Heat Transfer | Physics Optional Notes for UPSC PDF Download

 Page 1


WHAT IS HEAT TRANSFER? 
Heat is a type of energy that moves from hot things to cooler things. It can move in three 
main ways: 
1. Conduction: This happens in solids when the energy moves between particles. 
2. Convection: This occurs in fluids like liquids and gases when the particles themselves 
move, carrying the energy with them. 
3. Radiation: This is the fastest way heat can move, where it travels through space 
without needing anything in between to carry it. 
So, heat can spread from one thing to another by touching (conduction), by moving 
particles (convection), or even through empty space (radiation). 
Example: 
Imagine a hot cup of coffee cooling down. The heat is first transferred through the cup 
(conduction), then through the air around it (convection), and finally emitted as infrared 
radiation. 
 
 
 
 
 
 
 
Page 2


WHAT IS HEAT TRANSFER? 
Heat is a type of energy that moves from hot things to cooler things. It can move in three 
main ways: 
1. Conduction: This happens in solids when the energy moves between particles. 
2. Convection: This occurs in fluids like liquids and gases when the particles themselves 
move, carrying the energy with them. 
3. Radiation: This is the fastest way heat can move, where it travels through space 
without needing anything in between to carry it. 
So, heat can spread from one thing to another by touching (conduction), by moving 
particles (convection), or even through empty space (radiation). 
Example: 
Imagine a hot cup of coffee cooling down. The heat is first transferred through the cup 
(conduction), then through the air around it (convection), and finally emitted as infrared 
radiation. 
 
 
 
 
 
 
 
Difference between Conduction, Convection & Radiation 
Conduction Convection Radiation 
Heat Transfer due to 
Temperature difference 
 
Heat transfer due to 
density 
difference 
 
Heat transfer without 
any 
medium 
 
Due to free electron or 
vibration 
motion of molecules 
 
Actual motion of particles 
Electromagnetic 
radiation 
Heat transfer in solid 
body (in 
mercury also) 
 
Heat transfer in fluids 
(Liquid + 
gas) 
 
All 
Slow process Slow process 
Fast process (3×
10
8
 m/sec) 
Irregular path Irregular path Straight line (like light) 
 
Steady and variable state 
Imagine a metal rod called AB. One end, A, is put into a box with a heater, while the 
other end, B, is left open. The rod is wrapped with something that doesn't let heat 
escape sideways, like cotton or felt. We put three thermometers on the rod at three 
different spots labeled (1), (2), and (3). At the beginning, everything is at room 
temperature, and all three thermometers show the same room temperature. 
 
Then, we turn on the heater. End A starts to warm up first, and at the same time, the 
heat moves through the rod towards end B. 
Page 3


WHAT IS HEAT TRANSFER? 
Heat is a type of energy that moves from hot things to cooler things. It can move in three 
main ways: 
1. Conduction: This happens in solids when the energy moves between particles. 
2. Convection: This occurs in fluids like liquids and gases when the particles themselves 
move, carrying the energy with them. 
3. Radiation: This is the fastest way heat can move, where it travels through space 
without needing anything in between to carry it. 
So, heat can spread from one thing to another by touching (conduction), by moving 
particles (convection), or even through empty space (radiation). 
Example: 
Imagine a hot cup of coffee cooling down. The heat is first transferred through the cup 
(conduction), then through the air around it (convection), and finally emitted as infrared 
radiation. 
 
 
 
 
 
 
 
Difference between Conduction, Convection & Radiation 
Conduction Convection Radiation 
Heat Transfer due to 
Temperature difference 
 
Heat transfer due to 
density 
difference 
 
Heat transfer without 
any 
medium 
 
Due to free electron or 
vibration 
motion of molecules 
 
Actual motion of particles 
Electromagnetic 
radiation 
Heat transfer in solid 
body (in 
mercury also) 
 
Heat transfer in fluids 
(Liquid + 
gas) 
 
All 
Slow process Slow process 
Fast process (3×
10
8
 m/sec) 
Irregular path Irregular path Straight line (like light) 
 
Steady and variable state 
Imagine a metal rod called AB. One end, A, is put into a box with a heater, while the 
other end, B, is left open. The rod is wrapped with something that doesn't let heat 
escape sideways, like cotton or felt. We put three thermometers on the rod at three 
different spots labeled (1), (2), and (3). At the beginning, everything is at room 
temperature, and all three thermometers show the same room temperature. 
 
