Heat transfer

1. Heat Transfer (2151903)
Mechanical Department
Sem.: 5th
D (D2)
• Prepared By: Sajan Gohel (160123119010)

2.  Modes of heat transfer
 Effect of temperature on thermal conductivity of
different solids, liquids and gases.
 Derivation of generalized equation in cylindrical

3. Heat Transfer Modes
There are 3 modes of
heat transfer.
1. Conduction
2. Convection
3. Radiation

4. Conduction
• Heat transfer through a solid medium via
direct contact
• Expressed by Fourier’s Law

5. Convection
• Convection is the transfer of heat
from one place to another by the
movement of fluids.
• Two kinds of convection
• Forced convection: Fluid is
forced
• Natural or free convection: fluid is
induced by temperature difference

6.  Radiation is the transfer of heat from the body or
fluid for which no medium.
 Heat transfer due to emission of electromagnetic
waves is known as thermal radiation

7.  Thermals conductivity of pure metals is due to
migration of three electrons (Kc) and lattice
vibrations (Kl).
K = Ke + Kl
 In pure metals, heat is transferred due to movement
of free electron in clouds and also due to vibrational
energy in lattice structure.
 Thermal conductivity of pure metal is decreases
with the increasing in temperature.

9.  Thermal conductivity of gases is smaller then that
of solids because there intermolecular spacing is
much larger.
 The thermal conductivity of all the gases increases
with increases with increases in temperature.
 This is because at high temperature collision among
gas particles increases and heat transfer increases.
K = 0.006 to 0.05 W/mK
K tα∆
K tα∆

11.  Heat conduction in liquids is also same as in gases.
 In case of liquids, close spacing of molecules and
strong molecular attraction force compare to gases
cause more heat exchange via collision.
 So the thermal conductivity of liquids usually lies
between those of gases and solids.
 In most of the liquids value of thermal conductivity
tends to decrease with increase in temperature.

13.  Consider an element
volume having the
coordinates (r, , z), for
three dimension heat
conduction analysis.
Volume of cylinder =
r * d * dr * dz
φ
φ
φ
K = thermal cunductivity
C = specific heat
P = density

14. • Net heat accumulated in the cylinder due to
conduction of heat.
 Heat flow in (x - ) plane.
Heat influx, Q’r =
Heat efflux, Q’(r+dr) =
Heat accomodation in the cylinder in radial direction,
 Heat flow in (r - z) plane.
Heat influx,
Heat efflux,
φ
'r (Qr)drQ
r
∂
+
∂
' (dr )
T
Q k dz dt
r
φ
φ
∂
= −
∂
'( ) ' (Q' )rdQ d Q
r
φ φ φ φ φ
φ
∂
+ = +
∂
2
2
1
dQ'r ( * * )( )dt
T T
k dr rd dz
r r r
φ
∂ ∂
= +
∂ ∂
( )
T
k rd dz dt
r
φ
∂
−
∂

15.  Heat accomodation in the cylinder in tengential
direction,
Heat influx Q’z=
Heat efflux Q(z+dz)=
Heat accomodation in the cylinder in axial
direction,
2
2 2
1
dQ' ( * * )( ) dt
T
k dr rd dz
r
φ φ
φ
∂
=
∂
Heat flow in (r - ) plane.φ
( )
T
k rd dr dt
z
φ
∂
−
∂
'z (Q, z) dzQ
r
∂
+
∂
2 2 2
2 2 2 2
1 1
dQ'z ( * * )( )dt
T T T T
k dr rd dz
r r r r z
φ
φ
∂ ∂ ∂ ∂
= + + +
∂ ∂ ∂ ∂

16.  Heat generated within the element
total heat generated
 Energy stored in element
 From eq. , A+B=C
' ( * * * )*B Q g qg dr r d dz dtφ= = =
* * * ( * * * )* * *
* * *
T
C dr r d dz dr r d dz c dt
t
dr rd dz dt
ρ φ φ
φ
∂
=
∂
( * * * )* * *
T
C dr r d dz c dt
t
ρ φ
∂
=
∂

17.  Dividing both sides by
we have ...
This eq. Is known as general heat conduction eq.
* * *dr rd dz dtφ
1
* *
c T T
k t t
ρ
α
∂ ∂
=
∂ ∂