Heat Transfer : An Action due to Thermal Inequilibrium

P M V SubbaraoProfessor

Mechanical Engineering Department

A Natural Happening …..

A Wake-up Call to Earth

A Natural Engineering Process for the Existence, Growth and Performance.

A True Design Reason behind Existence of Natural Systems…..

A Strong Design Modification for the Performance of Artificial Systems….

A True Design Reason behind Geometry of Natural Systems…..

Indian Elephant

African Elephant

Mammoths

An Evolution to Perfection of Heat Transfer is Sustainable

A Reason behind Survival of Electonics

What is Heat Transfer?

• Thermal energy is related to the temperature of matter. • For a given material and mass, the higher the temperature,

the greater its thermal energy. • Heat transfer is a study of the exchange of thermal energy

through a body or between bodies which occurs when there is a temperature difference.

• When system and its surroundings are at different temperatures, thermal energy transfers from the one with higher temperature to the one with lower temperature.

• Thermal Energy always travels from hot to cold.• This spontaneous act is called Heat Action or Heat

Transfer.

Heat Transfer Between System & Surroundings

• Heat transfer is typically given the symbol Q, and is expressed in joules (J) in SI units.

• The rate of heat transfer is measured in watts (W), equal to joules per second, and is denoted by Q.

• The heat flux, or the rate of heat transfer per unit area, is measured in watts per area (W/m2), and uses q" for the symbol.

Heat Transfer in Manufacturing

• The need/role of heat transfer is a two fold issue.

• Heat Transfer by design.

– Casting

– Hot working

– Sintering

• Heat Transfer due to unavoidable conditions.

– Machining process.

What Causes Heat Transfer in Machining?

• First, almost all (90%-100%) of the work consumed in a machining operation finally convert into the thermal energy.

• There are several sources of thermal energy in cutting with a sharp tool:

• Viscous dissipation transformed into heat if the cut material are viscoplastic.

• Work done by friction converted to heat.

• Ambient heat source sometimes need be considered if thermal deformation is concerned.

• In non-traditional machining, other types of heat sources exist

Modes of Heat & Mass Transfer

• Conduction or Diffusion

• Radiation

• Convection

Conduction Heat Transfer

• Conduction is a significant mode of transfer when system and surroundings consist of solids or static fluids.

• Two mechanisms explain how heat is transferred by conduction: lattice vibration and particle collision.

• Conduction through solids occurs by a combination of the two mechanisms; heat is conducted through stationery fluids primarily by molecular collisions.

Conduction by lattice vibration or Particle Collisions

                                                                                                                               

Fourier law of heat conduction

L

TkA

L

TTkAQ coldhot

This is called as Fourier Law of Conduction

A Constitutive Relation

• The rate of heat transfer through the wall increases when:

• The temperatures difference between the left and right surfaces increase,

• The wall surface area increases, • The wall thickness reduces, • The wall is changed from brick to aluminum. • If we measure temperatures of the wall from

left to right and plot the temperature variation with the wall thickness, we get:

Circumstances Leading to Heat Conduction

Circumstances Leading to Heat Conduction in Machinging

Thermal Image of Laptop Casing

Graphite Covering

Thermal Image of Laptop Casing with Graphite cover

Statement of Fourier’s LawThe (mod of) heat flux, q’’, (the flow of heat per unit area and per unit time), at a point in a medium is directly proportional to the temperature gradient at the point.

x

TTTThot

xxx

x

Temperature gradient across the slab of thickness x:

xxx

xTxxT hotcold

)()(

The heat flux across the slab

xxx

xTxxT

xxx

xTxxTq

hotcold

hotcold

)()(

)()(''

TTcold

xxx

xTxxTkq hotcold )()(

''

Local Heat flux in a slab:

xxx

xTxxTkq hotcold

xx

)()(lim ''

0

dx

dTkqx ''

Global heat transfer rate:

dx

dTkAqx

Mathematical Description

• Temperature is a scalar quantity.

• Heat flux is defined with direction and Magnitude : A Vector.

• Mathematically it is possible to have:

kqjqiqq zyxˆ''ˆ''ˆ'' ''

Using the principles of vector calculus:

Tkq ''

kz

Tj

y

Ti

x

Tkq ˆˆˆ''