Modes of Heat Transfer

1. HEAT
• Heat: It is denoted by symbol Q and is defined as follows “heat is
something which appears at the boundary when a system changes its
state due to a difference in temperature between the system and
surroundings.”
• Heat appears only at the boundary while the change takes place inside
the system.
• Sign Convention: If heat flows from system to surroundings, the quantity
is said to be positive and if heat flows from surroundings to system it is
said to be negative.
In other words,
Heat received by system=+Q
Heat rejected by system=-Q

2. Difference between Heat Transfer and Thermodynamics:
• Let us take an example of a hot steel bar kept in a water bath.
• Thermodynamics predicts only the equilibrium temperature and state of
the system but it doesn’t predicts the time taken by the system to reach
that equilibrium and the temperature of the hot steel bar.
• Heat Transfer on the other hand helps in predicting the temperature of
both the bar and the water as a function of time.
• MODES OF HEAT TRANSFER:
There are three modes of heat transfer:
• Conduction
• Convection
• Radiation
• Heat transfer occurs as a result of combinations of these modes of heat
transfer. Heat always flows in the direction of lower temperature.

3. CONDUCTION
• The transfer of heat from one part of a substance to another part of the
same substance, or from one substance to another in physical contact
with it, without any displacement of molecules forming the substance.
• In solids, the heat is conducted by the following two mechanisms:
i. Lattice Vibrations (the faster moving molecules or atoms in the
hottest part of a body transfer heat impact some of their energy to
adjacent molecules).
ii. By transport of free electrons (Free electrons provide an energy flux
in the direction of decreasing temperature).
• In liquids, the process is similar but as they are more closely placed than
gases, the intermolecular forces comes into play.

4. • In gases, the kinetic energy of a molecules is a function of temperature.
The molecules are in constant random motion with energy and
momentum. When a molecule from high T region coincides with a
molecule of low T region, it loses energy by collisions.

5. • FOURIER’S LAW OF HEAT CONDUCTION:
•It states that,” for a homogeneous solid, the rate of
heat flow is directly proportional to area of section
at right angles to the direction of heat flow and to
change of temperature with respect to length of the
path of heat flow.”

6. • Mathematically,
Q ∝ A.(dt/dx)
Where, Q= Heat flow through the body per unit time (Watts)
A= Surface area of heat flow (m2)
dt= Temperature difference of the faces of block (K or ᵒC )
dx= Thickness of body in direction of flow (m)
Thus, Q= −𝒌.A(dt/dx)
Where k= constant of proportionality also known as thermal
conductivity of body.

7. • -ve sign is to take care of the decreasing temperature along the direction
of increasing thickness. The temperature gradient (dt/dx) is always
negative along positive x direction.
• Assumptions of Fourier Law:
Conduction of heat takes place under steady state conditions.
The heat flow is unidirectional.
The temperature gradient is constant and the temperature flow is linear.
There is no heat generation.
The material is homogeneous and isotropic.

8. • Essential Features of Fourier Law:
It is applicable to all matter. ( Solid, Liquid, Gas)
It is based on experimental evidence.
It is a vector expression indicating the heat flow rate is in the direction
of decreasing temperature.
It helps to define the thermal conductivity of medium through which
heat is conducted.

9. • The thermal conductivity of materials is defined as,” amount of energy
conducted through a unit area and unit thickness in unit time when the
difference in temperature between the faces causing heat flow is unit
temperature.”
• Conduction of heat occurs mostly in pure metals, less in alloys and much less
in non-metals.
• Thermal conductivity depends on the following factors:
Material Structure.
Moisture Content.
Density of material.
Pressure and temperature of operating conditions.
Units of k are W/mK or W/mᵒC

10. • Thermal conductivity of a metal varies when it is heated or treated with
mechanical process.
• Thermal conductivity of most metals decreases with the increasing
temperature.
• The dependence of thermal conductivity (k) on temperature for most
materials is mostly linear.

11. CONVECTION
• It is the mode of energy transfer between a solid surface and the
adjacent liquid or gas in motion and it involves the combined
effect of conduction and fluid motion. The faster the fluid motion,
the greater is the convection.
• The rate equation for the convective heat transfer between a
surface and an adjacent fluid is described by Newton’s Law of
Cooling.

12. Statement of Newton’s Law of Cooling:
•The coefficient of convective heat transfer
(h) is defined as “the amount of heat
transmitted for a unit temperature
difference between the fluid and unit area
of surface in unit time.”

13. •Q=h.A(ts-tf)
Where
Q= rate of conductive heat transfer
A= area exposed to heat transfer
ts=Surface Temperature
tf=Fluid Temperature
h=coefficient of convective heat transfer
Units of h are W/m2K or W/m2ᵒC

14. The value of ‘h’ depends on:
1. Thermodynamic and transport properties
2. Nature of fluid flow
3. Geometry of Surface
4. Prevailing thermal conditions.

15. RADIATION
•It is the transfer of heat through space or matter by
means other than conduction or convection.
•Radiant energy(being electromagnetic radiation) requires
no medium for propagation and will pass through
vaccum.

16. • LAWS OF RADIATION:
Wien’s Law: It states that the wavelength λ corresponding to the
maximum energy is inversely proportional to absolute
temperature T of hot body.
λmT=constant (or) λm∝ 𝟏/𝑻
Stefan-Boltzmann Law: The emissive power of black body is
directly proportional to fourth power of absolute temperature.
Q∝ 𝑻4

17. Mathematically, Q = F. 𝜎.A (T1
4 – T2
4)
Where, F= a factor depending on geometry and surface
properties.
𝜎 = 𝑆𝑡𝑒𝑓𝑎𝑛 − 𝐵𝑜𝑙𝑡𝑧𝑚𝑎𝑛𝑛 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡= 5.67×10 ̄ ̄⁸ W/ m2K4
A = Area of surface, m 2