Chemical engineering

1. Heat Transfer
Day-1(26.05.2020)
Dr. R. Srikanth
Professor
ANITS-Visakhapatnam
AP Government GATE Online
Classes

2. GATE Syllabus – Heat Transfer
• Steady and unsteady heat conduction
• Convection - thermal boundary layer and heat transfer
coefficients, boiling, condensation
• Radiation
• Evaporation
• Types of heat exchangers and evaporators and their
process calculations.
• Design of double pipe, shell and tube heat exchangers
• Single and multiple effect evaporators.

3. Heat Transfer
• How does the heat transfers?
• Heat transfer takes place from high
temperature to low temperature.

4. Heat transfer

5. Conduction
Conduction is the process whereby heat is transferred directly
through a material, any bulk motion of the material playing
no role in the transfer.
Those materials that conduct heat well are called thermal
conductors, while those that conduct heat poorly are known
as thermal insulators.
Most metals are excellent thermal conductors, while wood,
glass, and most plastics are common thermal insulators.
The free electrons in metals are responsible for the excellent
thermal conductivity of metals.

6. Conduction

7. Conduction
Particles in a solid are always
vibrating. If the solid gets hotter,
the particles vibrate more.
Note: the particles don't swap
places, or move around they just
vibrate more on the spot.
Heat energy

8. Conduction Of Heat
Through A Material

9. Convection
• Convection – when heat is carried by a moving fluid
Example: heat house with radiator

10. Convection
Convection is the process in which heat is carried
from place to place by the bulk movement of a fluid.
Convection currents are set up when a pan of water is heated.

11. Volcanic Eruption
During a volcanic eruption, smoke at the top of the
plume rises thousands of meters because of
convection.

12. Convection
Explains why breezes come from the ocean
in the day and from the land at night

13. Q: In the living room, the heating unit is placed in the floor but the
refrigerator has a top-mounted cooling coil. Why?
A: Air warmed by the baseboard heating unit is pushed to the top of
the room by the cooler and denser air. Air cooled by the cooling coil
sinks to the bottom of the refrigerator.

14. Natural and Forced Convection
• Natural convection – currents are the result of
buoyancy forces generated by differences in
density are in caused by temperature gradients
in fluid mass
– Flow of air across a heated radiator
• Forced convection – currents are set in motion
by action of a mechanical device such a pump
or agitator, flow is independent of density
gradients
– Heat flow to a fluid pumped through a heated pipe

15. Radiation
Radiation is the process in which energy is transferred by means
of electromagnetic waves.
Heat transfer by radiation can take place through vacuum. This is
because electromagnetic waves are involved in radiation and
they can propagate through empty space.
Radiation – when electromagnetic waves (radiation) carry heat
from one object to another.
Example: heat you feel when you are near a fire
Example: Heat from the sun
Formation of frost (ice) at night, T(air) > 0ºC

16. Radiation
•Energy carried by electromagnetic waves
•Light, microwaves, radio waves, x-rays
•Wavelength is related to vibration frequency

17. Radiation
average frequency  absolute temperature

18. Heat Transfer by Conduction
• Fourier’s law
• Temperature can vary with both location and time
• Heat flow occurs from hot to cold
n
t
k
dA
dq




Where A = area of isothermal surface
n = distance measured normally to surface
q = rate of heat flow across surface in direction normal to surface
T = temperature
k = proportionality constant

19. One-Dimensional Heat Flow
Hot Gas
B
Water
Temperature
700 C
25 C
c
III
II
I
I – at instant of exposure of
wall to high temperature
II – during heating at time t
III – at steady state

20. For Steady One-Dimensional Flow
• Thermal conductivity, k
– Proportionality factor that represents a physical
property of a substance
– q/A – rate of heat flow per unit area
– dT/dn – temperature gradient
– q – watts or Btu/h
– dT/dn - C/m or F/ft
– k – W/m-C or Btu-ft-h-F
dn
dT
k
A
q



21. • For small temperature ranges, k is constant
• For larger temperature ranges,
k = a + bT
Where a and b are empirical constants
• k for metals
– Stainless – 17 W/m-C
– Silver – 415 W/m-C
• k for liquids
– Water - 0.5 – 0.7 W/m-C
• k for gases
– Air – 0.024 W/m-C
• Solids with low k values are often used as insulators

22. Rate of heat transfer by conduction, Q/t through the length, L
across the cross-sectional area, A is given by the following
equation, where k is the thermal conductivity and ΔT is the
temperature difference between the two ends.
.
L
T
kA
t
Q 

SI Unit of Thermal Conductivity: J/(s · m · °C)
Conduction

23. Substance Thermal Conductivity, k [J/(s · m · C°)]
Metals
Aluminum 240
Brass 110
Copper 390
Iron 79
Lead 35
Silver 420
Steel (stainless) 14
Gases
Air 0.0256
Hydrogen (H2) 0.180
Nitrogen (N2) 0.0258
High conductivity
High conductivity
High conductivity

