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Heat Transfer : An Action due to Thermal Inequilibrium. P M V Subbarao Professor Mechanical Engineering Department. A Natural Happening …. A Wake-up Call to Earth. A Natural Engineering Process for the Existence, Growth and Performance.
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Heat Transfer : An Action due to Thermal Inequilibrium P M V Subbarao Professor Mechanical Engineering Department A Natural Happening …..
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….
African Elephant Indian Elephant A True Design Reason behind Geometry of Natural Systems….. Mammoths
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.
Fourier 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 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: T The heat flux across the slab x
Local Heat flux in a slab: Global heat transfer rate:
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: