Radiation Heat Transfer

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View Factor Orientation (or View factor or shape factor) plays an important role in radiation heat transfer. View factor is defined as, "fraction of radiation leaving surface 'i' and strike 'j' ". Summation Rule (View Factor) If there is are similar surfaces 'i' and 'j' , then: Blackbody Radiation Exchange Radiation Exchange between Opaque, Diffuse, Gray surfaces in an Enclosure 1. Opaque 2. Surfaces 3. Two surface enclosure Radiation Shield It is used to protect surfaces from radiation act like a reflective surface. References: Material from Class Lectures + Book named Fundamentals of Heat and Mass Transfer by Theodore L. Bergman + My knowledge.  Photoshoped pics  are developed.  Some pics and GIF from Google.   Videos from YouTube ( Engineering Sights ).

Phases and Heat Treatment

Components

These are pure metals. Combination of components is called Alloy
  • System  ↠  refers to specific body (region) of material under consideration.
  • Solid Solution  ↠  Solute atoms occupy solvent atoms substitutional and interstitial spaces.

Solubility Limit

It is defined as, "Maximum concentration of solute atoms that may dissolve in solvent to form solid solution at specific temperature".
  • It depends on temperature.

Phases

It is defined as, "a homogenous portion of a system that has uniform physical and chemical characteristics".
  • Single-phase system  ↠  homogenous system.
  • Two or more phase system  ↠  heterogenous system.

Microstructure

It is defined as, "a subject to direct microscopic observation using optical or electron microscopes".
  • Microstructure is characterized by number of phases present, their proportion and manner in which they are arranged.
  • Microstructure of alloy depends on alloying elements, concentrations, heat treatment (temperature, heating time at temperature, rate of cooling to room temperature)

Phase Equilibria

It is defined as, "a system in which more than one phase may exist (consistency w.r.t time)".
  • Equilibrium is best described in a quantity called Free Energy.
  • A change in temperature, pressure, composition for a system result in increase in free energy.

Phase Equilibrium Diagram

It is defined as, "Information about the control of phase structure of a particular system is displayed".
  • Microstructures may develop from phase transformation (altered due to temperature change, cooling). 
  • Common phase diagrams  ↠  temperature and composition are variable (pressure = constant).
  • Binary phase diagrams  ↠  represents relation between temperature, composition and quantities of phase.
Binary Amorphous System  ↠  There are 3 types of phases
  1. ∝-Solution  ↠  contains both material in solid form.
  2. L-Solution  ↠  contains both material in liquid form.
  3. ∝ + L Solution  ↠  contains both phase.
    • Liquidous line  ↠  above which phase is liquid and below it is mixture.
    • Solidous line  ↠  below which phase is solid and above it is mixture.

Interpretation of Phase Diagram

For a binary system of known composition and temperature at equilibrium, we use 3 kind of information
  1. Phases that are present  ↠  point is above or below the solidous or liquidous line.
  2. Composition of these phases  ↠  Draw a tie line (horizontal line through point which lie in mixture area), Note intersection of tie line and the phase boundaries, Drop perpendicular from these intersections  and note values.
  3. Percentages or Fractions of phases  ↠  Relative amount (as fraction or percentage) of phases present at equilibrium may be calculated using phase diagram.

Lever Rule

  1. Tie line is constructed across two-phase region at temperature of alloy.
  2. Overall alloy composition is located on tie line.
  3. The fraction of one phase is computed by taking length of tie line from overall alloy composition to phase boundary for the other phase and dividing by the total tie line length.
  4. The fraction of other phase is determined in the same manner.

The Iron-Iron Carbide Equilibrium Diagram

  • The metal iron is a primary constituent of some most important engineering alloys.
  • Ingot Iron  ↠  iron in its purest form.
  • Iron is an allotropic metal (exist in more than one lattice type depending upon temperature).
Phase changes of iron (info for cooling of pure iron): 
  • Iron at 2800 F (solidification)  ↠  BCC or δ-Form.
  • Iron at 2554 F (cooling)  ↠  FCC or γ-Form and Non-magnetic.
  • Iron at 1666 F  ↠  BCC or ⋉-Form and Non-magnetic.
  • Iron at 1414 F  ↠  ⋉-Iron becomes magnetic without change in lattice structure.
Temperature at which allotropic changes take place  ↠  depends on alloying elements.
  • Diagram between pure iron and iron carbide (interstitial compound) Fe3C containing 6.67 % carbon by weight, so called Iron-Iron Carbide Equilibrium Diagram.
Reaction Points:

Description of Structures 

1. Cementite or Iron Carbide (Fe3C)

  • It contains 6.67 % C, hard and brittle interstitial compound of low tensile strength (approx. 5000 psi) but high compressive strength
  • Hardest structure appears on diagram.
  • Crystal is orthorhombic.

2. γ-Solid Solution or Austenite

  • Interstitial solid solution of carbon dissolved in FCC iron (max. solubility is 2 % at 2065 F).
  • Tensile strength  ↠  150,000 psi (high toughness).
  • Elongation  ↠  10 % in 2 inch.
  • Rockwell hardness  ↠  40 approx.

3. Ledeburite 

  • Eutectic mixture of austenite and cementite.
  • Contains 4.3 % carbon formed at 2065 F.

4. Ferrite or ∝-Solid Solution

  • Interstitial solid solution of small amount of carbon dissolved in BCC structure.
  • Max. solubility  ↠  0.025 % at 1333 F and 0.008 % at room temperature.
  • Softest structure appears on diagram.

5. Pearlite

  • Eutectoid mixture of ferrite and cementite.
  • Contains 0.8 % Carbon formed at 1333 F.

