PHYSICS

HEAT TRANSFER

CONDUCTION

1.1 Conduction

Heat is an interesting form of energy. Not only does it sustain life, make us comfortable and help us prepare our food, but understanding its properties is key to many fields of scientific research. For example, knowing how heat is transferred and the degree to which different materials can exchange thermal energy governs everything from building heaters and understanding seasonal change to sending ships into space.

Heat can only be transferred through three means: conduction, convection and radiation. Of these, conduction is perhaps the most common, and occurs regularly in nature. In short, it is the transfer of heat through physical contact. It occurs when you press your hand onto a window pane, when you place a pot of water on an active element, and when you place an iron in the fire.

This transfer occurs at the molecular level — from one body to another — when heat energy is absorbed by a surface and causes the molecules of that surface to move more quickly. In the process, they bump into their neighbours and transfer the energy to them, a process which continues as long as heat is still being added.

Heat Conduction Through Solids Lattice Conduction

The molecules in a solid vibrate about their

own equilibrium positions at room

temperature. The vibrations of the

molecules approximate simple harmonic

motion. At the hot end of solid, the

molecules with more thermal energy vibrate

vigorously with greater amplitude. The

molecules impart the vibrations to adjacent

molecules via intermolecular forces

between molecules. The hotter molecules

collide with colder molecules. As a result,

energy is transferred from the molecules at

the hotter region to colder region.

Collision of Electrons

When a solid is heated at one end, the atoms there

vibrate more vigorously. The free electrons which collide

with these atoms gain kinetic energy. The free electrons

with greater kinetic energy collide with slow moving

electrons and others atoms from the colder region. As a

result, some energy is transferred to slower moving

electrons. Energy is transferred from hotter region to the

colder region of solid though random collision of

electrons. This method of heat transfer is known as

electronic conduction. Since electrons are lighter and

move faster, the transfer of energy though electronic

conduction is greater and faster compared to lattice

conduction. A good conductor of heat is also a good

conductor of electricity. Metal conduct heat though lattice

vibration and collisions of free electrons. Non-metals

conduct heat through lattice vibration only since it has no

free electrons, therefore, non-metals are generally poor

heat conductors.

In metals, not only do the atoms vibrate more when heated, but the free electrons charge around more as well. These transfer the energy much faster than just vibrations in bonds.

Difference between lattice conduction and electronic conduction

Lattice Conduction Electronic Conduction

Involve vibration of molecules

Molecules vibrate at equilibrium positions only

Slow

Occurs in metals and non-metals

Involves free moving electrons

Electrons move from one place to another

Fast

Occurs only in metals

Defining Thermal Conductivity

The process of heat conduction depends on four basic factors: the temperature gradient, the cross section of the materials involved, their path length, and the properties of those materials.

Defining Thermal Conductivity

Picture of a block of metal between two hot and cold object and insulated from its surroundings.

The temperature, , at both ends were maintained.The thickness of metal is d, now xCross section area of metal block is A.Temperature difference is So the instantaneous temperature gradient at any point = the rate of change in temperature with distance along the block

= = - = -

The unit for temperature gradient is or

* The temperature gradient has negative sign is due to that the temperature decreases as the distance x increases.

Defining Thermal Conductivity

Picture of a block of metal between two hot and cold object and insulated from its surroundings.

The rate of heat transfer perpendicular the cross section area, A depends on 3 criteria 1 The temperature gradient, - ( The greater the magnitude of

temperature gradient, the greater the rate of heat flow )2 The cross section area, A ( The larger the cross section are, the

the greater the rate of heat flow )3 The material of the solid ( Iron is a better conductor than a brick.

Hence, the rate of heat flow is greater in iron compared to that of brick )

Defining Thermal Conductivity

Picture of a block of metal between two hot and cold object and insulated from its surroundings.

Threfore,

A

Combining the above equation,

k = thermal conductivity of the material. The equation is also known as Fourier’s Law.

From the equation,

k =

Hence thermal conductivity, k is defined as the negative rate of heat flow per unit area perpendicular to the flow per unit temperature gradient. The unit for k is W

Defining Thermal Conductivity

Thermal conductivity is the ability of heat transferring heat though an object.

As saw from Fourier’s Law, the larger the value of k, the larger the value of − / while other factor being constant.𝑑𝑄 𝑑𝑡Therefore, good conductor of heat such as metals have higher value of k. Weaker conductor of heat have a lower value of k.

In some cases, while some metals was heated, the value k decreases slightly.

Defining Thermal Conductivity

Thermal conductivities for different materials.

Thermal Conduction in Perfectly Insulated Rod

Thermal Conduction in Perfectly Insulated Rod

M N

Rod Insulation Heat flow (uniform and parallel to each other)

The temperature at M and N are maintained at and accordingly, and The temperature at different points of rod are changing with time.The rate of heat flow is constant at every point along the rod.According to Fourier’s Law, the magnitude of is a constant since k, A and / are constant.𝑑𝜃 𝑑𝑥 In this case 0, since

From equation

= ), ( )

For rod of length L with a uniform cross section

area A and constant heat flow, then

), ( )

THERMAL RESISTANCE

What sorcery is this?

Thermal resistance is a heat property and a measurement of a

temperature difference by which an object or material resists a

heat flow.

Thermal Resistance

Thermal resistance along a conductor is very similar to the flow of charge

in an electrical conductor.

Potential difference is needed for electric charge to flow;

Temperature difference is needed for heat to flow.

Hence, analogous quantities for the 2 flows can be ascertained by

comparing the equations.

Thermal Resistance

Heat flow Q along a rod of length L

So, rate of heat flow, Rate of electric charge flow,

) = =

Thus, is analogous to V and is analogous to R.The term is known as thermal resistance .The unit for is K Finally, the rate of heat flow can also be written as .

L

Thermal Conduction in a Non-Insulated Rod

The two ends of the rod are maintained at temperature and respectively. ( ).Some heat escapes from the sides of the rod into the surrounding.As such, the rate of heat flow decreases as x increase along the rod.The temperature decreases as x increases along the rodFrom (k and A are constants), as decreases, the temperature gradient also decreases as x increases along the rod.Temperature fall is the steepest at the hot end.

Describing and Calculating Heat Conduction Through a Cross-Section Area of Layers of Different Materials

Heat Conduction through Layers of Different Materials

Tout = -10 ̊C

Tin = 25 ̊C

10 cm1.0cm

WOODICE

Kwood = 0.2 W/(mK)Kice = 2 W/(mK)

Calculating Heat Conduction through Layers of Different Materials

Calculating Heat Conduction through Layers of Different Materials

Given that cross-sectional area is 1.0 m2 Find the rate of heat flow.

W6912.0

1.012

01.0)10(25

......, 3, 2, 1, re whe

resistance thermaltotal

difference etemperatur

ni

Akl

TT

dt

dQ

dt

dQ

i

i

outin

THE END It is me, or it is hot right

here?