
 3. Radiation
➢Thermal radiation is energy emitted by matter that is at a non zero temperature.
➢Although we will focus on radiation from solid surfaces, emission may also
occur
from liquids and gases.
➢The energy of the radiation field is transported by electromagnetic waves (or
alternatively, photons).
➢ While the transfer of energy by conduction or convection requires the presence
of a material medium, radiation does not.
✓ In fact, radiation transfer occurs most efficiently in a vacuum.
➢ Radiation that is emitted by the surface originates from the thermal energy of
matter bounded by the surface, and the rate at which energy is released per unit
area (W/m2) is termed the surface emissive power E.
 ▪ There is an upper limit to the emissive power, which is prescribed by the
Stefan–Boltzmann law

▪ where Ts is the absolute temperature (K)

of the surface and 𝜎 is the Stefan–
Boltzmann constant

▪ Such a surface is called an ideal radiator

or blackbody.
▪ an idealized body which is a perfect
absorber and a perfect emitter

▪ The heat flux emitted by a real surface is

less than that of a blackbody at the same
temperature and is given by Radiation exchange: (a) at a surface and (b)
between a surface and large
surrounding
• where 𝜀 is a radiative property of the surface termed the emissivity. With values
in the range 0 ≤ 𝜀 ≤ 1
• this property provides a measure of how efficiently a surface
emits energy relative to a blackbody.
• Radiation may also be incident on a surface from its surroundings. The radiation
may originate from a special source, such as the sun, or from other surfaces to
which the surface of interest is exposed.
• we designate the rate incident radiation on a unit area of the surface as the
irradiation G.

▪ absorptivity 𝛼 0 ≤ 𝛼 ≤ 1 .
▪ If 𝛼 < 1 and the surface is opaque, portions of the irradiation are reflected.
▪ A blackbody absorbs the entire radiation incident on it. That is, a blackbody
is a perfect absorber (𝛼= 1) as it is a perfect emitter
the net rate of radiation heat transfer from the surface, expressed per unit area of the
surface, is

• This expression provides the difference between thermal energy that is released due
to radiation emission and that which is gained due to radiation absorption.

• There are many applications for which it is convenient to express the net radiation heat exchange in the form

radiation heat transfer coefficient hr is

the total rate of heat transfer from the surface is then

 Conservation of Energy for a Control Volume
• first law of thermodynamics is simply a statement that the total energy of a
system is conserved.
• the amount of energy in a system can change is if energy crosses its
boundaries.
• For a closed system (a region of fixed mass) energy crosses its boundaries
in two ways:
1. heat transfer through the boundaries to or from the system
2. work done on or by the system.
▪ The first law can also be applied to a control volume (or open system), a region
of space bounded by a control surface through which mass may pass

▪ Stored thermal and mechanical energy, Est.

▪ Thermal energy generation, Eg.
▪ Thermal and mechanical energy transport across the control
surfaces, that is, the inflow and outflow terms, Ein and Eout
• The stored thermal and mechanical energy is given by Est =KE +PE + Ut

▪ flow work (PV), is associated with work

done by pressure forces moving fluid
through the boundary
• 1.5.The inner and outer surface temperatures of a glass
window 5 mm thick are 15 and 5C. What is the heat
loss through a window that is 1 m by 3 m on a side?
The thermal conductivity of glass is 1.4 W/m . K .
•