Heat Treatment 

  • If have 0.8 % or less carbon in steel  ↠  Hypo-eutectoid Steel.
  • If have (0.8-2) % carbon in steel  ↠  Hyper-eutectoid Steel.
  • Hypo-eutectic Steel  ↠  < 4.3 % carbon in steel.
  • Hyper-eutectic Steel  ↠  (4.3-6.67) % carbon in steel.
Ques: Solubility of carbon in Austenite > that that in Ferrite?
Austenite has FCC crystal arrangement and packly closed together (i.e. high APF) than Ferrite.

Formation (or Growth) of Pearlite

Carbon in Austenite precipitate to form cementite (i.e. FCC → BCC). Carbon deposit on cementite boundary to form ferrite.

Classification of Steel

1. Method of Manufacture

  • This gives rise to Bessemer steel, Open-Hearth steel, Electric-Furnace steel, Crucible steel, etc.

2. Chemical Composition 

  • By means of numbering system, indicate approx. content of important elements in steel.
Steps are as follows:
  1. First digit of 4 or 5 numeral designation indicate type of steel used ( 1 → carbon steel, 2 → Nickel steel, 3 → Nickel-Chromium steel).
  2. If simply alloy steel, 2nd digit indicates approx. percentage of predominant alloying element.
  3. The last 2 or 3 digits usually indicate mean carbon content divided by 100.
Sometime steels are classified by broad range of carbon content:
  1. Low-carbon Steel  → up to 0.25 % carbon.
  2. Medium-carbon Steel  → 0.25 % - 0.55 % carbon.
  3. High-carbon Steel  → above 0.55 % carbon.

Heat Treatment of Steel

"A combination of heating and cooling operations, timed and applied to a metal or alloy in solid state in a way that will produce desired properties".
  1. Heat treatment processes for steel involve transformation or decomposition of Austenite.
  2. Nature and appearance of these transformation products determine the physical and mechanical properties of any given steel.
Steps for heat treatment of steel are:
  1. Heat material to temperature above critical range to form Austenite.
  2. Rate of heating to desired temperature is less important than other factors in heat-treatment cycle.
  3. Highly stressed material (by cold work)  →  heat more slowly than stress free to avoid distortion.
  4. Difference in temperature rise within thick or thin sections of variable cross-section should be considered  →  heat slow thinner sections to minimize thermal stress and distortion.

A. Full Annealing or Furnace Cooling

It is defined as, "process consists of heating steel to proper temperature and then cooling slowly through transformation range (in furnace)".
  • Purpose  →  refine grains, induce softness, improve electrical and magnetic properties, improve machinability.
  • Reason  →  Annealing is a very slow cooling process → close to follow Iron-Iron Carbide Equilibrium diagram (because of entire mass of furnace is cooled with material).
  • For Hypo-Eutectoid steel  →  rise temperature from A1 to A3 to get fine grain structure → than furnace cooling to get fine grain of Ferrite and Pearlite.
  • For Hyper-Eutectoid steel  →  use temperature above A3,1 but have poor machinability.
Microscopic study of proportions of ferrite and pearlite or pearlite and cementite present in an annealed steel enable us to determine approx. carbon content of steel.

B. Spheroidizing

It is defined as, "annealing process to improve the machinability".
  • Because annealed hyper-eutectoid steel with a microstructure of pearlite and cementite →  gives poor machinability.
Steps:
  1. Prolong holding at a temperature just below the lower critical line.
  2. Heating and cooling between temperature that are just above and below the lower critical line.
  3. Heating to a temperature above the lower critical line and then cooling very slowly in the furnace or holding at a temperature just below the lower critical line.

Stress-Relief Annealing

It is defined as, "process used to remove residual stresses due to heavy machining or other cold working processes".
  • Carried out below critical line (1000-1200 F)

Process Annealing

"It is similar to stress-relief annealing in sheet and wire industries carried out by heating the steel to a temperature below the lower critical line (1000-1200 F)".
  • Applied after cold working and soften the steel by recrystallization.

C. Normalizing 

It is defined as, "process carried out by heating approximately 100F above the upper critical temperature (A3 or ACM) line followed by cooling in still air to room temperature".
  • Purpose  →  to produce harder and stronger steel than full annealing.
  • Final heat treatment operation.
  • Cooling rate is high due to air cooling as compared with furnace cooling affects the transformation of austenite.

Precipitation (or Age) Hardening

It is defined as, "the strength and hardness of some metal alloys may be enhanced by the formation of extremely small, uniformly dispersed particles of a second phase within the original phase matrix induced by heat treatment".
  • Precipitate  →  small particles of the new-phase.
  • Age Hardening  →  because strength of material develops with time.

Types of Heat Treating

Steps are:
  1. An appreciable max. solubility of one component in the other.
  2. A solubility limit that rapidly decreases in concentration of the major component with temperature reduction.

a. Solution Heat Treating

It is defined as, "All solute atoms are dissolved to form a single-phase solid solution".
  • Consist of heating the alloy to a temperature within the ∝-phase (To) and waiting untill all the β-phase that may have been present is completely dissolved.

b. Precipitation Heat Treating

It is defined as, "The supersaturated ∝-solid solution is heated to an intermediate temperature T2 within ∝+β (or 2-) phase region at which diffusion rates become appreciable".
  • Aging  →  β-phase form fine dispersed particles of composition Cβ.
  • Overaging  →  strength or hardness increases with time and reaches a max. value, after that strength (and hardness) reduces after long time.
  • β-Particles Character  →  (i.e. strength and hardness) depend on precipitation temperature T2 and aging time.
Note:

References:

  • Material from Class Lectures + Book named Materials Science and Engineering: An Introduction by Callister and Rethwick + my knowledge. 
  • Pics and GIF from Google Images.  
  • Videos from YouTube (Engineering Sights).

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