Heat transfer is branch of thermodynamics in which due to temperature difference exist between two bodies heat flows from higher source temperature to lower source temperature.

1. Aldel Education Trust’s
ST. JOHN COLLEGE OF ENGINEERING AND MANAGEMENT, PALGHAR
(ST. JOHN POLYTECHNIC)
DEPARTMENT OF MECHANICAL ENGINEERING
SUB: THERMAL ENGINEERING (TEN)
22337
TOPIC:HEAT TRANSFER
PREPARED BY:-
Prof. Pranit Mehata
Lecturer, SJCEM
7972064172

2. INTRODUCTION
THE TRANSMISSION OF ENERGY FROM ONE REGION TO ANOTHER AS A RESULT OF
TEMPERATURE DIFFERENCE IS CALLED AS HEAT TRANSFER
HEAT FLOWS FROM A BODY AT HIGHER TEMPERATURE TO A BODY AT LOWER
TEMPERATURE
HEAT IS ALWAYS TRANSFERRED IN THE DIRECTION OF DECREASING
TEMPERATURE.
Conduction Convection Radiation

3. MODES OF HEAT TRANSFER
CONDUCTION: THE TRANSFER OF HEAT FROM ONE
PART OF A SUBSTANCE TO ANOTHER PART OF SAME
SUBSTANCE OR FROM ONE SUBSTANCE TO ANOTHER
IN PHYSICAL CONTACT WITH IT. IT TAKES PLACE IN
SOLID MEDIUM.
CONVECTION: THE TRANSFER OF HEAT WITHIN A
FLUID BY MIXING OF ONE PORTION OF THE FLUID
WITH ANOTHER. IT TAKES PLACE IN LIQUID
MEDIUM.
RADIATION: THE TRANSFER OF HEAT THROUGH
SPACE OR MATTER BY MEANS OTHER THAN
CONDUCTION OR CONVECTION (ELECTROMAGNETIC
WAVES)

5. FOURIER’S LAW OF HEAT CONDUCTION
 IT STATES THAT, “ THE RATE OF FLOW OF HEAT THROUGH A
SIMPLE HOMOGENEOUS SOLID IS DIRECTLY PROPORTIONAL
TO THE AREA OF THE SECTION AT RIGHT ANGLES TO THE
DIRETION OF HEAT FLOW AND TO THE CHANGE OF
TEMPERATURE WITH RESPECT TO THE LENGTH OF THE PATH
OF THE FLOW”.
 MATHEMATICALLY,
𝑄
𝐴
∝
𝑑𝑇
𝑑𝑥
∴
𝑸
𝑨
= −𝒌.
𝒅𝑻
𝒅𝒙
Where,
Q=Amount of heat flow through body per unit time, Watts
A= Surface area of heat flow, 𝑚2
dT=Temperature Difference, K
dx= Thickness of Body, m
k= Constant of Proportionality, Thermal Conductivity of Body
-Ve signs indicates there is decrease in
temperature along the direction of heat
flow

6. THERMAL CONDUCTIVITY OF MATERIAL
THE AMOUNT OF ENERGY CONDUCTED THROUGH A BODY OF UNIT AREA, AND UNIT
THICKNESS IN UNIT TIME WHEN THE TEMPERATURE DIFFERENCE BETWEEN THE FACES
CAUSING HEAT FLOW IS 1℃ IS CALLED AS THERMAL CONDUCTIVITY.
IT IS DENOTED BY 𝒌 AND IT’S UNIT IS
𝑾
𝒎𝑲
OR
𝑾
𝒎℃
MATERIALS HAVING HIGH THERMAL CONDUCTIVITY ARE GOOD CONDUCTOR OF HEAT
E.G. METALS
MATERIALS HAVING LOW THERMAL CONDUCTIVITY ARE GOOD INSULATORS E.G. CORK.
THERMAL CONDUCTIVITY DEPENDS UPON
1. MATERIAL STRUCTURE
2. MOISTURE CONTENT
3. DENSITY OF MATERIAL
4. PRESSURE AND TEMPERATURE

