Heat Transfer : An Action due to Thermal Inequilibrium P M V Subbarao Professor Mechanical...
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Transcript of Heat Transfer : An Action due to Thermal Inequilibrium P M V Subbarao Professor Mechanical...
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Heat Transfer : An Action due to Thermal Inequilibrium
P M V SubbaraoProfessor
Mechanical Engineering Department
A Natural Happening …..
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A Wake-up Call to Earth
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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….
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A True Design Reason behind Geometry of Natural Systems…..
Indian Elephant
African Elephant
Mammoths
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An Evolution to Perfection of Heat Transfer is Sustainable
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A Reason behind Survival of Electonics
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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.
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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.
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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.
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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
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Modes of Heat & Mass Transfer
• Conduction or Diffusion
• Radiation
• Convection
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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.
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Conduction by lattice vibration or Particle Collisions
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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:
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Circumstances Leading to Heat Conduction
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Circumstances Leading to Heat Conduction in Machinging
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Thermal Image of Laptop Casing
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Graphite Covering
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Thermal Image of Laptop Casing with Graphite cover
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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
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xxx
xTxxTkq hotcold )()(
''
Local Heat flux in a slab:
xxx
xTxxTkq hotcold
xx
)()(lim ''
0
dx
dTkqx ''
Global heat transfer rate:
dx
dTkAqx
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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''