25. Steady State Conduction
• For a flat slab of thickness, B
• R is the thermal resistance of the solid between
two points
R
T
B
T
k
x
x
T
T
k
A
q
dx
kA
q
dT
dx
dT
k
A
q











1
2
2
1

26. Resistances in Series
T
TC
TB
TA
RA RB RC
BA BB BC
T
TC
TB
TA
R
T
R
R
R
T
k
B
k
B
k
B
T
A
q
T
k
A
B
q
k
A
B
q
k
A
B
q
T
T
T
C
B
A
C
C
B
B
A
A
C
C
C
B
B
B
A
A
A
C
B
A




















/
/
/
R=SRi

27. composite wall
Note: the heat flow must
be the same through all
sections.
A relation quite like Ohm’s law in
electric-circuit theory
Rth = the thermal resistances of the
various materials
C
B
A R
R
R
T
T
q



 4
1
A
k
x
R
n
n
cond





th
overall
R
T
q
Heat flow through plane wall

28. Heat flow through radial system
cylinder
dr
dT
kA
q 

Fourier’s law:
rL
A 
2

dr
dT
krL
q 
2


Boundary conditions:
T=Ti at r=ri
T=T0 at r=r0

29. Heat Flow through a Cylinder
To Ti
dr
ri
r
ro
)
/
ln(
)
/
ln(
)
(
2
)
(
)
/
ln(
)
)(
2
(
2
2
i
o
i
o
L
i
o
i
o
L
i
o
o
i
L
i
o
o
i
r
r
T
T
r
r
r
r
r
r
r
r
r
L
A
r
r
T
T
A
k
q
r
r
T
T
L
k
q
dT
q
Lk
r
dr
rL
dr
dT
k
q
o
i
i
o












 





30. Heat flow through radial system
Multilayer cylinder
C
B
A k
r
r
k
r
r
k
r
r
T
T
L
q
)
/
ln(
)
/
ln(
)
/
ln(
)
(
2
3
4
2
3
1
2
4
1






31. Heat flow through radial system
Hollow sphere
0
0
/
1
/
1
)
(
4
r
r
T
T
k
q
i
i




Boundary conditions:
T=Ti at r=ri
T=T0 at r=r0
dr
dT
kA
q 
 A=4πr2
ri
r0

32. SOLVED PROBLEMS
Previous GATE Questions

33. Q1:
A Circular tube of outer diameter 5 cm and inner diameter 4
cm is used to convey hot fluid. The inner surface of the wall
of the tube is at a temperature of 80°C, while the outer surface
of the wall of the tube is at 25°C. What is the rate of heat
transport across the tube wall per meter length of the tube at
steady state, if the thermal conductivity of the tube wall is
10W/m-K?
A.13823 W/m
B.15487 W/m
C.17279 W/m
D.27646 W/m

34. ΔT = 80 -25 = 55; r0 = 0.025 m; ri = 0.02 m; k = 10
Substituting in the formula; q = 15487 W/m

35. Q2.
Two plates of equal thickness (t) and
cross-sectional area are joined
together to form a composite as
shown in the figure. If the thermal
conductivities of the plates are K and
2K, then the effective thermal
conductivity of the composite is
A. 3k/2
B. 4k/3
C. 3k/4
D. 2k/3

36. For steady state heat transfer Rtot = R1+R2 and
R = B/kA
For unit area; and equal thickness
Rtot = 2t/keff
R1 = t/k; R2 = t/2k
Rtot= t/k + t/2k = 3/2(t/k) = 2t/keff
So keff = 4/3 k

37. Q3:
The composite wall of an oven consists of three materials A,
B and C. Under steady state operating conditions, the outer
surface temperature Tso is 20°C, The inner surface
temperature Tsi is 600°C and the oven air temperature is T∞ =
800°C. For the following data:
Thermal conductivities KA = 20W/m-K; KC = 50W/m−K;
Thickness tA = 0.3m, tB = 0.15m and tC = 0.15m; Inner-wall
heat transfer coefficient h = 25W/m2−K
The thermal conductivity KB in W/m-K of the material B, is
calculated as
A. 35
B. 1.53
C. 0.66
D. 0.03

40. Q4:
The left face of a one dimensional slab of thickness
0.2m is maintained at 80°C and the right face is
exposed to air at 30°C. The thermal conductivity of
the slab is 1.2W/m-K and the heat transfer
coefficient from the right face is 10W/m2-K. At
steady state, the temperature of the right face in °C is
A. 77.2
B. 71.2
C. 63.8
D. 48.7

43. Q5:
A brick wall of 20 cm thickness has thermal conductivity of
0. 7 W m-1 K-1. An insulation of thermal conductivity 0.2 W
m-1 K-1 is to be applied on one side of the wall, so that the
heat transfer through the wall is reduced by 75%. The same
temperature difference is maintained across the wall before
and after applying the insulation. The required thickness (in
cm) of the insulation is _____