7. THERMAL CONDUCTIVITY OF MATERIAL
Thermal conductivity of a material is due to flow of electrons (in case of metals) and lattice
vibration waves (in case of liquids)
Pure metals have highest thermal conductivity (10 to 400 W/mK) it decreases with increase in
impurity.
Thermal conductivity of most metals decreases with the increase in temperature (except
Aluminum and Uranium)
In liquids thermal conductivity decreases with temperature (except water) due to decrease in
density.
In case of gases thermal conductivity increases with temperature.
POINTS TO REMEMBER

8. THERMAL RESISTANCE
AS PER OHM’S LAW WE HAVE
𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝐼 =
𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑑𝑉)
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑛𝑐𝑒 𝑅
BY ANALOGY FOURIER'S EQUATION MAY BE WRITTEN AS,
𝐻𝑒𝑎𝑡 𝐹𝑙𝑜𝑤 𝑅𝑎𝑡𝑒 𝑄 =
𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑑𝑇)
(
𝑑𝑥
𝑘𝐴)
BY COMPARING WE FIND THAT,
𝑹 =
𝒅𝒙
𝒌𝑨
THE QUANTITY
𝑑𝑥
𝑘𝐴
IS CALLED AS THERMAL RESISTANCE (𝑅𝑡ℎ)
(𝑹𝒕𝒉)𝒄𝒐𝒏𝒅 =
𝒅𝒙
𝒌𝑨

9. HEAT CONDUCTION THROUGH A PLANE WALL
Let,
𝐿=Thickness of the plane wall.
𝐴= Cross sectional area of the plane wall
𝑘= Thermal Conductivity of the wall material.
𝑡1, 𝑡2= Temperatures maintained at the two faces of 1
and 2 of the wall respectively.
Heat through the plane wall is given as,
𝑄 = 𝑘𝐴
(𝑡1 − 𝑡2)
𝐿
𝑸 =
(𝒕𝟏 − 𝒕𝟐)
𝑳/𝒌𝑨
𝐿/𝑘𝐴 is known as “Thermal Resistance of the Plane Wall”

10. HEAT CONDUCTION THROUGH A COMPOSITE
WALL
Let,
𝐿𝐴, 𝐿𝐵 , 𝐿𝐶=Thickness of the slabs A,B and C respectively.
𝐴= Cross sectional area of the plane wall
𝑘𝐴, 𝑘𝐵 , 𝑘𝐶= Thermal Conductivities of the A,B and C respectively
𝑡1, 𝑡4= Temperatures at the wall surfaces 1 and 4 respectively.
𝑡2, 𝑡3= Temperatures at the wall surfaces 2 and 3 respectively.
As Q is same,
𝑄 =
𝑘𝐴. 𝐴(𝑡1 − 𝑡2)
𝐿𝐴
=
𝑘𝐵. 𝐴(𝑡2 − 𝑡3)
𝐿𝐵
=
𝑘𝐶. 𝐴(𝑡3 − 𝑡4)
𝐿𝐶
Assuming no temperature drop occurs across the interface of
materials
𝑸 =
(𝒕𝟏 − 𝒕𝟒)
𝑳𝑨
𝒌𝑨. 𝑨
+
𝑳𝑩
𝒌𝑩. 𝑨
+
𝑳𝑪
𝒌𝑪. 𝑨
𝑸 =
(𝒕𝟏 − 𝒕(𝒏+𝟏))
𝟏
𝒏 𝑳
𝒌𝑨

11. HEAT CONDUCTION THROUGH HOLLOW CYLINDER
Let,
𝑟1, 𝑟2 =Inner and Outer Radii.
𝐴= Cross sectional area cylinder=2𝜋𝑟𝐿
𝑘 = Thermal Conductivity
𝑡1, 𝑡2= Temperatures at inner and outer surfaces.
Heat transfer rate through hollow cylinder is given as,
𝑸 =
(𝒕𝟏 − 𝒕𝟐)
𝐥𝐧(𝒓𝟐 𝒓𝟏)
𝟐𝝅𝒌𝑳
𝐥𝐧(𝒓𝟐 𝒓𝟏)
𝟐𝝅𝒌𝑳
is known as “Thermal Resistance of the Hollow Cylinder ”