Then, we turn on the heater. End A starts to warm up first, and at the same time, the 
heat moves through the rod towards end B. 
 
As the heat reaches each section, the temperatures at those spots start to rise, with T1 
being higher than T2, and T2 being higher than T3. This is called a changing state. In 
this state, the heat from end A keeps getting absorbed at each section, and the 
temperatures keep going up as time passes. 
 
After some time, end B's temperature becomes the same as the surrounding 
temperature, so it stops changing. This means the heat being absorbed at different 
sections of the rod also stops changing. There won't be any more rise in temperatures at 
any section. This is called a constant state, or a steady state. In this steady state, the 
temperatures at each section stay the same over time. 
CONDUCTION 
Fourier’s law states that the negative gradient of temperature and the time rate of heat 
transfer is proportional to the area at right angles of that gradient through which the heat 
flows. Fourier’s law is the other name of the law of heat conduction. 
(
d?? dt
)
x
=-KA(
dT
dx
) 
 
where,  
d?? dt
= Rate of heat flow, K= Conductivity of substance (property of medium) ?? = 
Area of cross section 
?  (
d?? dt
)
?? is the amount of heat flow in x-direction per unit time through a given 
crosssection area ' A '. 
? (
dT
dx
) is the temperature gradient at the place where (
d?? dt
) is measured. 
?  -ve sign indicates that heat flow in the direction of decreasing temperature. 
Thermal (temperature) gradient : 
Page 4


WHAT IS HEAT TRANSFER? 
Heat is a type of energy that moves from hot things to cooler things. It can move in three 
main ways: 
1. Conduction: This happens in solids when the energy moves between particles. 
2. Convection: This occurs in fluids like liquids and gases when the particles themselves 
move, carrying the energy with them. 
3. Radiation: This is the fastest way heat can move, where it travels through space 
without needing anything in between to carry it. 
So, heat can spread from one thing to another by touching (conduction), by moving 
particles (convection), or even through empty space (radiation). 
Example: 
Imagine a hot cup of coffee cooling down. The heat is first transferred through the cup 
(conduction), then through the air around it (convection), and finally emitted as infrared 
radiation. 
 
 
 
 
 
 
 
Difference between Conduction, Convection & Radiation 
Conduction Convection Radiation 
Heat Transfer due to 
Temperature difference 
 
Heat transfer due to 
density 
difference 
 
Heat transfer without 
any 
medium 
 
Due to free electron or 
vibration 
motion of molecules 
 
Actual motion of particles 
Electromagnetic 
radiation 
Heat transfer in solid 
body (in 
mercury also) 
 
Heat transfer in fluids 
(Liquid + 
gas) 
 
All 
Slow process Slow process 
Fast process (3×
10
8
 m/sec) 
Irregular path Irregular path Straight line (like light) 
 
Steady and variable state 
Imagine a metal rod called AB. One end, A, is put into a box with a heater, while the 
other end, B, is left open. The rod is wrapped with something that doesn't let heat 
escape sideways, like cotton or felt. We put three thermometers on the rod at three 
different spots labeled (1), (2), and (3). At the beginning, everything is at room 
temperature, and all three thermometers show the same room temperature. 
 
Then, we turn on the heater. End A starts to warm up first, and at the same time, the 
heat moves through the rod towards end B. 
 
As the heat reaches each section, the temperatures at those spots start to rise, with T1 
being higher than T2, and T2 being higher than T3. This is called a changing state. In 
this state, the heat from end A keeps getting absorbed at each section, and the 
temperatures keep going up as time passes. 
 
