UNIT--3 -ppt-1.pptx
- 1. UNIT - 3 Thermal properties of metals- Heat capacity, thermal expansion, thermal conductivity, thermal stress, thermal fatigue, thermal shock. Electrical properties of metals- Electrical conductivity, electronics and ionic conduction, energy band structures in solids, electrical resistivity of metals, electrical characteristics of alloys used for commercial purposes.
- 2. Thermal properties of metals Introduction: Engineering materials are important in everyday life because of their versatile structural properties. Other than these properties, they do play an important role because of their physical properties. Prime physical properties of materials include: electrical properties; thermal properties; magnetic properties; and optical properties. Selection of materials for use at elevated temperatures or temperature changes require, an engineer to know and understand their thermal properties.
- 3. Physical property of a solid body related to application of heat energy is defined as a thermal property. Thermal properties like heat capacity, thermal expansion, thermal conductivity, and thermal stresses. It is important to know and understand the concept of thermal expansion, which is the root cause for thermal stresses. Thermal stresses are stresses leading to failure of engineering structures at elevated temperatures.
- 4. Heat capacity: Many engineering solids when exposed to heat an increase in temperature i.e. it absorbs heat energy. This property of a material i.e. material’s ability to absorb heat energy is called its heat capacity, C. It is defined as the energy required to change a material’s temperature by one degree. Mathematically, it is expressed as: C= dT/dQ, J/mol-K or Cal/mol-K Where dQ is the energy required to produce a temperature change equal to dT.
- 6. Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to a given mass of a material to produce a unit change in its temperature. Heat capacity is an extensive property. Heat capacity for a particular object (J/.C), and specific heat capacity for any amount of a particular substance (J/g.C). Heat capacity of a body is defined as the amount of heat absorbed or rejected to change the temperature by one unit.
- 7. Heat capacity is not an intrinsic property i.e. total heat a material can absorb depends on its volume / mass. Hence another parameter called specific heat, c, it defined as heat capacity per unit mass (J/kg-K, Cal/kg-K). Specific heat capacity of a body of a substance is defined as the amount of heat absorbed or rejected to change the temperature of unit mass of it by one unit. With increase of internal energy, geometrical changes may occur. Accordingly, heat capacity is measured either at constant volume, Cv, or at constant external pressure, Cp.
- 8. The magnitude of Cp is always greater than Cv but only marginally. Heat energy absorption of a (solid, liquid or gaseous) material exists in mode of thermal energy vibrations of constituent atoms or molecules, apart from other mechanisms of heat absorption such as electronic contribution. With increase of energy, atoms vibrate at higher frequencies. However, the vibrations of adjacent atoms are coupled through atomic bonding, which may lead to movement of lattices.
- 9. This may be represented as elastic waves (phonon) or sound waves. Vibration contribution of heat capacity of solids varies with temperature according to the following relation at low temperatures: Cv = AT3 Cv is equal to zero at 0 K, but increase rapidly with temperature, A is temperature independent constant. It represents increased ability of atomic vibrations or enhanced energy of lattice waves with ascending temperature.
- 11. The above temperature is called Debye temperature, θd, dependence of volumetric heat capacity value reaches saturation. For many solids, value of θd is below room temperature.
- 12. Figure : Heat capacity as a function of temperature
- 13. Thermal expansion: After heat absorption, vibrating atoms behaves as they have larger atomic radius, which leads to increase in materials dimensions. This phenomenon is called thermal expansion. When the materials are heated, their size and volume increase in small increments, this phenomenon is known as thermal expansion. It is quantified in terms of thermal expansion coefficient. Most of the materials expand and contract due to temperature changes.
- 17. Linear coefficient of thermal expansion (α) defined as the change in the dimensions of the material per unit length, and is expressed as: α = lf-l0/l0(Tf-T0) where T0 and Tf are the initial and final temperatures (in K), l0 and lf are the initial and final dimensions of the material and ε is the strain. α has units as (°C)-1. Linear expansion α = Δl / l0ΔT; α = β /2; α = γ /3. Superficial expansion β = Δa / a0ΔT; Cubical expansion γ = Δv / v0ΔT Fine ceramics have low coefficients of thermal expansion-less than half those of stainless steels.
- 18. An instrument known as dilatometer is used to measure the thermal expansion coefficient. It is also possible to trace thermal expansion using XRD( X-ray diffraction). At microscopic level, thermal expansion can be attributed to the increase in the average distance between the atoms. The coefficient of thermal expansion of a material is related to the strength of the atomic bonds. The relation between inter-atomic distance and potential energy is shown in the figure.
