Modes of Heat and Mass Transfer

P M V Subbarao

Associate Professor

Mechanical Engineering Department

IIT Delhi

Just as Intelligent as an Human Being .. ..

Modes of Heat & Mass Transfer

• Conduction or Diffusion

• Convection

• Radiation

Conduction Heat Transfer

• Conduction is at transfer through solids or stationery fluids.

• When you touch a hot object, the heat you feel is transferred through your skin by conduction.

• 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

                                                                                                                               

Circumstances Leading to Heat Conduction

The Chip Carrier • The chip is housed in a chip carrier or

substrate made of ceramic, plastic, or glass in order to protect its delicate circuitry from detrimental effects of the environment.

• The basic part:

– The chip

– Bond

– Lead frame

– Bond Wires

– Lid

– Pins

• The design of the chip carrier is the first level of thermal control of electronic devices.

Heat Generation & Conduction through A Basic Chip

The circuitry of an electronic component through which electrons flow and thus heat is generated is referred as the junction

Junctions are the sites of heat generation and thus the hottest spots in a component.

Modern chips can with stand a Maximum Junctions temperature of

150 oC. Lower Junction temperatures are desirable for extended and lower

Maintenance costs. The basic thermal issue is : Heat generation in 1 micron chip made of

silicon wafer.

Fourier’s law of heat conduction

• 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:

L

TkA

L

TTkAq coldhot

x

This is called as Fourier Law of Conduction

A Constitutive Relation

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''

Further Physical Description

• Will k be same in all directions?• Why k cannot be different each direction?• Why k cannot be a vector?

kkjkikk zyxˆˆˆ

Will mathematics approve this ?

What is the most general acceptable behavior of k, approved by both physics and mathematics?

Most General form of Fourier Law of Conduction

dx

dTkqx ''

Tkq ''

Tkq ''

kkjkikk zyxˆˆˆ

We are at cross roads !!!!!

Physical-mathematical Feasible Model

• Taking both physics and mathematics into consideration, the most feasible model for Fourier’s Law of conduction is:

Tkq .~~

''

Thermal conductivity of a general material is a tensor.

z

T

y

Tx

T

kkk

kkk

kkk

q

q

q

zzzyzx

yzyyyx

xzxyxx

z

y

x

''

''

''

Surprising Inventions !!!

z

Tk

y

Tk

x

Tkq xzxyxxx ''

z

Tk

y

Tk

x

Tkq yzyyyxy ''

z

Tk

y

Tk

x

Tkq zzzyzxy ''

Fire Resistant Wood

• Among the assessment properties of wood composite of structural members in building construction, fire performance is important and getting more attention nowadays.

• A new composite called molded carbon phenolic spheres (CPS), a mixture of sugi wood charcoal powders and phenol formaldehyde resin molded with a hot press is developed by a research group in Japan.

• The heat due to a fire accident should be thrown out fast outside the building.

Spread of Fire in A Room

Micro-structure of CPS

Thermal Performance