After some time, end B's temperature becomes the same as the surrounding 
temperature, so it stops changing. This means the heat being absorbed at different 
sections of the rod also stops changing. There won't be any more rise in temperatures at 
any section. This is called a constant state, or a steady state. In this steady state, the 
temperatures at each section stay the same over time. 
CONDUCTION 
Fourier’s law states that the negative gradient of temperature and the time rate of heat 
transfer is proportional to the area at right angles of that gradient through which the heat 
flows. Fourier’s law is the other name of the law of heat conduction. 
(
d?? dt
)
x
=-KA(
dT
dx
) 
 
where,  
d?? dt
= Rate of heat flow, K= Conductivity of substance (property of medium) ?? = 
Area of cross section 
?  (
d?? dt
)
?? is the amount of heat flow in x-direction per unit time through a given 
crosssection area ' A '. 
? (
dT
dx
) is the temperature gradient at the place where (
d?? dt
) is measured. 
?  -ve sign indicates that heat flow in the direction of decreasing temperature. 
Thermal (temperature) gradient : 
The rate of decrease in temperature with distance from hot end of the rod is known as 
temperature gradient or in the direction of heat energy flow, the rate of fall in 
temperature w.r.t. distance is called as temperature gradient. It is denoted by -dT/dx 
Thermal conductivity (?? ) : It's depends on nature of material. 
 
? For an ideal or perfect conductor of heat the value of ?? =8 
? For an ideal or perfect bad conductor or insulator the value of K=0 
? For cooking the food, low specific heat and high conductivity utensils are most 
suitable. 
Heat flow from a uniform rod at steady state : 
? In steady state temperature of each element of the rod becomes constant w.r.t. 
to time i.e. rate of heat flow at energy cross-section of the rod will be same. 
 
 
In steady state 
dT
dt
 is same for each element 
d?? dt
=KA
dT
dx
 
?  for uniform rod ( K& A same for each element) 
?
dT
dx
 is same ?
dT
dx
=
?T
?x
?
d?? dt
=kA(
?T
?x
) 
Example. 
  
Page 5


WHAT IS HEAT TRANSFER? 
Heat is a type of energy that moves from hot things to cooler things. It can move in three 
main ways: 
1. Conduction: This happens in solids when the energy moves between particles. 
2. Convection: This occurs in fluids like liquids and gases when the particles themselves 
move, carrying the energy with them. 
3. Radiation: This is the fastest way heat can move, where it travels through space 
without needing anything in between to carry it. 
So, heat can spread from one thing to another by touching (conduction), by moving 
particles (convection), or even through empty space (radiation). 
Example: 
Imagine a hot cup of coffee cooling down. The heat is first transferred through the cup 
(conduction), then through the air around it (convection), and finally emitted as infrared 
radiation. 
 
 
 
 
 
 
 
Difference between Conduction, Convection & Radiation 
Conduction Convection Radiation 
Heat Transfer due to 
Temperature difference 
 
Heat transfer due to 
density 
difference 
 
Heat transfer without 
any 
medium 
 
Due to free electron or 
vibration 
motion of molecules 
 
Actual motion of particles 
Electromagnetic 
radiation 
Heat transfer in solid 
body (in 
mercury also) 
 
Heat transfer in fluids 
(Liquid + 
gas) 
 
All 
Slow process Slow process 
Fast process (3×
10
8
 m/sec) 
Irregular path Irregular path Straight line (like light) 
 
Steady and variable state 
Imagine a metal rod called AB. One end, A, is put into a box with a heater, while the 
other end, B, is left open. The rod is wrapped with something that doesn't let heat 
escape sideways, like cotton or felt. We put three thermometers on the rod at three 
different spots labeled (1), (2), and (3). At the beginning, everything is at room 
temperature, and all three thermometers show the same room temperature. 
 
