Modes of Heat Transfer- Conduction, Convection, Radiation

Table of Contents

Introduction Heat Transfer/ What is Heat Transfer?

The heat will always be transferred from higher temperature to lower temperature independent of the mode. The energy transferred is measured in Joules (kcal or Btu). The rate of energy transfer, more commonly called heat transfer, is measured in Joules/second (kcal/hr or Btu/hr).
Heat transfer plays a major role in the design of many other devices, such as car radiators, solar collectors, various components of power plants, and even spacecraft.

Heat Transfer Mechanisms

Heat can be transferred in three different modes: conduction, convection, and radiation.
All modes of heat transfer require the existence of a temperature difference, and all modes are from the high-temperature medium to a lower temperature one.

Heat is transferred by three primary modes:

Conduction (Energy transfer in a solid)
Convection (Energy transfer in a fluid)
Radiation (Does not need a material to travel through)

Conduction

Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles. Conduction can take place in solids, liquids, or gases.
In gases and liquids, conduction is due to the collisions and diffusion of the molecules during their random motion.
In solids, it is due to the combination of vibrations of the molecules in a lattice and the energy transport by free electrons.
The rate of heat conduction through a medium depends on the geometry of the medium, its thickness, and the material of the medium, as well as the temperature difference across the medium.
We know that wrapping a hot water tank with glass wool (an insulating material) reduces the rate of heat loss from the tank. The thicker the insulation, the smaller the heat loss.
We also know that a hot water tank will lose heat at a higher rate when the temperature of the room housing the tank is lowered. Further, the larger the tank, the larger the surface area and thus the rate of heat loss.

Consider steady heat conduction through a large plane wall of thickness Δx = L and area A, as shown in the figure. The temperature difference across the wall is ΔT = T2-T1
The rate of heat conduction through a plane layer is proportional to the temperature difference across the layer and the heat transfer
area but is inversely proportional to the thickness of the layer. That is,

Rate of heat conduction ∝ ( Area) (Temperature Difference ) / Thickness

Fourier’s law of heat conduction

Fourier’s law of conduction of heat is expressed as

Q ∝ A × (dt / dx)

Where,
Q = heat flow through a body per unit time (in watts W)
A = Surface area of heat flow m2,
dt = Temperature difference in oC or K
dx = Thickness of the body in the direction of flow, m.

Hence, we can express the Heat Conduction formula by

Q = – k × A (dt / dx)

Where

k = thermal conductivity of the body and it is a Constant of proportionality

Heat is conducted in the direction of decreasing temperature, and the temperature gradient becomes negative when temperature decreases with increasing x. The negative sign in Eq. ensures that heat transfer in the positive x-direction is a positive quantity.

Factors affecting the conduction of heat:-

i)The cross-sectional area of the rod (A)
ii)The temperature difference between the two surfaces of the conductor (θ1- θ2)
iii) Time for which heat flows. (t)
iv)Distance between two surfaces. (d)

Applications of conduction-

1. Fins provided on a motorcycle engine
2. Electric fuse cut off
3. Electric heater
4. Carbonization of coal
5. Melting of iron in a blast furnace
6. Fission reactions in nuclear fuel rods of nuclear reactors.
7. Electrical wiring in housing
8. Electric discharge machining in manufacturing

Typical units of measure for conductive heat transfer are:

Per unit area (for a given thickness)

Metric (SI): Watt per square meter (W/m)

Overall

Metric (SI) : Watt (W) or kilowatts (kW)

Thermal Conductivity

The thermal conductivity of a material can be defined as the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference.
The thermal conductivity of a material is a measure of the ability of the material to conduct heat.
A high value for thermal conductivity indicates that the material is a good heat conductor, and a low value indicates that the material is a poor heat conductor or insulator.
Note that materials such as copper and silver that are good electrical conductors are also good heat conductors, and have high values of thermal conductivity.
Materials such as rubber, wood, and styrofoam are poor conductors of heat and have low conductivity values.

Convection

Convection is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion, and it involves the combined effects of conduction and fluid motion.
The faster the fluid motion, the greater the convection heat transfer. In the absence of any bulk fluid motion, heat transfer between a solid surface and the adjacent fluid is by pure conduction.
The presence of bulk motion of the fluid enhances the heat transfer between the solid surface and the fluid, but it also complicates the determination of heat transfer rates.
Consider the cooling of a hot block by blowing cool air over its top surface (Figure).

For example, in the absence of a fan, heat transfer from the surface of the hot block in the figure will be by natural convection since any motion in the air, in this case, will be due to the rise of the warmer (and thus lighter) air near the surface and the fall of the cooler (and thus heavier) air to fill its place.
Heat transfer between the block and the surrounding air will be by conduction if the temperature difference between the air and the block is not large enough to overcome the resistance of air to movement and thus to initiate natural convection currents.

Energy is first transferred to the air layer adjacent to the block by conduction.
This energy is then carried away from the surface by convection, that is, by the combined effects of conduction within the air that are due to the random motion of air molecules and the bulk or macroscopic motion of the air that removes the heated air near the surface and replaces it by the cooler air.

