CONDUCTION ( Heat Transfer – 1 )

By MacanyTech Editorials
Heat transfer1

Through this article you are able to take a wide knowledge about the following aspects.

  • What is conduction, Conduction of heat in solids, liquids and in gases,  Examples for conduction, Experiments based on conduction
  • Laws and theories based on conduction

Introduction

Conduction is the transfer of heat by the vibration of particles and also through the free electrons. This is most effective in solids. Heat transfer will continue until all particles have the same kinetic energy and are the same temperature.

  1. By the vibration of particles:  The atoms or the molecules in the hottest part of the body have a high kinetic energy. Due to the high kinetic energy they move faster. Then they transfer heat by impacts some of their energy to adjacent molecules or atoms.
  2. Through the free electrons:  Electrons can also carry heat. That is why metals are generally very good conductors of heat. The electrons in metal are delocalized electrons. They are free to move. When they absorb energy (heat), they vibrate more quickly. Then they can move here and there. As a result of that they can pass energy more quickly. As they move through the metal, free electrons crash in to metal ions.

Most of the people think that conduction occurs only in solids. But it is wrong. Heat conduction occurs in both liquids and gases, but it is not same as solids. The mechanism of the heat conduction in liquids and the mechanism of the heat conduction in gases are nearly same.

Mechanism of heat conduction in liquids:  Conduction of heat occurs in liquids by transfer of vibrational forces between molecules. When the liquid molecules absorb heat, their kinetic energy increases. As a result of that, the vibrational forces are high.

Mechanism of heat conduction in gases:  The mechanism of heat conduction in gases is simple. When a molecule which has a high temperature collides with a molecule which has a low temperature, energy is lost due to the collisions. The kinetic energy of a gas molecule is a function of temperature.

Examples for conduction of heat:

  • When you put hot water to a cup, after few seconds you feel cup has been hot.
  • When walking on the beach on a hot summer day, feet get warm. (that means sand conduct heat)
  • When ironing a cloth, the cloth gets hot.
  • When you hold a piece of ice on your hand, the piece of ice starts to get melt.
  • A radiator is a good example for the heat conduction.
  • When you attempt to eat a hot pocket, your mouth gets burnt.

Experiments based on conduction of heat:

This a simple experiment which can be used to demonstrate conduction of heat.

  • Take a Bunsen burner, an aluminium rod, small amount of wax.
  • Keep wax pieces all over the aluminium rod.
  • Place on end of the aluminium rod to the flame of the Bunsen burner.
  • After a few time, you can see wax pieces start to get melt from side of flame to the other end.

Fourier’s law of Heat Conduction

‘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 direction of heat flow, and to change of temperature with respect to the length of the path of the heat flow’’.

At the steady state, the rate of heat transfer depends on the nature of the materials and the temperature difference.

Mathematically, it can be represented by the equation:

Fourier’s law of Heat Conduction

Where,

Q = Heat flow through a body per unit time (in watts), W

A = Surface area of heat flow (perpendicular to the direction of flow), m2

dt = Temperature difference of the faces of block (homogeneous solid) of thickness ‘dx’ through which heat flows, °C or K

dx = Thickness of body in the direction of flow, m

Thus,

Where,

k = Constant of proportionality and is known as thermal conductivity of the body.

The minus sign in this equation tells that the heat flows from regions of higher to lower temperature. This shows that the second law of thermodynamics is in practical.

Fourier’s law is based on some assumptions. They are as follows.

  1. Conduction of heat takes place under steady state conditions
  2. The heat flow is unidirectional
  3. The temperatures gradient is constant and the temperature profile is linear
  4. There is no internal heat generation
  5. The bounding surfaces are isothermal in character
  6. The material is homogeneous and isotropic (i.e., the value of thermal conductivity is constant in all directions)

Followings are some essential features of Fourier’s law:

  1. It is applicable to all matter (may be solid, liquid or gas).
  2. It is based on experimental evidence and cannot be derived from first principle.
  3. It is a vector expression indicating that heat flow rate is in the direction of decreasing temperature and is normal to an isotherm.
  4. It helps to define thermal conductivity ‘k’ (transport property) of the medium through which heat is conducted.

Thermal conductivity of materials

The amount of energy conducted through a body of unit area, and unit thickness in unit time when the difference in temperature between the faces causing heat flow is unit temperature difference.

From the above equation;

Thermal conductivity of materials

If a metal has a high thermal conductivity, it is a good conductor of heat. If a material has a low thermal conductivity, it is a good thermal insulator. So insulators show low thermal conductivities. It is due to their porosity.

Thermal conductivity depends on the followings:

  • Material structure
  • Moisture content
  • Density of the material
  • Pressure
  • Temperature

Following table shows the thermal conductivities of some materials in room temperature.

Materialk  (W/mK)MaterialK (W/mK)
Gases Solids 
SO20.009Styrofoam0.036
CO20.018Corrugated cardboard0.064
H20.025Paper0.13
H2O0.025Sand0.33
Air0.026Glass0.35 – 1.3
Liquids Ice2.2
Gasoline0.13Lead34
Ethanol0.18Steel45
Water0.55 – 0.10Aluminium224
Mercury8.4Copper385
Sodium85Silver410

Thermal conductivity of a material is due to the flow of free electrons.

The Wiedemann and Franz law

This law is based on experiment results regarding thermal and electrical conductivities of a material.

‘‘The ratio of the thermal and electrical conductivities is the same for all metals at the same temperature; and that the ratio is directly proportional to the absolute temperature of the metal.’’

Mathematically,

Where,

k = Thermal conductivity of metal at temperature T (K)

σ = Electrical conductivity of metal at temperature T (K)

C = Constant (for all metals) is referred to as Lorenz number (= 2.45 × 10–8 WΩ/K2; Ω stands for ohms).

This law conveys that the materials which are good conductors of electricity are also good conductors of heat.

Thermal Resistance

Where;

Thermal Resistance

T = Temperature of the object

t = Ambient temperature

P = Power object using

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Here we come to the end of part 1. Stay tuned for the next part. We will publish it here on our website www.macanytech.com. For email notification please subscribe our news alert service.

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