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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.

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modes of heat and mass transfer

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
Modes of Heat & Mass Transfer
  • Conduction or Diffusion
  • Convection
  • Radiation
conduction heat transfer
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.
the chip carrier
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
Fourier’s law of heat 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:

This is called as Fourier Law of Conduction

statement of fourier s law
Statement of Fourier’s Law

The (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.

Temperature gradient across the slab of thickness Dx:


The heat flux across the slab



Local Heat flux in a slab:

Global heat transfer rate:

mathematical description
Mathematical Description
  • Temperature is a scalar quantity.
  • Heat flux is defined with direction and Magnitude : A Vector.
  • Mathematically it is possible to have:

Using the principles of vector calculus:

further physical description
Further Physical Description
  • Will k be same in all directions?
  • Why k cannot be different each direction?
  • Why k cannot be a vector?

Will mathematics approve this ?

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

physical mathematical feasible model
Physical-mathematical Feasible Model
  • Taking both physics and mathematics into consideration, the most feasible model for Fourier’s Law of conduction is:

Thermal conductivity of a general material is a tensor.

fire resistant wood
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.