Types of Convection:

Forced Convection- Convection is called forced convection if the fluid is forced to flow over the surface by external means such as a fan, pump, or the wind.
Natural or Free Convection- In contrast, convection is called natural (or free) convection if the fluid motion is caused by buoyancy forces that are induced by density differences due to the variation of temperature in the fluid (Figure)

Convection Formula :

The rate of convection heat transfer is observed to be proportional to the temperature difference, and is conveniently expressed by Newton’s law of cooling as,

Q = hA ( Ts – T∞)

Where,

h is the convection heat transfer coefficient in W/m^2 °C.

A is the surface area through which convection heat transfer takes place.

Ts is the surface temperature

T∞ is the temperature of the fluid sufficiently far from the surface.

The convection heat transfer coefficient h is not a property of the fluid. It is an experimentally determined parameter whose value depends on all the variables influencing convection such as the surface geometry, the nature of fluid motion, the properties of the fluid, and the bulk fluid velocity.

Units of measure for the rate of convective heat transfer are:

Metric (SI) : Watt (W) or kilowatts (kW)

Applications of convection-

1. Forced Convection is used to cool down the headed plate.
2. Forced Convection is used to cool down the heated engine of the vehicle.
3. Forced convection is used to cool down the laptop and supercomputer etc.
4. Forced convection is used to cool down the human body in the summer season.
5. Radiator – Puts warm air out at the top and draws in cooler air at the bottom.

Difference Between Conduction and Convection ;

Comparison between conduction and convection are as follows ;

Sr. no.	Conduction	Convection
1.	It is the mode of heat transfer from one part of substance to another part of same substance or one substance to another without displacement of molecules or due to the vibrations of molecules.	It is the mode of heat transfer from one part of a substance to another part of same substance or one substance to another with a displacement of molecules or due to the fluid flowing.
2.	It is the mode of heat transfer in which fluid particles do not mix with each other.	It is the mode of heat transfer in which fluid particles mix with each other.
3.	It occurs in solid.	It occurs in liquid and gases.
4.	It governs by Fourier‟s law of heat conduction.	It governs by Newton‟s law of convection heat transfer.
5.	Example: Heat flow from one end to other end of metal rod.	Example: Heat flow from boiler shell to water.

Thermal Radiation

Radiation is the energy emitted by matter in the form of electromagnetic waves (or photons) as a result of the changes in the electronic configurations of the atoms or molecules.
Unlike conduction and convection, the transfer of energy by radiation does not require the presence of an intervening medium. In fact, energy transfer by radiation is the fastest (at the speed of light) and it suffers no attenuation in a vacuum. This is how the energy of the sun reaches the earth.

The mechanism of the heat flow by radiation consists of three distinct phases:

1.Conversion of thermal energy of the hot source into electromagnetic waves:

All bodies above absolute zero temperature are capable of emitting radiant energy. The energy released by a radiating surface is not continuous but is in the form of successive and separate (discrete) packets or quanta of energy called photons. The photons are propagated through space as rays; the movement of a swarm of photons is described as electromagnetic waves.

2. Passage of wave motion through intervening space:

The photons, as carries of energy, travel with unchanged frequency in straight paths with speed equal to that of light.

3. Transformation of waves into heat:

When the photons approach the cold receiving surface, there occurs reconversion of wave motion into thermal energy which is partly absorbed, reflected, or transmitted through the receiving surface.
In heat transfer studies we are interested in thermal radiation, which is the form of radiation emitted by bodies because of their temperature. It differs from other forms of electromagnetic radiation such as x-rays, gamma rays, microwaves, radio waves, and television waves that are not related to temperature.

Radiation Heat transfer equation :

The net exchange of heat between the two radiating surfaces is due to the face that one at a higher temperature radiates more and receives less energy for its absorption.

Q = σ ε Ai Fij ( Ti^4 – Tj^4 )

Where,

Q = Heat flow rate from surface i to j
σ = Stephan- boltzman constant
ε = Emmissivity
Ai = area of surface i
Fij = Form factor between surface i and j
Ti and Tj = absolute temperatures of the surfaces

The maximum rate of radiation that can be emitted from a surface at an absolute temperature (in K) is given by the Stefan–Boltzmann law as

Eb = σb AT^4

Where Eb is the energy radiated by the black body, σb is the Stefan Boltzman constant

Stefan Boltzman constant

Terms Related to radiation :

Transmissivity:

It is the fraction of energy that is transmitted through the body.
Or
The ratio of the amount of energy transmitted to the amount of energy incident on a body.

Black body: A black body is an object that absorbs all the radiant energy reaching its surface from all the directions with all the wavelengths.

Grey Body: A gray body is defined as a body whose absorptivity of a surface does not vary with variation in temperature and wavelength of the incident radiation. It absorbs a definite percentage of incident energy irrespective of wavelength. Its absorptivity lies between 0 to 1.

Reflectivity:
It is defined as the ratio of the amount of energy reflected in the amount of energy incident on a body.

Typical units of measure for the rate of radiant heat transfer

Metric (SI) ——Watt per square meter (W/m

Example of radiation: Energy emitted by the sun reaches the earth through radiation.

Applications of heat transfer:

1) Fins provided on the motorcycle engine.
2) Cooling jackets provided in cylinder blocks
3) Radiator
4) Heat carried away by exhaust gases
5) Heat transfer from sun rays into the cabin/car
6) HVAC system etc.

More Resources /articles

Modes of Heat Transfer- Conduction, Convection, Radiation

Introduction Heat Transfer/ What is Heat Transfer?

Heat Transfer Mechanisms

Conduction