Then, we turn on the heater. End A starts to warm up first, and at the same time, the 
heat moves through the rod towards end B. 
 
As the heat reaches each section, the temperatures at those spots start to rise, with T1 
being higher than T2, and T2 being higher than T3. This is called a changing state. In 
this state, the heat from end A keeps getting absorbed at each section, and the 
temperatures keep going up as time passes. 
 
After some time, end B's temperature becomes the same as the surrounding 
temperature, so it stops changing. This means the heat being absorbed at different 
sections of the rod also stops changing. There won't be any more rise in temperatures at 
any section. This is called a constant state, or a steady state. In this steady state, the 
temperatures at each section stay the same over time. 
CONDUCTION 
Fourier’s law states that the negative gradient of temperature and the time rate of heat 
transfer is proportional to the area at right angles of that gradient through which the heat 
flows. Fourier’s law is the other name of the law of heat conduction. 
(
d?? dt
)
x
=-KA(
dT
dx
) 
 
where,  
d?? dt
= Rate of heat flow, K= Conductivity of substance (property of medium) ?? = 
Area of cross section 
?  (
d?? dt
)
?? is the amount of heat flow in x-direction per unit time through a given 
crosssection area ' A '. 
? (
dT
dx
) is the temperature gradient at the place where (
d?? dt
) is measured. 
?  -ve sign indicates that heat flow in the direction of decreasing temperature. 
Thermal (temperature) gradient : 
The rate of decrease in temperature with distance from hot end of the rod is known as 
temperature gradient or in the direction of heat energy flow, the rate of fall in 
temperature w.r.t. distance is called as temperature gradient. It is denoted by -dT/dx 
Thermal conductivity (?? ) : It's depends on nature of material. 
 
? For an ideal or perfect conductor of heat the value of ?? =8 
? For an ideal or perfect bad conductor or insulator the value of K=0 
? For cooking the food, low specific heat and high conductivity utensils are most 
suitable. 
Heat flow from a uniform rod at steady state : 
? In steady state temperature of each element of the rod becomes constant w.r.t. 
to time i.e. rate of heat flow at energy cross-section of the rod will be same. 
 
 
In steady state 
dT
dt
 is same for each element 
d?? dt
=KA
dT
dx
 
?  for uniform rod ( K& A same for each element) 
?
dT
dx
 is same ?
dT
dx
=
?T
?x
?
d?? dt
=kA(
?T
?x
) 
Example. 
  
In a steady state with a thermal conductivity of 0.1 watts per meter per Kelvin and an area of 8  
square  centimeters : 
(a) Determine the position 'x' where the temperature 'T' is 60 degrees Celsius . 
(b) Calculate the rate of change of temperature '(d?/dt)'. 
Solution: (a) Steady state 
 ?  Change same, kA(
100-60
x
)=kA(
100-0
10
)
 ?400=x×100?x=4 m
 (b) 
d?? dt
=kA
?T
?x
=
0.1×8×10
-4
(100-0)
10
 ?8×10
-
watt 
 
 
Example.  
What is the amount of heat lost per second when steam at 373 Kelvin flows through a 
tube with a radius of 5 centimeters and a length of 2 meters? The tube has a thickness 
of 5 millimeters and is made of a material with a thermal conductivity of 390 watts per 
meter per Kelvin. The surrounding temperature is 0 degrees Celsius. 
Solution: Using the relation ?? =
???? (?? 1
-?? 2
)?? ?? 
Here, heat is lost through the cylindrical surface of the tube. 
A=2?? r (radius of the tube) (length of the tube) =2?? ×0.05×2=0.2?? m
2
 
K=390 W m
-1
 K
-1
 
T
1
=373 K,  T
2
=0
°
C=273 K,  L=5 mm=0.005 m and t=1 s 
? ?? =
390×0.2?? ×(373-273)×1
0.005
=
390×0.2?? ×100
0.005
=49×10
5
 J. 
For non-uniform rods :