Heat conduction is the transfer of heat from one body to another through direct contact. It mainly occurs in solids via molecular interactions and lattice vibrations, and in metals also via the drift of free electrons. Heat conduction follows Fourier's law, where the rate of heat transfer is proportional to the temperature gradient and thermal conductivity of the material. Thermal conductivity varies with temperature and is highest in metals like silver and copper. The lumped heat analysis method can be used to simplify problems involving transient heat conduction when the Biot number is low (<0.1), by assuming the temperature inside a solid is uniform.

1. HEAT CONDUCTION
K .Koushik
Moksith

2. • It is the transfer of heat from one body to other body by
means of physical contact.
•Its majorly can seen in solids .
•It can also be seen in liquids and gases but its
negligible.

3. Physical mechanism
There are 2 mechanisms
1)By molecular interactions

4. 1) Molecular interaction
on taking heat, the molecules remains stationary but they
vibrate in their lattice which imparts energy on
neighbouring particles in the direction of low temperature
and hence conduction takes place.
2)By drift of free electrons
• In case of metals they have more free electrons which
moves and collides with other electrons on supplying heat
energy thus causes the heat transfer.

5. EXAMPLES
In Manufacturing In Heat Exchanger
In Electronics In Everyday
Life

6. Fourier's law of conduction
• Rate of heat conduction is proportional to the area
measured normal to the direction of heat flow, and to the
temperature gradient in that direction.

9. Thermal conductivity
• Thermal conductivity (k) is the intrinsic property of a
material which relates its ability to conduct heat.
• Thermal conductivity is defined as the quantity of heat (Q)
transmitted through a unit thickness (x) in a direction
normal to a surface of unit area (A) due to a unit
temperature gradient (∆T) under steady state conditions
and when the heat transfer is dependant only on
temperature gradient.

10. Variation of thermal conductivity with
temperature
• Thermal conductivity varies with temperature of the
body rather than the surrounding temperature.
• Thermal conductivity of any material is dependent on two
things:
 Motion of free electrons
Lattice vibrations

11. Variation of thermal conductivity with
temperature
• The thermal conductivity of metals decreases with
increases of temperature because on increasing
temperature, the molecular vibrations increases and thus
abrupt the flow of free electrons and hence the
conductance of heat is reduced.
• Where as the thermal conductivity of solids increases with
increase of temperature because on increasing
temperature, the molecular vibration increases thus
conductance increases

12. Thermal conductivity of some metals

13. Variation of thermal conductivity in
engineering applications
K = a + bT + cT^(2)
T------------- temperature at T
K ------------ thermal conductivity at temperature a,b,c---------
constants
If variation of thermal conductivity is assumed to be linear
then
K = K’(1+βT)
Where K’ and β are constants

14. Thermal conductivity of some
materials at 20 C
SI.NO Substance K(W/mK)
1 Silver(pure) 407.0
2 Copper(pure) 386.0
3 Aluminium(pure) 175.6
4 Mild steel 37.2
5 Lead 29.8
6 Stainless steel 19.3
7 Wood 0.15
8 Asbestos 0.095
9 Water 0.51
10 Air 0.022
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15. Types of states
Steady state
• A system is said to be in steady state if its temperature
does not vary with time.
Unsteady state (Transient state)
• A system is said to be in unsteady state if its temperature
changes with time

16. Unsteady state is classified into
• Periodic flow- the temperature varies on regular basis
• Examples- cylinder of an IC engine surface of earth
during a period of 24 hours.
• Non periodic flow- the temperature at any point within
the system varies non linear with time
• Examples- cooling of bars ,heating of ingot in a furnace

17. Conduction resistance
It is the reciprocal of thermal conductance
It is the property of material which offers resistance to the
conduction of heat.
Given by L/KA
Units--------- K/W

18. BIOT Number
• It is the ratio of internal conduction resistance to the
surface convection resistance (OR)
• Ratio of heat transfer resistance in the interior of the
system (L/k) to the resistance between the surroundings
and the system surface (1/h)
B = hL/ k
H--------------heat transfer co-efficient(W/m^2K)
L--------------- characteristic length
K---------------Thermal conductivity

19. FOURIER NUMBER

20. Significance of Biot Number
• Biot number shows how convection and
conduction heat transfer phenomena are
related.
• Small values of this number shows that the
conduction is the main heat transfer method
• High values of this number indicates that the
convection is the main heat transfer mechanism.

21. Significance of Fourier Number
• Fourier number is able to determine the
characteristic "time" of the problem.
• This time is important in studies because it
indicates if the phenomenon is quick or slow.
• Practically, in a transient analysis, the simulation
time is in the same order of magnitude with the
respective characteristic time calculated by the
Fourier number.

22. Lumped heat analysis
• When the internal resistance is negligible.
• That is when convectional resistance at the surface is
more than the conduction resistance.
• Examples – heat treatment of metals by quenching, time
response of thermocouples and thermometers.
• In unsteady conditions the complexity increases because
the time also varies.
• So to reduce this problem this lumped heat analysis is
taken into account.
• It is generally used when biot number (B) is <0.1

23. • Some assumptions has to be made according to this
analysis .They are
• The temperature throughout the solid is taken as
constant at a given time.
• Whole solid whose energy at any time is a function of its
temperature and total heat capacity is considered as
one lump.

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