12. CRITICAL THICKNESS OF INSULATION
𝒓𝟐 = 𝒓𝒄 =
𝒌
𝒉𝒐
𝒓𝟐 = 𝒓𝒄 =
𝟐𝒌
𝒉𝒐
 The thickness upto which heat flow
increases and after which heat flow
decreases is called as Critical
Thickness.
 In case of cylinders and spheres it is
called as Critical Radius.
 The insulation radius at which
resistance to heat flow is minimum
is called as Critical Radius (𝒓𝒄).
 It is dependent on the thermal
quantities 𝒌 and 𝒉𝒐 and
independent on 𝒓𝟏

14. NEWTON’S LAW OF COOLING
IT STATES THAT, “THE RATE OF HEAT FLOW IS
DIRECTLY PROPORTIONAL TO AREA BETWEEN TWO
FILMS AND TEMPERATURE DIFFERENCE ACROSS
THE FILM”.
MATHEMATICALLY,
𝑄 ∝ 𝐴 𝑡𝑠 − 𝑡𝑓
∴ 𝑸 = 𝒉𝑨 𝒕𝒔 − 𝒕𝒇
Where,
Q=Rate of heat transfer,
A= Surface area of heat flow, 𝑚2
𝑡𝑠 =Surface Temperature
𝑡𝑓 = Fluid Temperature
h= Co-efficient of convective heat transfer.

15. CONVECTIVE HEAT TRANSFER COEFFICIENT
THE AMOUNT OF HEAT TRANSMITTED FOR A UNIT TEMPERATURE DIFFERENCE
BETWEEN THE FLUID AND UNIT AREA OF SURFACE IN UNIT TIME IS CALLED AS
CONVECTIVE HEAT TRANSFER COEFFICIENT.
IT IS DENOTED BY 𝒉 AND IT’S UNIT IS
𝑾
𝒎𝟐℃
OR
𝑾
𝒎𝟐𝑲
THE VALUE OF ℎ DEPENDS ON THE FOLLOWING FACTORS:
1. DENSITY, VISCOSITY AND SPECIFIC HEAT
2. NATURE OF FLUID FLOW
3. GEOMETRY OF THE SURFACE
4. PREVAILING THERMAL CONDITIONS
(𝑹𝒕𝒉)𝒄𝒐𝒏𝒗 =
𝟏
𝒉𝑨

16. TYPES OF CONVECTION
Natural or Free Convection
When the fluid flows on hot
or cold surface due to
temperature difference only
the heat transferred under
such condition is known as
Natural convection
The force which acts on the
fluid to cause its motion is
called as buoyancy force.
Low heat transfer coefficient.
Forced Convection
When the fluid flows on hot
or cold surface under external
force, the heat transferred
under such condition is
known as Forced convection
The force which acts on the
fluid to cause the motion is
due to a fan or blower.
High heat transfer
coefficient.

17. RADIATION

18. RADIATION
RADIATION-HEAT TRANSFERRED BY
THE FLOW OF ELECTROMAGNETIC
RADIATION, LIKE HEAT FELT FROM
THE CAMPFIRE.
RADIATION IS THE ONLY TYPE OF
HEAT TRANSFER THAT CAN HAPPEN IN
VACUUM.
 HEAT TRANSFER THROUGH WAVES.

19. ABSORPTIVITY, REFLECTIVITY AND
TRANSMISSIVITY
When incident radiation (G) called as irradiation impinges on
surface.
 A part is reflected (Gr)
 A part is transmitted (Gt)
 A part us absorbed (Ga)
By the conservation of energy principle
𝐺 = 𝐺𝑟 + 𝐺𝑡 + 𝐺𝑎
∴
𝐺𝑎
𝐺
+
𝐺𝑟
𝐺
+
𝐺𝑡
𝐺
=
𝐺
𝐺
𝜶 + 𝝆 + 𝝉 = 𝟏
Where,
𝜶= Absorptivity (The ratio of amount of radiation absorbed to amount of incident radiation on a body.)
𝝆=Reflectivity (The ratio of amount of radiation reflected to amount of incident radiation on a body.)
𝝉= Transmissivity (The ratio of amount of radiation transmitted to amount of incident radiation on a body.)

20. TYPES OF BODIES
BLACK BODY: A BODY IN WHICH NEITHER REFLECTS NOR TRANSMITS ANY PART OF
INCIDENT RADIATION BUT ABSORBED ALL OF IT IS CALLED A BLACK BODY. FOR BLACK
BODY, 𝛼 = 1, 𝜌 = 0, 𝜏 = 0.
WHITE BODY: IF ALL THE INCIDENT RADIATION FALLING ON BODY ARE REFLECTED IS
CALLED AS A WHITE BODY. FOR WHITE BODY, 𝛼 = 0, 𝜌 = 1, 𝜏 = 0.
OPAQUE BODY: WHEN NO INCIDENT RADIATION IS TRANSMITTED THROUGH THE BODY
IS CALLED AS OPAQUE BODY. FOR OPAQUE BODY 𝛼 = 0, 𝜌 = 0, 𝜏 = 1.
GRAY BODY: IF THE RADIATIVE PROPERTIES Α, Ρ, Τ OF A BODY ARE ASSUMED TO BE
UNIFORM OVER THE ENTIRE WAVELENGTH OF SPECTRUM THEN SUCH A BODY IS
CALLED AS GRAY BODY. FOR GRAY BODY ABSORPTIVITY OF SURFACE DOES NOT VARY
WITH TEMPERATURE AND WAVELENGTH OF INCIDENT RADIATION.

21. STEFAN-BOLTZMANN LAW
THE LAW STATES THAT, “THE EMISSIVE
POWER OF A BLACK BODY IS DIRECTLY
PROPORTIONAL TO THE FOURTH POWER
IF ITS ABSOLUTE TEMPERATURE”.
MATHEMATICALLY,
𝐸𝑏 ∝ 𝑇4
𝑬𝒃 = 𝝈𝑻𝟒
Where,
𝐸𝑏= Emissive power of black body.
𝜎= Stefan Boltzmann Constant=5.67 × 10−8
𝑊 𝑚2
𝐾4
T= Absolute Temperature
𝑬𝒃 = 𝟓. 𝟔𝟕(
𝑻
𝟏𝟎𝟎
)𝟒
𝑄 = 𝐹𝜎𝐴 𝑇1
4
− 𝑇2
4
∴ 𝑄 =
𝑇1 − 𝑇2
1/[𝐹𝜎𝐴(𝑇1 + 𝑇2)(𝑇1
2
+ 𝑇2
2
)
(𝑹𝒕𝒉)𝒓𝒂𝒅 = 𝟏/[𝑭𝝈𝑨(𝑻𝟏 + 𝑻𝟐)(𝑻𝟏
𝟐
+ 𝑻𝟐
𝟐
)

22. EMISSIVE POWER AND EMISSIVITY
EMISSIVE POWER: THE TOTAL AMOUNT OF RADIATION EMITTED BY A BODY PER
UNIT AREAAND TIME IS CALLED AS EMISSIVE POWER. IT IS EXPRESSED IN 𝑊 𝑚2
.
EMISSIVITY (𝜺): THE RATIO OF THE EMISSIVE POWER IF ANY BODY TO THE
EMISSIVE POWER OF BLACK BODY AT SAME TEMPERATURE IS CALLED AS
EMISSIVITY. MATHEMATICALLY, 𝜺 =
𝑬
𝑬𝒃
Value of 𝜺
For Black body 𝜺 = 1
For White body 𝜺 = 𝟎
For Gray body 𝟎 < 𝜺 < 𝟏
𝜺 ∝ 𝜶 Kirchhoff’s Law

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