- 19. As shown in the figure, the potential energy curve has trough and is characterized by a minimum. This minimum corresponds to the equilibrium inter-atomic distance. With increase in temperature of the material, vibrational amplitude increase, and the mean of it represents the average inter-atomic distance. The average inter-atomic distance increases with the temperature of a material.
- 20. Figure 15.2: Change if inter-atomic distance with temperature.
- 21. If a very deep energy trough caused by strong atomic bonding is characteristic of the material, the atoms separate to a lesser and the material has low linear coefficient of thermal expansion. This relationship also suggests that materials having a high melting temperature – also due to strong atomic bonds – have low thermal expansion coefficients. Most ceramics having strong atomic bonds, thus, have low thermal expansion coefficients compared with metals and polymers.
- 22. Thermal conductivity: The ability of a material to transport heat energy from high temperature region to low temperature region is defined as thermal conductivity. Similar to diffusion coefficient, thermal conductivity is a microstructure sensitive property. The heat energy, Q, transported across a plane of area A in presence of a temperature gradient ΔT/Δl is given by Q = kA ΔT/Δl where k is the thermal conductivity of the material. It has units as W/m.K. Metals have k values in the range 20-400, ceramics 2-50, while polymers have in order of 0.3.
- 25. Heat energy in solids transported by two mechanisms: lattice vibrations (phonons) and free electrons. Valence electrons gain energy, move toward the colder areas of the material, and transfer their energy to other atoms. The amount of energy transported depends on number of excited electrons, their mobility i.e. type of material, lattice imperfections, and temperature. The thermal energy associated with phonons is transported in the direction of their motion.
- 26. Thus thermal conduction of metals is primarily due to movement of electrons. It is the same for electrical conduction. Both conductivities are related through the following relation: k/σT= L where L – Lorentz constant, 5.5x10-9 cal.ohm/sec.K2 or 2.44x10-8 W.ohm/ K2. σ = Electrical conductivity, K= Heat conductivity
- 27. With increase in temperature, both number of carrier electrons and contribution of lattice vibrations increase. Thus thermal conductivity of a metal is expected to increase. However, because of greater lattice vibrations, electron mobility decreases. The combined effect of these factors leads to very different behaviour for different metals. For example: thermal conductivity of iron initially decreases then increases slightly; thermal conductivity decreases with increase in temperature for aluminium; while it increases for platinum.
- 28. In ceramics, phonons are primarily responsible for thermal conduction. Since the electronic contribution is absent, the thermal conductivity of most ceramics is lower than that of metals. However, main reason for experimentally observed low conductivity of ceramics is the level of porosity, as phonons are effectively scattered by imperfections. The scattering of phonons becomes more pronounced with rising temperature. Hence, the thermal conductivity of ceramic materials normally diminishes with increasing temperature.
- 29. Advanced ceramic materials like AlN, SiC are good thermal conductors, they are also electrical insulators. Therefore these materials are useful as electronic packaging substrates where heat dissipation is needed. Thermal conductivity of polymers is even low, compared with ceramic materials. Vibration and movement/rotation of molecular chains transfer heat energy. In these materials thermal conductivity depends on degree of crystallinity; a polymer with highly crystalline and ordered structure will have higher conductivity than amorphous polymer.
- 32. Q.1 A lump of iron of mass 2kg is heated from 400c to 10000c. If the heat supplied is 192 kcal find its thermal capacity, also find the specific heat of iron.
- 33. Solution: Given data: m = 2kg; t1 = 400c; t2 = 10000c: dQ = 192 kcal (1 cal = 4.2 J); dT = t2-t1 = 9600 •Thermal capacity : dQ/dT = 192 x 103 x 4.2/ 960 = 840 J/K. •Specific heat of iron: 1/m x dQ/dT = 1/2 x 840 = 420 J/Kg/K.
- 34. Q.2: Compute the heat transfer amount for a material in which thermal conductivity is 0.181. The cross-sectional area is 1200 square m and a thickness of 2m. The hot temperature is 250-degree c where the cold temperature is 25 degrees C.
- 35. Solution: As given in the problem, Thermal conductivity of material, K =0.181 Cross Sectional Area, A = 1200; Thickness, d = 2 m Hot side temperature, THOT = 250 degrees C Cold side temperature, TCOLD = 25 degrees C Now, applying the formula, Q= K×A × (THOT–TCOLD) /d Substituting the known values, Q= 0.181×1200 × (250–25) /2 = 48870/2 J/sec = 24435 Watt; Therefore the heat transfer will be 24435 watt.
- 38. Q.2: Compute the heat transfer amount for a material in which thermal conductivity is 0.5. The cross-sectional area is 1200 square m and a thickness of 0.2m. The hot temperature is 58-degree c where the cold temperature is 12 degrees C.
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