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 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 life and lower

Maintenance costs. The basic thermal issue is : Removal Heat generated in 1 micron thick

chip made of silicon wafer.

Global heat transfer rate due to conduction :

dx

dTkAqx

Summary of Fourier’s Law of Conduction

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

Another Physical Phenomena analogous to Heat

Conduction

Diffusive Mass Transfer

Physics of Mass Transfer

• During a mass transfer process individual chemical species travels from high concentration region to low concentration region.

• In this regard mass transfer is analogous to heat transfer.

• Conduction (Diffusion) Mass Transfer is governed by Fick’s Law of diffusion.

• Fick's laws of diffusion were derived by Adolf Fick in the year 1855.

Rate of molecular

flow=

Difference in concentration

Resistance: depends on ability of molecules to pass through, k and membrane dimensions, Dx and A

Fick's law of diffusion

dx

dCDAJ x

where C is the concentration, Jx is the rate of mass diffusion, and D is the diffusion coefficient.

In two or more dimensions

CDAJ

Equations based on Fick's law have been commonly used to model transport processes in foods, neurons, biopolymers, pharmaceuticals, porous soils, population dynamics, semiconductor doping process, etc.

A large amount of experimental research in polymer science and food science has shown that a more general approach is required to describe transport of components in materials undergoing glass transition.

Heat Convection

• Convection uses the motion of fluids to transfer heat.

• In a typical convective heat transfer, a hot surface heats the surrounding fluid, which is then carried away by fluid movement such as wind.

• The warm fluid is replaced by cooler fluid, which can draw more heat away from the surface.

• Since the heated fluid is constantly replaced by cooler fluid, the rate of heat transfer is enhanced.

Natural Convection

• Natural convection (or free convection) refers to a case where the fluid movement is created by the warm fluid itself.

• The density of fluid decrease as it is heated; thus, hot fluids are lighter than cool fluids.

• Warm fluid surrounding a hot object rises, and is replaced by cooler fluid.

• The result is a circulation of air above the warm surface

Forced Convection

• Forced convection uses external means of producing fluid movement.

• Forced convection is what makes a windy, winter day feel much colder than a calm day with same temperature.

• The heat loss from your body is increased due to the constant replenishment of cold air by the wind.

• Natural wind and fans are the two most common sources of forced convection.