45. Q6:
The inner wall of a furnace is at a temperature of
700°C. The composite wall is made of two
substances, 10 and 20 cm thick with thermal
conductivities of 0.05 and 0.1W/m-°C respectively.
The ambient air is at 30°C and the heat transfer
coefficient between the outer surface of wall and air
is 20W/m2-°C. The rate of heat loss from the outer
surface in W/m2 is
A. 165.4
B. 167.5
C. 172.5
D. 175

46. 


th
overall
R
T
q
For unit area
R1 = t1 /k1 = 2
R2 = t2/k2 = 2
R3 = 1/h = 0.05
Rtot = 4.05
ΔT = 700-30 = 670
So q/A = 165.4 W/m2

47. Q7:
A composite wall consists of two plates A and B
placed in series normal to the flow of heat. The
thermal conductivities are KA and KB and the
specific heat capacities are CpA and CpB for plates A
and B respectively. Plate B has twice the thickness
of plate A. At steady state, the temperature
difference across plate A is greater than that across
plate B, when
A. CpA > CpB
B. CpA < CpB
C. KA < 0.5KB
D. KA > 2KB

48. • Steady state heat transfer
depends on Temperature
gradient and slab
resistance
• Resistance intern depends
on thermal conductivity.
• As thickness of slab 2 is
twice than 1, so k1 should
be less than k2
• Ans: KA < 0.5KB

49. Q8:
At steady state the temperature
variation in a plane wall, made
of two different solids I and II
shown below
Then the thermal conductivity of
material I:
A. Is smaller than that of II
B. Is greater than that of II
C. Is equal to that of II
D. Can be greater than or
smaller than II

50. Q9:
A composite wall is made of four different materials of
construction in the fashion shown below.
The resistance (in K/W) of each of the sections of the wall is
indicated in the diagram. The overall resistance (in K/W,
rounded off to the first decimal place) of the composite wall, in
the direction of heat flow, is _______

53. Q10:
The figure below shows steady state temperature profiles for
one dimensional heat transfer within a solid slab for the
following cases:
P : Uniform heat generation with left surface perfectly insulated
Q : Uniform heat generation with right surface perfectly insulated
R : Uniform heat consumption with left surface perfectly insulated
S : Uniform heat consumption with right surface perfectly insulated

54. Match the profiles with appropriate cases.
A. P-I, Q-III, R-II, S-IV
B. P-II, Q-III, R-I, S-IV
C. P-I, Q-IV, R-II, S-III
D. P-II, Q-IV, R-I, S-III
Ans: A

55. Q11:
Heat is generated uniformly within a solid
slab. The slab separates fluid 1 from fluid 2.
The heat transfer coefficients between the
solid slab and the fluid are h1 and h2 (h2 > h1)
respectively. The steady state temperature
profile (T vs x) for one-dimensional heat
transfer is correctly shown by,

56. Answer A

57. Q12:
For the composite wall shown below (Case 1), the
steady state interface temperature is 180°C. If the
thickness of layer P is doubled (Case 2), then the rate
of heat transfer (Assuming 1-dimensional
conduction) is reduced by
A. 20%
B. 40%
C. 50%
D. 70%

60. Q13:
A stagnant liquid film of 0.4 mm thickness is
held between two parallel plates. The top plate
is maintained at 40°C and the bottom plate is
maintained at 30°C . If the thermal
conductivity of the liquid is 0.14 W/(m-K),
then the steady state heat flux (in W/m2)
assuming one-dimensional heat transfer, is
A. 3.5
B. 350
C. 3500
D. 7000

61. k = 0.14; ΔT = 10; Δx = 0.4mm = 0.4*10-3m
Q/A = 3500 W/m2
𝑄
𝐴
= −𝑘
∆𝑇
∆𝑥

62. Q14:
The wall of a pipe of radius 1 m is at a uniform
temperature of 200 °C, and is covered by insulation
of thickness 0.1 m. The ambient air outside the
insulated pipe is at 20 °C and has heat transfer
coefficient of 10 W m-1 K-1. The thermal
conductivity of the insulation material is 0.05 W m-1
K-1. If the heat transfer occurs at steady state, the
temperature (in °C) of the outer surface of insulation
is __________ (rounded off to second decimal
place).

63. The problem can be solved by equating the
heat flux in both cases
i.e.
heat flux through conduction = heat flux through convection
𝑄 =
∆𝑇
𝑅𝑇
= ℎ𝐴 𝑇𝑠 − 𝑇𝑓𝑙𝑢𝑖𝑑
Answer: 28.196°C

64. Q15:
Consider a solid block of unit thickness for which the thermal
conductivity decreases with an increase in temperature. The opposite faces
of the block are maintained at constant but different temperatures: T(x=0)
>T(x=1). Heat transfer is by steady state conduction in x-direction only.
There is no source or sink of heat inside the block. In the figure below,
identify the correct temperature profile in the block.
Answer: C